Gemini-1.5 Pro on 4.NBT.B.6
Common Core Standard 4.NBT.B.6
This standard covers the following:
Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models.
Problem: There are 535 fish in a large tank and a shark eats 461 of them in one sitting. If the shark continues this pattern and only eats when there are 461 or more fish to consume, how many fish will be leftover after its dinner?
Gemini-1.5 Pro:
Reasoning: Since there are 535 fish and the shark eats 461, there will be 535-461= <<535-461=74>> 74 fish left. ### Answer: 74
Expected answer: 74
Correct? Yes
Problem: A baker baked a total of 928 cookies. He decided to distribute equal amounts of cookies to 186 orphanages. After giving out as many entire sets of cookies as possible to each orphanage, how many cookies does the baker have left?
Gemini-1.5 Pro:
Reasoning: Each orphanage receives 928 / 186 = <<928/186=4>>4 cookies, with a remainder. The remainder represents the leftover cookies. We can find the remainder by multiplying the number of orphanages by the number of cookies each received, and subtracting that from the total number of cookies: 928 - (186 * 4) = <<928-(186*4)=184>>184 ### Answer: 184
Expected answer: 184
Correct? Yes
Problem: In the previously mentioned scenario, consider that the baker only baked 173 cookies instead of 928. He still plans on distributing equal amounts of cookies to the 186 orphanages. After giving out as many full sets as possible to each orphanage, how many cookies will the baker have left over this time?
Gemini-1.5 Pro:
Reasoning: Since the baker only has 173 cookies, and 173 is less than the number of orphanages (186), he can't even give a full set to one orphanage. Therefore, he will give out 0 cookies and all 173 will remain. ### Answer: 173
Expected answer: 173
Correct? Yes
Problem: A pizza store has 975 slices of pizza ready to serve. If each pizza box can contain 196 slices, how many left over slices will there be after all the pizza boxes are full?
Gemini-1.5 Pro:
Reasoning: The pizza store can fill 975 / 196 = <<975/196=4>>4 pizza boxes completely. Since 4 pizza boxes use 4 x 196 = <<4*196=784>>784 slices, there are 975 - 784 = <<975-784=191>>191 slices left over. ### Answer: 191
Expected answer: 191
Correct? Yes
Problem: A wizard casts a spell to summon 932 magical stones. Each powerful creature he summons requires 193 stones. After summoning several creatures, how many stones will the wizard have left?
Gemini-1.5 Pro:
Reasoning: It is unclear how many creatures the wizard summoned. Without that information, we cannot determine how many stones were used or how many are left. ### Answer: Cannot be determined.
Expected answer: 160
Correct? No
Problem: A builder has a job to install 660 square foot tiles in a house. Each tile can cover 335 square feet. After installing tiles evenly across the available space, how many square feet will the last tile need to cover?
Gemini-1.5 Pro:
Reasoning: The builder needs to cover 660 / 335 = <<660/335=1.97>>1.97 tiles worth of space. This means he will need to use 2 tiles in total. The last time will need to cover 660 - 335 = <<660-335=325>>325 square feet. ### Answer: 325
Expected answer: 325
Correct? Yes
Problem: A builder realizes that he made a mistake and the tiles can actually cover 337 square feet instead of 335 square feet. Given the same total area of 660 square feet, how many square feet will the last tile now need to cover?
Gemini-1.5 Pro:
Reasoning: We still know from before that the builder needs to use 2 tiles to cover the entire area. The last tile will need to cover 660 - 337 = <<660 - 337 = 323>>323 square feet. ### Answer: 323
Expected answer: 323
Correct? Yes
Problem: A juice company produced 473 gallons of juice. If the company bottles the juice in 22-gallon containers, how many gallons of juice will be left after filling up all the containers?
Gemini-1.5 Pro:
Reasoning: The company can fill 473/22 = <<473/22=21.5>>21.5 containers. Since we can't have half a container, the company can fill 21 containers. That means 21*22 = <<21*22=462>>462 gallons of juice are used to fill up the containers. Therefore, 473-462 = <<473-462=11>>11 gallons of juice will be left. ### Answer: 11
Expected answer: 11
Correct? Yes
Problem: A juice company initially thought they produced 473 gallons of juice, but they realized they actually produced 599 gallons. They used the same 22-gallon containers as before. After filling up all the containers, how many gallons of juice do they now have left over?
Gemini-1.5 Pro:
Reasoning: The company can fill 599/22 = <<599/22=27.23>>27.23 containers. Since we can't have a fraction of a container, they can fill 27 containers. This means they used 27*22 = <<27*22=594>>594 gallons of juice to fill up all the containers. Therefore, they have 599-594 = <<599-594=5>>5 gallons of juice left over. ### Answer: 5
Expected answer: 5
Correct? Yes
Problem: A toy factory produced 979 toy cars in a day. If they packed these cars into boxes, each containing 108 cars, how many toy cars will be left unpacked at the end of the day?
Gemini-1.5 Pro:
Reasoning: The factory can pack 979/108 = <<979/108=9...7>>9 boxes of toy cars, with some leftover. The remainder after the division tells us how many cars are left unpacked, which is 7. ### Answer: 7
Expected answer: 7
Correct? Yes
Problem: The toy factory now produced 979 toy cars in a day and decided to package these cars into larger boxes, each containing 684 cars. After all the cars have been packed into the larger boxes, how many toy cars would be left unpacked at the end of the day?
Gemini-1.5 Pro:
Reasoning: We need to figure out how many groups of 684 cars can be formed from 979 cars. This is the same as finding the quotient of 979 divided by 684. 979 divided by 684 is 1 with a remainder of 295. <<979/684= 1 remainder 295>> ### Answer: 295
Expected answer: 295
Correct? Yes
Problem: A crayon factory has the capacity to make 994 crayons in one operation. However, each box only holds 425 crayons. If they operate at full capacity, how many crayons will be left out of the boxes after the operation?
Gemini-1.5 Pro:
Reasoning: We need to find the remainder when 994 crayons are divided into boxes of 425. This is the same as finding the remainder of 994 divided by 425. 994 divided by 425 is 2 with a remainder of 144. ### Answer: 144 crayons.
Expected answer: 144
Correct? Yes
Problem: Let's now consider that the crayon factory only made 223 crayons in one operation, while each box still holds 425 crayons. Again, how many crayons are left over and fail to make it into a box?
Gemini-1.5 Pro:
Reasoning: Since the factory made fewer crayons (223) than the number a box holds (425), none of the crayons will be put into boxes. Therefore, all 223 crayons will be left out. ### Answer: 223 crayons.
Expected answer: 223
Correct? Yes
Problem: A wildlife reserve has 740 tigers. The reserve is divided into different zones, and each zone can only hold up to 696 tigers. If tigers are distributed evenly among the zones, how many tigers will be left in the last zone?
Gemini-1.5 Pro:
Reasoning: First find the maximum number of tigers that can be evenly distributed among the zones: 740 / 696 = 1 with a remainder. This means there is 1 full zone, and a partially filled zone. To find the number of tigers in the last zone, find the remainder: 740 - 696 = 44 tigers. ### Answer: 44
Expected answer: 44
Correct? Yes
Problem: Consider the wildlife reserve again. This time, however, the zones have been expanded and each can now accommodate up to 908 tigers. If the 740 tigers are distributed evenly among the expanded zones, how many tigers will be left in the last zone?
Gemini-1.5 Pro:
Reasoning: Since each zone can hold more tigers than the total number of tigers, all tigers can fit in the first zone. This means the last zone will be empty. ### Answer: 0
Expected answer: 740
Correct? No
Problem: A hat shop makes 830 hats every week. In order to make special edition boxes, the shop plans to put 421 hats in each box. If all the hats are evenly distributed among the boxes, how many hats will be left over?
Gemini-1.5 Pro:
Reasoning: We need to find the remainder when 830 is divided by 421. Performing the division 830 / 421, we get a quotient of 1 and a remainder of 409. ### Answer: 409
Expected answer: 409
Correct? Yes
Problem: There are 871 fish in a lake. A fisherman catches 575 fish every month. If the fish repopulate at the same rate that the fisherman is depleting them, how many fish will be left after a month?
Gemini-1.5 Pro:
Reasoning: Since the fish repopulate at the same rate the fisherman catches them, there will be no change in the number of fish in the lake. ### Answer: 871
Expected answer: 296
Correct? No
Problem: There are 891 beach balls, and every beach bag can fit 119 beach balls. If all the beach balls are evenly placed into the bags, how many beach balls will not fit and left over?
Gemini-1.5 Pro:
Reasoning: If we divide the total number of beach balls (891) by the number of beach balls each bag can hold (119), we find out how many full bags we can fill: 891 / 119 = 7 with a remainder. This remainder represents the leftover beach balls. To find the remainder, multiply the number of full bags (7) by the capacity of each bag (119): 7 * 119 = 833 Finally, subtract the number of beach balls in the full bags (833) from the total number of beach balls (891) to find the number of leftover beach balls: 891 - 833 = 58 ### Answer: 58
Expected answer: 58
Correct? Yes
Problem: If instead there were 901 beach balls and every beach bag can fit 119 beach balls. After evenly placing the balls into bags, how many beach balls would be left over now?
Gemini-1.5 Pro:
Reasoning: We can find the number of leftover beach balls by dividing the total number of beach balls (901) by the capacity of each beach bag (119) and then finding the remainder. 901 divided by 119 is 7 with a remainder. To find the remainder, we can multiply the whole number result (7) by the divisor (119): 7 * 119 = 833. Finally, subtract the product from the dividend to find the remainder: 901 - 833 = 68. This remainder represents the leftover beach balls. ### Answer: 68
Expected answer: 68
Correct? Yes
Problem: There are 544 stars in a particular constellation. These stars are grouped into smaller clusters of 446 stars each. If these clusters are evenly split, how many stars will remain ungrouped?
Gemini-1.5 Pro:
Reasoning: Dividing the total number of stars by the number of stars per cluster, we get 544 / 446 = <<544/446=1.22>>1.22. This means there is 1 complete cluster and 0.22 of another cluster. Since we can't have a fraction of a cluster, we focus on the whole number, which is 1. One cluster contains 446 stars, so 544 total stars - 446 stars in the cluster = <<544-446=98>>98 stars remain ungrouped. ### Answer: 98
Expected answer: 98
Correct? Yes
Problem: Considering the previous scenario with the constellation, suppose there were only 278 stars in the constellation instead of 544, and they were still to be grouped into smaller clusters of 446 stars each. If the clusters are evenly distributed, how many stars will now remain ungrouped?
Gemini-1.5 Pro:
Reasoning: We try to divide the total number of stars (278) by the number of stars per cluster (446), which gives us 278 / 446 = <<278/446=0.62>>0.62. This result is less than 1, meaning we can't form even a single full cluster. Therefore, all 278 stars would remain ungrouped because there aren't enough to form a cluster of 446. ### Answer: 278
Expected answer: 278
Correct? Yes
Problem: A manufacturer produces 805 socks in one shift. They are packaged into sets of 132 each. After the packaging, how many socks will remain unpackaged?
Gemini-1.5 Pro:
Reasoning: We need to find the remainder when 805 is divided by 132. This represents the socks that are left over after making as many full sets of 132 as possible. 805 divided by 132 is 6 with a remainder of 13. ### Answer: 13
Expected answer: 13
Correct? Yes
Problem: If instead of producing 805 socks, the manufacturer produced 634 socks in one shift, how many socks would remain unpackaged after being bundled into sets of 132 each?
Gemini-1.5 Pro:
Reasoning: We need to find the remainder when 634 is divided by 132. This represents the socks that are left over after making as many full sets of 132 as possible. 634 divided by 132 is 4 with a remainder of 106. ### Answer: 106
Expected answer: 106
Correct? Yes
Problem: An astronomy club has 759 members that want to view a rare celestial event through their club's telescope. However, the telescope can only handle 228 people viewing the event each night. If they distribute the viewing evenings evenly amongst all members, how many people will view the event on the final night?
Gemini-1.5 Pro:
Reasoning: First, we'll find how many full nights of viewing are needed by dividing the total members by the telescope's capacity: 759 members / 228 members/night = 3.33 nights. Since we can't have a fraction of a night, we know there will be 3 full nights of viewing. Next, we need to determine how many members will be on the final, partially filled, night. We multiply the number of full nights by the telescope's capacity: 3 nights * 228 members/night = 684 members. Finally, subtract the number of members viewing on the full nights from the total number of members to find the number of members viewing on the final night: 759 members - 684 members = 75 members. ### Answer: 75
Expected answer: 75
Correct? Yes
Problem: A similar astronomy club from a neighboring town also wants to take part in viewing this rare celestial event. They have 593 members interested in participating. If they follow the same pattern of distributing the viewing nights evenly amongst all members, with only 228 people viewing the event each night, how many people from this club will view the event on the final night?
Gemini-1.5 Pro:
Reasoning: We will follow a similar process as before. Dividing the total members by the telescope's capacity, we get: 593 members / 228 members/night = 2.6 nights. This tells us there will be 2 full nights of viewing. Multiplying the number of full nights by the telescope capacity: 2 nights * 228 members/night = 456 members. Subtracting to find the remaining number of members for the final night: 593 members - 456 members = 137 members. ### Answer: 137
Expected answer: 137
Correct? Yes
Problem: A postman has to deliver 891 letters. Each mailbox can only hold 616 letters. If he puts equal numbers of letters in each mailbox, how many letters will remain in the last mailbox?
Gemini-1.5 Pro:
Reasoning: We need to find the remainder when 891 is divided by 616. Dividing 891 by 616 gives us a quotient of 1 and a remainder of 275 (891 = 616 * 1 + 275). ### Answer: 275
Expected answer: 275
Correct? Yes
Problem: In the previous scenario, assuming the postman had to originally deliver 524 letters instead of 891, and each mailbox can still only accommodate 616 letters. How many letters will remain in the last mailbox now?
Gemini-1.5 Pro:
Reasoning: Since the postman only has 524 letters to deliver, which is less than the capacity of a single mailbox (616), he can fit all the letters in the last mailbox. Therefore, there will be no remaining letters. ### Answer: 0
Expected answer: 524
Correct? No
Problem: A total of 941 flies are jumping around the pond. Every time a frog jumps, it eats exactly 258 flies. After a series of jumps where each jump the frog eats the same number of flies, how many flies are left?
Gemini-1.5 Pro:
Reasoning: First, find the maximum number of times the frog can jump by dividing the total number of flies by the number of flies eaten per jump: 941 flies / 258 flies/jump = 3 jumps with a remainder. Then multiply the number of full jumps by the number of flies eaten per jump to find the total number of flies eaten: 3 jumps * 258 flies/jump = 774 flies. Finally, subtract the number of flies eaten from the initial number of flies to find the number of flies remaining: 941 flies - 774 flies = 167 flies. ### Answer: 167
Expected answer: 167
Correct? Yes
Problem: Previously, a frog ate flies from a total of 941 flies with 258 flies eaten in each jump. Now, consider that instead of 941 flies there initially were 146 flies hopping around the pond. Given that the frog still eats 258 flies in each jump, how many flies would be left after a series of jumps?
Gemini-1.5 Pro:
Reasoning: Since the frog eats 258 flies per jump and there are only 146 flies, the frog cannot complete a full jump. ### Answer: 146
Expected answer: 146
Correct? Yes
Problem: A large park has a capacity of 991 spaces for cars to park. If all the spaces are evenly distributed between 66 rows, how many spare spaces will be there in the last row after max spaces are filled?
Gemini-1.5 Pro:
Reasoning: Each row in the parking lot can hold 991 / 66 = <<991/66=15>> cars with some spaces left over since the result of the division is not a whole number. The last row will hold 991 - (66*15) = <<991-(66*15)=1>> spare space. ### Answer: 1
Expected answer: 1
Correct? Yes
Problem: In the same large park, suppose they restructure the parking with larger spaces to accommodate bigger vehicles. Now, the adjusted parking lot configurations can hold 471 cars in each row. After filling up the rows, how many spare spaces would be there in the last row now?
Gemini-1.5 Pro:
Reasoning: The parking lot's total capacity of 991 spaces remains unchanged. With a new capacity of 471 cars per row, only 991 / 471 = <<991/471=2>> rows can be fully filled. The last row will, therefore, have 991 - (471 * 2) = <<991-(471*2)=49>> spare spaces. ### Answer: 49
Expected answer: 49
Correct? Yes
Problem: There are 193 liters of water that need to be divided evenly among 167 water bottles. If each bottle holds the same amount of water, how many liters overflows and can't be distributed to the bottles?
Gemini-1.5 Pro:
Reasoning: Each bottle holds 193/167 = <<193/167=1.15568862275>>1.16 liters (rounded to the nearest hundredth). Since we can't have a fraction of a liter, we multiply the decimal portion of the answer by the total liters: .16 x 193 = <<.16*193=30.88>>30.88 liters. ### Answer: 30.88 liters
Expected answer: 26
Correct? No
Problem: A dragon lays 996 jewel eggs in rows. Each row can hold 319 eggs. If the dragon distributes the eggs evenly among the rows, how many eggs would be left over to be put in the last row?
Gemini-1.5 Pro:
Reasoning: First find the total number of full rows by dividing the total number of eggs by the number of eggs per row: 996 eggs / 319 eggs/row = 3 rows with a remainder Multiply the number of full rows by the number of eggs per row to find how many eggs fit perfectly: 3 rows * 319 eggs/row = 957 eggs Subtract the eggs that fit perfectly from the total number of eggs to find the remainder: 996 eggs - 957 eggs = 39 eggs. ### Answer: 39
Expected answer: 39
Correct? Yes
Problem: Now, consider if the dragon had only laid 8 jewel eggs and continued to distribute them among rows that could hold 319 eggs. How many eggs would be left over to be put in the last row?
Gemini-1.5 Pro:
Reasoning: Since the dragon only laid 8 eggs, which is less than the capacity of a single row (319 eggs), all 8 eggs would be placed in the last row. ### Answer: 8
Expected answer: 8
Correct? Yes
Problem: A lamp manufacturer produces 691 bulb units. If a pack includes 205 bulbs, how many bulbs would be left unpacked after filling as many packs as possible?
Gemini-1.5 Pro:
Reasoning: We need to determine the highest multiple of 205 that is less than or equal to 691. This represents the maximum number of packs we can fill. 205 x 3 = 615 and 205 x 4 = 820, so the highest multiple is 615, meaning we can fill 3 complete packs. To find the remaining bulbs, we subtract the number of bulbs used in the packs from the total number of bulbs: 691 total bulbs - 615 bulbs in packs = 76 bulbs unpacked. ### Answer: 76
Expected answer: 76
Correct? Yes
Problem: If the lamp manufacturer produced 739 bulb units instead of 691, how many bulbs would be left unpacked after filling as many packs as possible with 205 bulbs each?
Gemini-1.5 Pro:
Reasoning: We can find the number of bulbs left unpacked by finding the remainder when 739 is divided by 205. The largest multiple of 205 less than 739 is 615 (3 x 205 = 615). Subtracting this from the total number of bulbs gives us: 739 - 615 = 124. ### Answer: 124
Expected answer: 124
Correct? Yes
Problem: On a farm, there are 330 bales of hay to be stored evenly in barns. Each barn can store up to 259 bales. After filling up the barns as evenly as possible, how many bales of hay will be left for the last barn?
Gemini-1.5 Pro:
Reasoning: We need to find the remainder when 330 bales are divided into groups of 259. We perform the division: 330 / 259 = 1 with a remainder of 71. ### Answer: 71
Expected answer: 71
Correct? Yes
Problem: A construction company is installing 166 windows on a building. They have determined that one installation team can install 137 windows per day. If all windows are equally distributed amongst teams each day, how many windows will remain for the team to install on the next day?
Gemini-1.5 Pro:
Reasoning: Let's figure out how many full teams can be utilized for the installation. We divide the total windows by the number of windows a single team can install: 166 windows / 137 windows/team = <<166/137=1.21167883212>>1.21 teams. This indicates we can have 1 full team working and some windows leftover for another team to handle. A full team will install 137 windows, leaving 166 total windows - 137 windows = <<166-137=29>>29 windows remaining. ### Answer: 29
Expected answer: 29
Correct? Yes
Problem: There are 533 campers coming for a camping event at a park. Each tent can host 445 people. If the campers are evenly distributed among the tents, how many campers will be left over after all the tents are filled?
Gemini-1.5 Pro:
Reasoning: We need to find the remainder when 533 campers are divided into groups of 445. This is the same as finding the remainder when 533 is divided by 445. 533 divided by 445 is 1 with a remainder of 88. ### Answer: 88
Expected answer: 88
Correct? Yes
Problem: Now suppose that the park upgraded their tents and each tent can now host 886 people. With the same group of 533 campers, how many campers will be left over after all the tents are filled?
Gemini-1.5 Pro:
Reasoning: Since each tent can now hold 886 campers, and there are only 533 campers, the first tent will be filled with all 533 campers. There will be no campers remaining to fill other tents. ### Answer: 0
Expected answer: 533
Correct? No
Problem: There are 999 seashells collected from a beach. They are grouped in beach-themed souvenir sets, each containing 474 shells. After grouping, how many seashells will be left without a set?
Gemini-1.5 Pro:
Reasoning: We need to find the remainder after dividing the total seashells (999) by the number of shells per set (474). This means we need to calculate 999 modulo 474. 999 divided by 474 is 2 with a remainder of 51 (999 = 474 * 2 + 51). ### Answer: 51
Expected answer: 51
Correct? Yes
Problem: In continuation of the previous scenario with seashells, imagine instead that there were initially only 234 seashells collected from the beach, but the souvenir sets are still made up of 474 shells each. How many shells would be left after attempting to form these sets?
Gemini-1.5 Pro:
Reasoning: Since there are only 234 seashells, which is less than the 474 shells required for even one souvenir set, no sets can be made. ### Answer: 234
Expected answer: 234
Correct? Yes
Problem: A tailor has 366 meters of fabric. If each skirt requires 160 meters of fabric, how many meters of fabric will be left after making as many skirts as possible?
Gemini-1.5 Pro:
Reasoning: The tailor can make 366/160 = 2 skirts with some fabric left over. The tailor will use 2*160 = 320 meters of fabric to make 2 skirts. The tailor will have 366-320 = 46 meters of fabric left. ### Answer: 46 meters.
Expected answer: 46
Correct? Yes
Problem: A tailor realized that she has made a mistake. Actually, she has only 21 meters of fabric at her disposal, not 366. If each skirt requires 160 meters of fabric, how many meters of fabric will be left after making as many skirts as possible?
Gemini-1.5 Pro:
Reasoning: The tailor cannot make a single skirt with 21 meters of fabric, because one skirt requires 160 meters. Therefore, the tailor will make 0 skirts and all of the fabric will be left. ### Answer: 21 meters.
Expected answer: 21
Correct? Yes
Problem: A toymaker made 993 dolls to be packed in boxes for shipment. Each box can hold 327 dolls. How many dolls will she have left once all the boxes are packed to their capacities?
Gemini-1.5 Pro:
Reasoning: We can find how many dolls will be left over by finding the remainder when 993 is divided by 327. 993 divided by 327 is 3 with a remainder of 9. ### Answer: 9
Expected answer: 12
Correct? No
Problem: A child has 964 stuffed animals that they want to divide equally among their 839 friends. If they distribute the stuffed animals evenly, how many will the child have left over?
Gemini-1.5 Pro:
Reasoning: We need to perform the division 964 / 839 to find out how many stuffed animals each friend will receive and the remainder. The result of 964 / 839 is 1 with a remainder of 125. ### Answer: 125
Expected answer: 125
Correct? Yes
Problem: The child from the previous problem has gotten even more stuffed animals and now has a total of 964 stuffed animals. If they still want to divide them equally among their 892 friends, how many stuffed animals will be left over after distributing them?
Gemini-1.5 Pro:
Reasoning: To find the number of leftover stuffed animals, we need to divide the total number of stuffed animals (964) by the number of friends (892). The remainder of this division represents the leftover stuffed animals. Performing the division 964 / 892, we get a quotient of 1 and a remainder of 72. ### Answer: 72
Expected answer: 72
Correct? Yes
Problem: A toy factory produces 369 teddy bears in a day. The bears are packaged in boxes and each box can hold 270 teddy bears. How many teddy bears will be left if all the teddy bears are evenly packed in the boxes?
Gemini-1.5 Pro:
Reasoning: We need to find the remainder when 369 teddy bears are divided into boxes of 270. This is the same as finding the remainder when 369 is divided by 270. 369 divided by 270 is 1 remainder 99. ### Answer: 99
Expected answer: 99
Correct? Yes
Problem: Earlier, the toy factory produced 369 teddy bears in a day and they were packaged in boxes with each box holding 270 teddy bears. Now, suppose that the toy factory increased its production and now makes 813 teddy bears in a day while still packing them in boxes that can hold 270 teddy bears. How many teddy bears will be left now if all the teddy bears are evenly packed in the boxes?
Gemini-1.5 Pro:
Reasoning: We need to find the remainder when 813 teddy bears are divided into boxes of 270. This is the same as finding the remainder when 813 is divided by 270. 813 divided by 270 is 3 remainder 3. ### Answer: 3
Expected answer: 3
Correct? Yes
Problem: A village has a yearly tradition of building snowmen. This year, the villagers make 804 snowballs to build their snowmen. Each snowman needs exactly 184 snowballs. After all snowmen are built, how many snowballs are left leftover?
Gemini-1.5 Pro:
Reasoning: The villagers can build 804/184 = <<804/184=4>>4 snowmen. Since they used 4*184 = <<4*184=736>>736 snowballs to build the snowmen, there are 804-736 = <<804-736=68>>68 snowballs left. ### Answer: 68
Expected answer: 68
Correct? Yes
Problem: In the same village, another year, there were only 444 snowballs made to build the snowmen. If each snowman still requires exactly 184 snowballs, how many snowballs would be left over after as many complete snowmen as possible are built?
Gemini-1.5 Pro:
Reasoning: With 444 snowballs, the villagers can build a maximum of 2 complete snowmen because 184*2 = 368 and 184*3 = 552 (which is more than 444). Therefore, they used 368 snowballs to build the snowmen, leaving 444-368 = <<444-368=76>>76 snowballs leftover. ### Answer: 76
Expected answer: 76
Correct? Yes
Problem: A jewelry store has 843 rings to be placed equally into 839 boxes. If each box is filled, how many rings will be left over?
Gemini-1.5 Pro:
Reasoning: When 843 rings are divided into groups of 839, 843 / 839 = <<843/839=1...4>>1 remainder 4. This means we can fill 1 box completely and will have 4 rings left over. ### Answer: 4
Expected answer: 4
Correct? Yes
Problem: The jewelry store just received an additional shipment and now has a total of 843 rings. However, this time they must be equally placed into 804 boxes. If every box is filled, how many rings will be left over now?
Gemini-1.5 Pro:
Reasoning: When 843 rings are divided into groups of 804, 843 / 804 = <<843/804=1...39>>1 remainder 39. This means we can fill 1 box completely and will have 39 rings left over. ### Answer: 39
Expected answer: 39
Correct? Yes
Problem: A fireplace manufacturing company has 819 bricks to build fireplaces, and each fireplace requires 583 bricks. If they build as many fireplaces as possible, how many bricks will they have left over?
Gemini-1.5 Pro:
Reasoning: The company can build 819 / 583 = <<819/583=1.404802744425386>>1 fireplace, with some bricks leftover. Since we can't have a fraction of a fireplace, the company can build 1 fireplace. They will use 1 * 583 = <<1*583=583>>583 bricks to build the fireplace. The company will have 819 - 583 = <<819-583=236>>236 bricks left over. ### Answer: 236
Expected answer: 236
Correct? Yes
Problem: The company received a new delivery of bricks, now they have 486 bricks in total. If they continue making fireplaces, each requiring 583 bricks as before, how many bricks will they have left after building as many full fireplaces as they can?
Gemini-1.5 Pro:
Reasoning: The company can build 486 / 583 = <<486/583=0.8336192109777015>>0.83 fireplaces. Since we can't build parts of fireplaces, they can build 0 full fireplaces with the new delivery. That means they will use 0 * 583 = <<0*583=0>>0 bricks for building. Therefore, they will still have 486 - 0 = <<486-0=486>>486 bricks remaining. ### Answer: 486
Expected answer: 486
Correct? Yes
Problem: A marshmallow factory produces 998 marshmallows per minute. However, the packaging machine can only hold 957 marshmallows at a time. What will be the number of marshmallows left un-packaged in a minute after all the packaging machines are filled?
Gemini-1.5 Pro:
Reasoning: To find the number of marshmallows left unpacked, we need to find the difference between the number of marshmallows produced and the number of marshmallows that fit in the packaging machines. This is calculated as 998 - 957 = <<998-957=41>>41 marshmallows. ### Answer: 41
Expected answer: 41
Correct? Yes
Problem: The marshmallow factory upgraded its packaging machine and now it can hold 804 marshmallows at a time instead of 957. If the factory continues to produce 998 marshmallows per minute, what will be the number of marshmallows left un-packaged in a minute after all the packaging machines are filled with the new capacity?
Gemini-1.5 Pro:
Reasoning: With the upgraded packaging machine, the factory will have 998 - 804 = <<998-804=194>>194 marshmallows left unpacked each minute. ### Answer: 194
Expected answer: 194
Correct? Yes
Problem: There are 984 roses in the castle's garden. Princess likes to place 426 roses in every tribute for her loyal subjects. If she distributes roses evenly to create as many tributes as possible, how many roses will be left undistributed in the castle's garden?
Gemini-1.5 Pro:
Reasoning: We need to find the remainder when 984 is divided by 426. Dividing 984 by 426, we get a quotient of 2 and a remainder of 132 (984 = 426 * 2 + 132). ### Answer: 132
Expected answer: 132
Correct? Yes
Problem: In the same castle's garden, there were originally 984 roses, but the princess has decided to use only 730 roses for each tribute to her loyal subjects instead of the previous 426. Now, if she distributes roses evenly to create as many tributes as possible, how many roses will be left undistributed in the castle's garden?
Gemini-1.5 Pro:
Reasoning: We need to find the remainder when 984 is divided by 730. Dividing 984 by 730, we get a quotient of 1 and a remainder of 254 (984 = 730 * 1 + 254). ### Answer: 254
Expected answer: 254
Correct? Yes
Problem: A song has 334 words in it. If each line in the song has 23 words, how many words would be in the incomplete line at the end of the song?
Gemini-1.5 Pro:
Reasoning: The song has 334/23 = <<334/23=14.52>>14.52 lines, which means it has 14 complete lines and one incomplete line. A complete line has 23 words, so 14 complete lines have 23*14 = <<23*14=322>>322 words. The incomplete line at the end of the song has 334-322 = <<334-322=12>>12 words. ### Answer: 12
Expected answer: 12
Correct? Yes
Problem: Suppose the song writer decided to change the structure of the song and made each line contain 314 words instead. Now with the same total of 334 words, how many words would be left in the incomplete line at the end of the song?
Gemini-1.5 Pro:
Reasoning: With 314 words per line, and a total of 334 words, there can only be 1 complete line in the song, because 314*2 is already larger than 334. After the 1st line, there are 334-314 = <<334-314=20>>20 words left for the incomplete line. ### Answer: 20
Expected answer: 20
Correct? Yes
Problem: A teacher has 928 pages of study materials that he wants to print for his students. His printer can only print 336 pages in one go. After filling the printer a number of times, how many pages will he have left over to print?
Gemini-1.5 Pro:
Reasoning: We need to find out how many times 336 fits into 928, which is the same as finding the quotient of 928 divided by 336. 928 divided by 336 is 2 with a remainder. To find the remainder, we multiply the quotient (2) by the divisor (336), giving us 672, and subtract that from the original number (928), resulting in 256. ### Answer: 256
Expected answer: 256
Correct? Yes
Problem: In the same scenario, suppose the teacher decides to use a different printer that can print 409 pages in one go. After filling this printer a number of times, how many pages will he have left over to print?
Gemini-1.5 Pro:
Reasoning: We need to find out how many times 409 fits into 928. 928 divided by 409 is 2 with a remainder. To find the remainder, we multiply 2 (the times 409 fits into 928) by 409 (the number of pages the printer can print), which gives us 818. Finally, we subtract 818 from 928 (the total number of pages). ### Answer: 110
Expected answer: 110
Correct? Yes
Problem: Scientists have spotted 972 sharks in an area. The scientists tag groups of 667 sharks each. How many sharks are left untagged after the scientists finish tagging as many complete groups as possible?
Gemini-1.5 Pro:
Reasoning: The scientists tag 972 / 667 = <<972/667=1.457...>> approximately 1.46 groups, which means they tag 1 full group. This leaves 972 - 667 = <<972-667=305>>305 sharks untagged. ### Answer: 305
Expected answer: 305
Correct? Yes
Problem: Following up on the previous question, the scientists later spotted a new group of 758 sharks in a different area. Again, they were trying to tag the sharks in groups of 667. How many sharks were left untagged after all complete groups have been tagged in this new area?
Gemini-1.5 Pro:
Reasoning: The scientists were able to tag 758 / 667 = <<758/667=1.136...>> approximately 1.14 groups of sharks, which means they fully tagged 1 group. That leaves 758 - 667 = <<758-667 = 91>>91 sharks untagged in this new area. ### Answer: 91
Expected answer: 91
Correct? Yes
Problem: There are 686 blocks of cheese in the dairy shop. Each box can contain 349 blocks of cheese. If all the blocks of cheese are evenly distributed in the boxes, how many blocks of cheese would be left over after all the boxes are filled?
Gemini-1.5 Pro:
Reasoning: To find out how many blocks of cheese would be left over, we can calculate the remainder when the total number of blocks is divided by the number of blocks each box can hold. This can be represented mathematically as 686 modulo 349. Calculating the remainder, we get 686 % 349 = 0. ### Answer: 0
Expected answer: 337
Correct? No
Problem: There were 513 centimeters of snowfall recorded this winter. A snowplow can clear up to 170 centimeters of snow at a time. If the snowplow runs continuously, how many centimeters of snow will be left over after the final pass?
Gemini-1.5 Pro:
Reasoning: We need to find the remainder when 513 is divided by 170. Since 170 x 3 = 510, the snowplow will clear 510 centimeters of snow in 3 passes. That leaves 513 - 510 = <<513-510=3>>3 centimeters of snow. ### Answer: 3 centimeters.
Expected answer: 3
Correct? Yes
Problem: Suppose that instead of 513 centimeters, there were 460 centimeters of snowfall this winter. If the same snowplow, which can clear up to 170 centimeters of snow at a time, runs continuously, how many centimeters of snow would then be left over after the final pass?
Gemini-1.5 Pro:
Reasoning: Let's figure out how many full passes the snowplow can make. Two passes clear 170 * 2 = <<170*2=340>>340 centimeters. A third pass would clear more than the remaining snow, so there will only be two full passes. After two passes, there are 460 - 340 = <<460-340=120>>120 centimeters of snow remaining. ### Answer: 120 centimeters.
Expected answer: 120
Correct? Yes
Problem: A compass maker has 661 needles to install in compasses. Each compass uses 510 needles. After installing as many full compasses as he can, how many needles will the compass maker have left?
Gemini-1.5 Pro:
Reasoning: The compass maker can make 661/510 = <<661/510=1>>1 full compass. The compass maker will have 661-510 = <<661-510=151>>151 needles left. ### Answer: 151
Expected answer: 151
Correct? Yes
Problem: A furniture factory has manufactured 380 chairs to distribute to its retail shops. Each shop can only hold 310 chairs in its storage. If the factory evenly distributes all the chairs to the shops, how many chairs will be left at the factory?
Gemini-1.5 Pro:
Reasoning: The factory can evenly distribute the chairs to 380/310 = <<380/310=1.23>>1.23 shops. Since we can't have a fraction of a shop, the chairs can be evenly distributed to only 1 shop. Therefore, 380-310 = <<380-310=70>>70 chairs will be left at the factory. ### Answer: 70
Expected answer: 70
Correct? Yes
Problem: Now suppose the factory decides to distribute these chairs amongst its smaller distributors, each of which can only hold 143 chairs. Now, how many chairs will be left at the factory after distributing them evenly?
Gemini-1.5 Pro:
Reasoning: The factory can evenly distribute the 380 chairs to 380/143 = <<380/143=2.65>>2.65 distributors. Since we can't have fractions of distributors, this means the chairs can be evenly distributed to only 2 distributors. That means a total of 2*143 = <<2*143=286>>286 chairs are distributed. Therefore, 380-286 = <<380-286=94>>94 chairs will be left at the factory. ### Answer: 94
Expected answer: 94
Correct? Yes
Problem: A farmer has gathered 929 tomatoes from his field. He plans to sell them in boxes, with 154 tomatoes in each box. After packing them evenly in boxes, how many tomatoes will be left over?
Gemini-1.5 Pro:
Reasoning: We perform the division 929/154 = <<929/154=6.03...>>6 with a remainder. This means the farmer can fill 6 boxes completely. The number of tomatoes left over is the remainder of the division, which is found by multiplying the decimal part of the result by the divisor: 0.03... * 154 = <<round(0.0322077922*154)>>5. ### Answer: 5
Expected answer: 5
Correct? Yes
Problem: The farmer realized he made an error and actually collected 929 tomatoes from his field, but this time he wants to sell them in bigger boxes that can accommodate 834 tomatoes each. After packing these tomatoes evenly in these larger boxes, how many tomatoes will be left over?
Gemini-1.5 Pro:
Reasoning: We perform the division 929/834 = <<929/834=1.11...>>1 with a remainder. This means the farmer can fill 1 box completely. The number of tomatoes left over is 929-834 = <<929-834=95>>95. ### Answer: 95
Expected answer: 95
Correct? Yes
Problem: A sporting goods store has 454 pairs of ice skates in total. The store distributes the skates evenly among 128 boxes. How many pairs of ice skates will be left over after all the boxes are filled up equally?
Gemini-1.5 Pro:
Reasoning: We need to find the remainder after dividing the total number of ice skates (454) by the number of boxes (128). This means we're looking for the remainder in the calculation 454 / 128. 454 divided by 128 is 3 with a remainder of 70. ### Answer: 70
Expected answer: 70
Correct? Yes
Problem: If the sporting goods store originally had 976 pairs of ice skates instead of 454, and they still distribute the skates evenly among 128 boxes as before, how many pairs of ice skates will be left over after all the boxes are filled equally?
Gemini-1.5 Pro:
Reasoning: We need to find the remainder when 976 (the total number of skates) is divided by 128 (the number of boxes). 976 divided by 128 is 7 with a remainder of 80. ### Answer: 80
Expected answer: 80
Correct? Yes
Problem: A windmill generates 506 units of power per day. Every day, a small village consumes power in increments of 385 units. At the end of the day, after the village has consumed as much power as it can in full increments, how much power is left over?
Gemini-1.5 Pro:
Reasoning: We need to find the remainder when 506 (total power) is divided by 385 (power consumed in each increment). This means the leftover power is 506 - 385 = <<506-385=121>>121 units. ### Answer: 121 units.
Expected answer: 121
Correct? Yes
Problem: Following the scenario of the windmill and the small village, let's now consider that the windmill had a great day and managed to generate 506 units of power. However, due to development demands, the daily consumption of the village has increased to 920 units. At the end of the day, with the power being consumed in complete units, how much power is left over?
Gemini-1.5 Pro:
Reasoning: The windmill only generated 506 units of power, which is less than the village's consumption of 920 units. Therefore, there wouldn't be any power left over. In fact, the village would experience a power shortage. ### Answer: 0 units.
Expected answer: 506
Correct? No
Problem: Superhero Blast Man has 338 energy units in his power cells. Each energy blast he fires uses 16 energy units. After using equal units of energy firing blasts, how many energy units will Blast Man have left in his power cells?
Gemini-1.5 Pro:
Reasoning: Blast Man can fire 338/16 = <<338/16=21.125>> 21 blasts with his energy units, with some energy units left over. Blast Man will use 21*16 = <<21*16=336>>336 energy units firing the blasts. Blast Man will have 338-336 = <<338-336=2>>2 energy units left. ### Answer: 2
Expected answer: 2
Correct? Yes
Problem: Now, imagine that Superhero Blast Man has boosted his power cells and now has 338 energy units in his power cells. But this time, each energy blast he fires now uses 46 energy units. After using equal units of energy firing blasts, how many energy units will Blast Man have left in his power cells?
Gemini-1.5 Pro:
Reasoning: Blast Man can fire 338/46 = <<338/46=7.34782608696>>7 blasts with his energy units, with some energy units left over. Blast Man will use 7*46 = <<7*46=322>>322 energy units firing blasts. Blast Man will have 338-322 = <<338-322 = 16>>16 energy units left over. ### Answer: 16
Expected answer: 16
Correct? Yes
Problem: A school district has 530 students who need to be transported and each school bus can carry 144 students. If all students are equally spread across the buses, how many students will be on the last school bus?
Gemini-1.5 Pro:
Reasoning: First, find the number of full buses by dividing the total students by the bus capacity: 530 students / 144 students/bus = 3 full buses with some students leftover. Then, multiply the number of full buses by the bus capacity to find the number of students on the full buses: 3 buses * 144 students/bus = 432 students. Finally, subtract the number of students on full buses from the total number of students to find the number of students on the last bus: 530 total students - 432 students = 98 students. ### Answer: 98
Expected answer: 98
Correct? Yes
Problem: A wizard has 999 spells in his book. He tries to distribute them equally among 951 apprentice wizards but they don't divide evenly. How many spells will the wizard have left after giving out as many as he can to his apprentices?
Gemini-1.5 Pro:
Reasoning: To find out how many spells are left over, we need to find the remainder when 999 is divided by 951. We can calculate this: 999 = (951 * 1) + 48 ### Answer: 48
Expected answer: 48
Correct? Yes
Problem: If the wizard had instead 999 spells and he tries to distribute them equally among 801 apprentice wizards, how many spells will the wizard have left after giving out as many as he can to his apprentices?
Gemini-1.5 Pro:
Reasoning: To find out how many spells are left over, we need to find the remainder when 999 is divided by 801. We can calculate this: 999 = (801 * 1) + 198 ### Answer: 198
Expected answer: 198
Correct? Yes
Problem: A scooter manufacturing company has produced 767 scooters. Each delivery truck they use can carry 369 scooters. If they distribute the scooters evenly among the trucks, how many scooters will be left after all the trucks are loaded?
Gemini-1.5 Pro:
Reasoning: We need to find the remainder when 767 scooters are divided into groups of 369. This is the same as finding the remainder when 767 is divided by 369. 767 divided by 369 is 2 with a remainder of 29. ### Answer: 29
Expected answer: 29
Correct? Yes
Problem: There are 846 water droplets in a cloud. Each raindrop needs 722 droplets to form. If all droplets are used to form raindrops, how many droplets would be left unconverted in the cloud after reaching the maximum number of rain drops?
Gemini-1.5 Pro:
Reasoning: We can find the leftover droplets by calculating the remainder of dividing the total droplets by the droplets needed per raindrop. This is represented as 846 modulo 722 or 846 % 722. 846 divided by 722 is 1 with a remainder of 124. ### Answer: 124
Expected answer: 124
Correct? Yes
Problem: There was a slight miscalculation in the cloud's droplet count. There are actually 846 water droplets in the cloud, but each raindrop needs 442 droplets to form instead of 722. With this updated droplet count per raindrop, how many droplets would be left unconverted in the cloud after reaching the maximum number of rain drops?
Gemini-1.5 Pro:
Reasoning: We need to find the remainder when 846 is divided by 442. 846 divided by 442 is 1 with a remainder of 404. ### Answer: 404
Expected answer: 404
Correct? Yes
Problem: Unicorn Village, a magical place where 265 unicorns live, is divided into 146 equal sections where these magical creatures reside. If each section is occupied by an equal number of unicorns, how many unicorns will live in the last incomplete section?
Gemini-1.5 Pro:
Reasoning: First, let's find out how many complete sections will be filled with unicorns: 265 unicorns / 146 unicorns per section = 1 full section and a remainder. To find the remainder, which represents the unicorns in the last incomplete section, we multiply the decimal part of the result above by the number of unicorns per section: 0.8219... * 146 unicorns per section ≈ 120 unicorns. ### Answer: 120
Expected answer: 119
Correct? No
Problem: In a game, there are 923 players waiting to enter a match. Only 383 players can enter a match at a time. If players enter matches evenly, how many players will be left waiting after filling all the matches?
Gemini-1.5 Pro:
Reasoning: To find out how many full matches can be filled, we divide the total players by the number of players per match: 923 players / 383 players/match = <<923/383=2.41>> 2.41 matches. Since we can only have whole matches, this means 2 matches will be completely filled. Two full matches would hold 2 matches * 383 players/match = <<2*383=766>> 766 players. Subtracting the players in filled matches from the total players gives us the number of players left waiting: 923 players - 766 players = <<923-766=157>> 157 players. ### Answer: 157 players.
Expected answer: 157
Correct? Yes
Problem: In the same game, a new day dawns with 456 players waiting to join a match. The match capacity remains the same, permitting 383 players at a time. If players are allocated evenly across the matches, how many players will be left waiting after all available matches are filled?
Gemini-1.5 Pro:
Reasoning: We can determine the number of full matches by dividing the total players by the match capacity: 456 players / 383 players/match = <<456/383=1.19>> 1.19 matches. Since we can only have complete matches, only 1 match will be filled entirely. One full match accommodates 383 players. To find the number of players left waiting, we subtract the players in the full match from the total: 456 players - 383 players = <<456-383=73>> 73 players. ### Answer: 73 players.
Expected answer: 73
Correct? Yes
Problem: A pirate ship has 923 cannonballs on board. They want to equally disperse them between 499 different crates. After evenly distributing them as much as possible, how many cannonballs will be left uncrated?
Gemini-1.5 Pro:
Reasoning: We need to find the remainder when 923 is divided by 499. Performing the division, 923 divided by 499 equals 1 with a remainder of 424. ### Answer: 424
Expected answer: 424
Correct? Yes
Problem: Keeping in line with the previous pirate ship themed problem, let's consider the following scenario: The same pirate ship initially started with 462 cannonballs instead of 923. After the pirates evenly distribute these cannonballs into the same 499 crates, can any be leftover? If so, how many cannonballs will be left uncrated?
Gemini-1.5 Pro:
Reasoning: Since they only have 462 cannonballs and 499 crates, there won't be enough cannonballs to put even one in each crate. Therefore, all 462 cannonballs will be left uncrated. ### Answer: 462
Expected answer: 462
Correct? Yes
Problem: A kite store has 530 string spools to attach to their kites. They distribute them to 518 kites, each getting one string spool. After each kite gets a spool, how many spools are left in the store?
Gemini-1.5 Pro:
Reasoning: The store has 530 - 518 = <<530-518=12>>12 string spools left. ### Answer: 12
Expected answer: 12
Correct? Yes
Problem: A dairy farm produces 913 gallons of milk in a day. If every milk jug holds 39 gallons, how many gallons will be left over after all the jugs are filled?
Gemini-1.5 Pro:
Reasoning: The farm can fill 913/39 = <<913/39=23.41>> 23.41 jugs. Since we can't have a fraction of a jug, this means the farm can fill 23 jugs completely. 23 jugs will hold 23*39 = <<23*39=897>> 897 gallons of milk. This leaves 913-897 = <<913-897=16>> 16 gallons of milk leftover. ### Answer: 16
Expected answer: 16
Correct? Yes
Problem: The dairy farm has adjusted its production and now produces 913 gallons of milk in a day. If they started using larger milk jugs that hold 230 gallons each, how many gallons will be left over after all the jugs are filled?
Gemini-1.5 Pro:
Reasoning: The farm can fill 913/230 = <<913/230=3.97>> 3.97 jugs. Since we can't have a fraction of a jug, this means the farm can fill 3 jugs completely. 3 jugs will hold 3*230 = <<3*230=690>> 690 gallons of milk. This leaves 913-690 = <<913-690=223>> 223 gallons of milk leftover. ### Answer: 223
Expected answer: 223
Correct? Yes
Problem: A doll seller received a shipment of 603 new dolls to put on the shelves. She arranged all the dolls in rows, with 369 dolls in each row. After filling up the rows as much as possible, how many dolls were left unarranged?
Gemini-1.5 Pro:
Reasoning: She can make 603/369 = <<603/369=1.63>>1 full row, with some dolls leftover. This means that 603-369 = <<603-369=234>>234 dolls were left over. ### Answer: 234
Expected answer: 234
Correct? Yes
Problem: In the previous doll problem, if the doll seller initially received a shipment of 44 new dolls instead of 603, and still arranged them in rows of 369 dolls, how many dolls would be left unarranged after filling up the rows as much as possible?
Gemini-1.5 Pro:
Reasoning: Since the doll seller only received 44 dolls, which is less than the number of dolls in a single row (369), she wouldn't be able to fill up any rows. Therefore, all 44 dolls would be left unarranged. ### Answer: 44
Expected answer: 44
Correct? Yes
Problem: A jewelry maker has 850 beads to make necklaces. They use 631 beads for each necklace. After using as many beads as possible, how many beads will the jewelry maker have left over?
Gemini-1.5 Pro:
Reasoning: We can find the number of leftover beads by finding the remainder after dividing the total beads by the beads per necklace: 850 % 631 = <<850%631=219>>219 ### Answer: 219
Expected answer: 219
Correct? Yes
Problem: The jewelry maker decides to change the design and now each necklace uses only 150 beads instead of 631 beads. After they distribute the 850 beads as equally as possible among the new necklaces, how many beads will the jewelry maker have left over?
Gemini-1.5 Pro:
Reasoning: We can find the number of leftover beads by finding the remainder after dividing the total beads by the new number of beads per necklace: 850 % 150 = <<850%150=50>>50 ### Answer: 50
Expected answer: 100
Correct? No
Problem: A gardener has 952 grapes that he wants to package into boxes. If each box can hold 380 grapes, how many grapes will be left after the gardener has filled as many boxes as possible?
Gemini-1.5 Pro:
Reasoning: The gardener can fill 952 / 380 = <<952 / 380 = 2.505>> 2 boxes, leaving some grapes leftover. Since we can't have half a box, the gardener filled 2 boxes, using 2 * 380 = <<2 * 380 = 760>>760 grapes. The gardener has 952 - 760 = <<952 - 760 = 192>>192 grapes left. ### Answer: 192
Expected answer: 192
Correct? Yes
Problem: The gardener's friend gave him an additional 183 grapes from his own garden. If the gardener decides to package these grapes as well into boxes with each box holding 380 grapes, how many grapes will remain after packaging the new grapes into as many boxes as possible?
Gemini-1.5 Pro:
Reasoning: After receiving grapes from his friend, the gardener has a total of 192 + 183 = <<192 + 183 = 375>>375 grapes. Since each box holds 380 grapes, and the gardener only has 375, he won't be able to fill a whole box. ### Answer: 375
Expected answer: 183
Correct? No
Problem: On a treasure map, there are 236 steps mentioned on the guide. If every 44 steps I make leads me to a significant place or clue, how many steps will be left after I reach the last significant place or clue?
Gemini-1.5 Pro:
Reasoning: We first need to find out how many groups of 44 steps are there in 236 steps by dividing 236 by 44, 236 / 44 = 5 remainder 16. This means there are 5 significant places or clues along the way, and after reaching the last one, there are 16 steps left. ### Answer: 16
Expected answer: 16
Correct? Yes
Problem: Sarah blew 932 bubbles using her new bubble machine. The machine is designed to form groups of 507 bubbles each before releasing them. After forming complete groups, how many bubbles does it make in its final, incomplete group?
Gemini-1.5 Pro:
Reasoning: The bubble machine made 932 / 507 = <<932/507=1>>1 complete group of bubbles, with some left over. This means there were 932 - (1 * 507) = <<932-(1*507)=425>>425 bubbles in the final group. ### Answer: 425
Expected answer: 425
Correct? Yes
Problem: Suppose Sarah uses her bubble machine again, this time to blow 904 bubbles. The machine is still designed to form groups of 507 bubbles each before releasing them. After forming complete groups, how many bubbles does it make in its final, incomplete group?
Gemini-1.5 Pro:
Reasoning: The bubble machine made 904 / 507 = <<904/507=1>>1 complete group of bubbles, with some left over. This means there were 904 - (1 * 507) = <<904-(1*507)=397>>397 bubbles in the final group. ### Answer: 397
Expected answer: 397
Correct? Yes
Problem: At the park, there are 931 kids who want to use the swings. Each swing set can accommodate 34 kids at a time. If all the swing sets are filled continuously, how many kids will be waiting for their turn after all the swing sets are occupied?
Gemini-1.5 Pro:
Reasoning: We need to find out how many full swing sets can be filled with 931 kids, which means we need to divide: 931 kids / 34 kids/swing set = <<931/34=27.38>>27.38 swing sets. We can only have a whole number of swing sets, so we round down to 27 swing sets. This means 27 swing sets * 34 kids/swing set = <<27*34=918>>918 kids can swing at once. Therefore, 931 total kids - 918 kids on swings = <<931-918=13>>13 kids are waiting. ### Answer: 13
Expected answer: 13
Correct? Yes
Problem: In the previous scenario, let's say that some of the kids finished their swinging and left the park. Now, there are only 708 kids waiting to use the swings. Each swing set can still accommodate 34 kids at a time. Given this new number, how many children will be waiting for their turn after all the swing sets are occupied?
Gemini-1.5 Pro:
Reasoning: We repeat the process from before to find out how many swing sets will be filled: 708 kids / 34 kids/swing set = <<708/34=20.82>>20.82 swing sets. Again, we round down to the nearest whole number, so we have 20 full swing sets. This means 20 swing sets * 34 kids/swing set = <<20*34=680>>680 kids can swing at once. Therefore, 708 total kids - 680 kids on swings = <<708-680=28>>28 kids are waiting. ### Answer: 28
Expected answer: 28
Correct? Yes
Problem: John has 943 dollar bills in his possession. He tries to stuff them in wallets that can each contain 433 dollar bills. After fully loading as many wallets as he can, how many dollar bills does he have left?
Gemini-1.5 Pro:
Reasoning: We perform the calculation 943 / 433 = 2 R 77. This indicates John can fully load 2 wallets, with a remainder of 77 dollar bills. ### Answer: 77
Expected answer: 77
Correct? Yes
Problem: Suppose John originally had 586 dollar bills instead of 943. He still tries to stuff them in wallets that can each contain 433 dollar bills. After fully loading as many wallets as he can, how many dollar bills does he have left now?
Gemini-1.5 Pro:
Reasoning: Since 586 is larger than 433 but smaller than twice 433, John can still only fully load 1 wallet. To find the remaining number of dollar bills, we calculate 586 - 433 = 153. ### Answer: 153
Expected answer: 153
Correct? Yes
Problem: A helicopter pilot plans to transport 240 passengers over several trips. He can carry 177 passengers in one trip. How many passengers will be left behind after the helicopter makes the first full trip?
Gemini-1.5 Pro:
Reasoning: After the first trip, there will be 240-177 = <<240-177=63>>63 passengers left behind. ### Answer: 63
Expected answer: 63
Correct? Yes
Problem: A gardener has 982 flowers to plant in flowerbeds. Each flowerbed can fit 555 flowers. After filling up as many flowerbeds as possible, how many flowers will the gardener have left to plant?
Gemini-1.5 Pro:
Reasoning: The gardener can fill up 982 / 555 = <<982/555=1.7675...>>1 flowerbed, but since we can't have a fraction of a flowerbed, this means the gardener can completely fill 1 flowerbed. This will leave the gardener with 982 - 555 = <<982-555=427>>427 flowers left over. ### Answer: 427
Expected answer: 427
Correct? Yes
Problem: The gardener received an additional shipment, bringing the total number of flowers up to 867. If he continues to plant the flowers in flowerbeds of 555 each, how many flowers will he have left to plant after filling up as many flowerbeds as possible?
Gemini-1.5 Pro:
Reasoning: The gardener can fill up 867 / 555 = <<867/555=1.5621...>>1 flowerbed. This will leave the gardener with 867 - 555 = <<867-555=312>>312 flowers left over. ### Answer: 312
Expected answer: 312
Correct? Yes
Problem: A farmer grows 203 strawberry plants. She wants to divide her plants into groups of 5 to sell. How many plants will be remaining if she divides them equally?
Gemini-1.5 Pro:
Reasoning: We need to find the remainder when 203 is divided by 5. 203 divided by 5 is 40 with a remainder of 3. ### Answer: 3
Expected answer: 3
Correct? Yes
Problem: The farmer harvested another field and got an additional 76 strawberry plants. Again, she wants to divide the new plants into groups of 5 to sell. How many plants will be remaining if she divides these new strawberries equally?
Gemini-1.5 Pro:
Reasoning: We need to find the remainder when 76 is divided by 5. 76 divided by 5 is 15 with a remainder of 1. ### Answer: 1
Expected answer: 1
Correct? Yes
Problem: A gardener has 355 carrots. He wants to create bundles of 16. After creating as many bundles as he can, how many carrots will he have left?
Gemini-1.5 Pro:
Reasoning: The gardener can create 355/16 = <<355/16=22.1875>>22 bundles of carrots. Since the gardener can only make whole bundles, he made 22 bundles. To make 22 bundles, the gardener used 22*16 = <<22*16=352>>352 carrots. The gardener has 355-352 = <<355-352=3>>3 carrots left. ### Answer: 3
Expected answer: 3
Correct? Yes
Problem: A total rainfall of 612 inches fell over a certain city in 29 consecutive days. If the rain fell in the same amount every day, how many inches of rain would be left to make the days evenly rainy?
Gemini-1.5 Pro:
Reasoning: First find the average rainfall per day: 612 inches / 29 days = 21.10 inches/day (rounded to two decimal places). The remainder when 612 is divided by 29 represents the extra inches of rain beyond what would make an even distribution: 612 % 29 = 5 inches. To make the days evenly rainy, we would need to remove this excess rain. ### Answer: 5 inches
Expected answer: 3
Correct? No
Problem: A truck company has got 514 boxes for delivery. Each truck can hold up to 371 boxes. If each truck is loaded to its full capacity, how many boxes will be left over?
Gemini-1.5 Pro:
Reasoning: We need to find the remainder after dividing the total number of boxes by the capacity of each truck: 514 modulo 371. Calculating the remainder: 514 % 371 = 143. ### Answer: 143
Expected answer: 143
Correct? Yes
Problem: In a large sandbox, children create 684 sandcastles over the summer. The sandcastles were grouped into sets of 230 for a photography contest. After all the sets were completed, how many sandcastles were left that didn't form a complete set?
Gemini-1.5 Pro:
Reasoning: We can find how many complete sets were formed by dividing the total number of sandcastles by the number in each set: 684 sandcastles / 230 sandcastles/set = <<684/230=2.97>>2.97 sets. Since we only care about complete sets, we'll use the whole number, 2 sets. Then we can find the number of sandcastles in the complete sets: 2 sets * 230 sandcastles/set = <<2*230=460>> 460 sandcastles. Finally, subtract the number of sandcastles in complete sets from the total number of sandcastles to find the number left over: 684 sandcastles - 460 sandcastles = 224 sandcastles. ### Answer: 224
Expected answer: 224
Correct? Yes
Problem: Continuing from the prior problem, suppose that in another large sandbox, children now create 533 sandcastles over the summer instead of 684. If they still group the sandcastles in sets of 230 for a photography contest, how many sandcastles will be left now that don't form a complete set?
Gemini-1.5 Pro:
Reasoning: We can find how many complete sets were formed by dividing the total number of sandcastles by the number in each set: 533 sandcastles / 230 sandcastles/set = <<533/230=2.32>> 2.32 sets. Again, we only care about complete sets, so we'll use the whole number, 2 sets. Then we can find the number of sandcastles in the complete sets: 2 sets * 230 sandcastles/set = <<2*230=460>> 460 sandcastles. Finally, subtract the number of sandcastles in complete sets from the total number of sandcastles to find the number left over: 533 sandcastles - 460 sandcastles = 73 sandcastles. ### Answer: 73
Expected answer: 73
Correct? Yes
Problem: A toy manufacturer has a production run of 735 toy cars. They package the cars in packs of 348 for bulk shipments. If all the toy cars are divided equally among packs, how many toy cars will be left over after all full packs have been filled?
Gemini-1.5 Pro:
Reasoning: To find the number of toy cars left over, we need to find the remainder when the total number of toy cars (735) is divided by the number of cars per pack (348). We perform the division: 735 ÷ 348 = 2 remainder 39 ### Answer: 39
Expected answer: 39
Correct? Yes
Problem: The toy manufacturer decides in the next production run to make only 77 toy cars instead of 735. Again, they package the cars in packs of 348 for bulk shipments. If all the toy cars are divided equally among these packs, how many toy cars will be left over after all full packs have been filled?
Gemini-1.5 Pro:
Reasoning: Since the manufacturer is only making 77 toy cars, which is less than the number of cars in a single bulk pack (348), they will not be able to fill any packs. Therefore, all 77 cars will be left over. ### Answer: 77
Expected answer: 77
Correct? Yes
Problem: In a forest, there are 386 animals. Each woodlands territory can support 95 animals. If the existing animals are evenly distributed among the territories, how many animals will be left in the last not fully occupied territory?
Gemini-1.5 Pro:
Reasoning: We need to find the remainder after dividing the total number of animals by the capacity of each territory: 386 divided by 95. 386 / 95 = 4 remainder 6 ### Answer: 6
Expected answer: 6
Correct? Yes
Problem: In the same forest, a new report finds that there were actually 497 animals instead of the initially thought 386. If these animals were evenly distributed among the territories, each still supporting 95 animals, how many animals would be in the last not fully occupied territory now?
Gemini-1.5 Pro:
Reasoning: We need to find the remainder after dividing the new total number of animals (497) by the capacity of each territory (95). 497 / 95 = 5 remainder 22 ### Answer: 22
Expected answer: 22
Correct? Yes
Problem: A forest has 801 trees. A tree disease starts to spread and is expected to affect 646 trees. If all the diseased trees have to be cut down evenly, how many trees are likely to stay healthy after the disease has affected all possible trees?
Gemini-1.5 Pro:
Reasoning: We need to subtract the number of diseased trees from the total number of trees: 801 trees - 646 trees = <<801-646=155>>155 trees. ### Answer: 155 trees
Expected answer: 155
Correct? Yes
Problem: A rope manufacturer has made a rope of 934 meters in length. This rope is supposed to be cut into smaller pieces, each piece being 902 meters in length. After cutting into the maximum possible number of equal pieces, how many meters will the last piece of the rope be?
Gemini-1.5 Pro:
Reasoning: Dividing the total rope length by the length of each smaller piece gives us 934 / 902 = <<934/902=1.035>>1.035. This means we can get 1 full piece and a fraction of another piece. To find the length of the last piece, we multiply the decimal part of the previous division by the length of each smaller piece: 0.035 * 902 meters = <<0.035*902=31.57>>31.57 meters. ### Answer: 31.57 meters
Expected answer: 32
Correct? No
Problem: A dairy farm produces 561 liters of milk each day. The milk is packaged into 550-liter containers. How many liters of milk are left over each day after filling the containers?
Gemini-1.5 Pro:
Reasoning: We need to find the remainder after dividing the total milk produced (561 liters) by the container size (550 liters). The leftover milk is 561 - 550 = <<561-550=11>>11 liters. ### Answer: 11 liters
Expected answer: 11
Correct? Yes
Problem: If the dairy farm increased its production and started producing 729 liters of milk each day instead of 561 liters, how many liters of milk would be left over each day after filling the 550-liter containers?
Gemini-1.5 Pro:
Reasoning: With the increased production, we again need to find the remainder after dividing the new total milk produced (729 liters) by the container size (550 liters). The leftover milk would be 729 - 550 = <<729-550=179>>179 liters. However, since each container holds 550 liters, we need to account for the fact that a portion of that leftover milk could fill another container. Therefore, the actual leftover milk is 179 - 550 = <<-371=-371>>-371 liters. Since we get a negative value, this means that all the leftover milk can fit into another container, with some space remaining. We need to find the difference between the container's capacity and this negative value to find the actual remaining space. The actual leftover milk is 550 - 371 = <<550-371=179>>179 liters. ### Answer: 179 liters
Expected answer: 179
Correct? Yes
Problem: Jon has 259 puzzle pieces. If each puzzle requires 258 pieces, how many pieces will be left over once he completes a full puzzle?
Gemini-1.5 Pro:
Reasoning: Jon will have 259-258 = <<259-258=1>>1 piece left over. ### Answer: 1
Expected answer: 1
Correct? Yes
Problem: In the previous problem, Jon had 259 puzzle pieces and each puzzle requires 258 pieces. Suppose instead each puzzle needs 542 pieces. How many pieces would Jon have left over after finishing as many full puzzles as possible with his 259 pieces?
Gemini-1.5 Pro:
Reasoning: Since 542 is more than 259, Jon cannot complete a full puzzle. Therefore, he will have all 259 pieces left over. ### Answer: 259
Expected answer: 259
Correct? Yes
Problem: A jewelry maker has 673 beads. She plans to use exactly 49 beads for each bracelet. How many beads will she have left after creating as many bracelets as possible with the exact number of beads?
Gemini-1.5 Pro:
Reasoning: The jewelry maker can make 673 / 49 = <<673/49=13.73>>13 bracelets with the beads. Since she can't make a fraction of a bracelet, we only look at the whole number, 13. That means she used 13 x 49 = <<13*49=637>>637 beads for the bracelets. The jewelry maker will have 673-637 = <<673-637=36>>36 beads left over. ### Answer: 36
Expected answer: 36
Correct? Yes
Problem: The jewelry maker received an additional shipment, and now she has a total of 673 beads. This time, she wants to make larger bracelets which use exactly 545 beads each. After creating as many large bracelets as possible, how many beads will she have left over?
Gemini-1.5 Pro:
Reasoning: The jewelry maker can make 673 / 545 = <<673/545=1.23>>1.23 bracelets with the beads. Since she can't make a fraction of a bracelet, she can only make 1 complete bracelet. That means she'll use 1 x 545 = 545 beads for the bracelets. The jewelry maker will have 673 - 545 = <<673-545=128>>128 beads left over. ### Answer: 128
Expected answer: 128
Correct? Yes
Problem: A police station received 927 calls within a week. They have 311 operators who can handle the same number of calls each week. However, when the calls are divided equally, how many calls will the last operator handle?
Gemini-1.5 Pro:
Reasoning: When the calls are divided equally, each operator will handle 927/311 = <<927/311=3>>3 calls. So, the last operator will handle 927-311*3 = <<927-311*3=1>> call. ### Answer: 1
Expected answer: 305
Correct? No
Problem: John has 764 pieces for his jigsaw puzzle, and every package should contain 589 pieces. If he separates these pieces into full packages, how many pieces will be left outside without a package?
Gemini-1.5 Pro:
Reasoning: To find out how many full packages John can make, we divide the total pieces by the number of pieces per package: 764 pieces / 589 pieces/package = <<764/589=1.2971>>1.2971 packages. This means John can make 1 full package. To find out how many pieces are left over, we multiply the decimal part of the previous result (0.2971) by the number of pieces per package: 0.2971 * 589 pieces/package ≈ 176 pieces. ### Answer: 176
Expected answer: 175
Correct? No
Problem: A dressmaker has 984 meters of fabric. She uses 217 meters of fabric to make each dress. After using all the fabric she can to make as many dresses as possible, how many meters of fabric will she have left?
Gemini-1.5 Pro:
Reasoning: The dressmaker can make 984/217 = <<984/217=4>>4 dresses. The dressmaker will use 4*217 = <<4*217=868>>868 meters of fabric to make the dresses. She will have 984-868 = <<984-868=116>>116 meters of fabric left. ### Answer: 116 meters.
Expected answer: 116
Correct? Yes
Problem: In the previous scenario, let's now suppose that the dressmaker has 984 meters of fabric, but this time she uses 585 meters of fabric to make each dress. Again, she uses all the fabric she can to make as many dresses as possible. With this change, how many meters of fabric will she have left after all the dresses are made?
Gemini-1.5 Pro:
Reasoning: The dressmaker can make 984/585 = <<984/585=1.68>>1.68 dresses. Since we can't make fractions of dresses, she can make only 1 whole dress. The dressmaker will use 585 meters of fabric to make the dress. She will have 984-585 = <<984-585=399>>399 meters of fabric left. ### Answer: 399 meters.
Expected answer: 399
Correct? Yes
Problem: A company donates 639 sleeping bags for a camping event. Each campsite is supplied with 374 sleeping bags. If all the sleeping bags are divided equally among the campsites, how many sleeping bags will there be left?
Gemini-1.5 Pro:
Reasoning: We need to find the remainder when 639 is divided by 374. 639 divided by 374 is 1 with a remainder of <<639-374=265>>265. ### Answer: 265
Expected answer: 265
Correct? Yes
Problem: The same company from our previous question receives an updated request for sleeping bags. Now instead of 639, they only need to donate 613. If each campsite is still supplied with 374 sleeping bags, how many sleeping bags will be left after all the campsites are filled?
Gemini-1.5 Pro:
Reasoning: We need to find the remainder when 613 is divided by 374. 613 divided by 374 is 1 with a remainder of <<613-374=239>>239. ### Answer: 239
Expected answer: 239
Correct? Yes
Problem: A pizza restaurant made 620 pizzas today. They package up the pizzas in boxes that hold 578 each for delivery. If the pizzas are evenly distributed into these boxes, how many pizzas will be left over that don't fit into a box?
Gemini-1.5 Pro:
Reasoning: We need to find the remainder when 620 pizzas are divided into boxes of 578. This is the same as finding the remainder when 620 is divided by 578. 620 divided by 578 is 1 with a remainder of 42. ### Answer: 42
Expected answer: 42
Correct? Yes
Problem: The owner of the pizza restaurant decides to make 74 more pizzas tomorrow, bringing the total to 694 pizzas. If they are again distributed into boxes that hold 578 pizzas each, how many pizzas will be left out without a box this time?
Gemini-1.5 Pro:
Reasoning: We need to find the remainder when 694 pizzas are divided into boxes of 578. This is the same as finding the remainder when 694 is divided by 578. 694 divided by 578 is 1 with a remainder of 116. ### Answer: 116
Expected answer: 116
Correct? Yes
Problem: A factory made a total of 820 robots. It can store 684 robots in one storage unit. If the robots are evenly stored, how many robots will not fit and remain outside of the storage units?
Gemini-1.5 Pro:
Reasoning: We need to find the remainder after dividing the total robots by the storage capacity of one unit: 820 divided by 684. 820 ÷ 684 = 1 with a remainder of 136. ### Answer: 136
Expected answer: 136
Correct? Yes
Problem: In the same factory, another production run is completed, this time manufacturing a total of 820 upgraded robots. However, the storage units for these new models can only hold 625 robots each. If the robots are evenly stored, how many upgraded robots will not fit and remain outside the storage units now?
Gemini-1.5 Pro:
Reasoning: We need to find the remainder after dividing the total number of upgraded robots by the storage capacity of the new storage units: 820 divided by 625. 820 ÷ 625 = 1 with a remainder of 195. ### Answer: 195
Expected answer: 195
Correct? Yes
Problem: A cloud changes its shape by reducing its water droplets. Initially, there were 516 droplets in the cloud. If the cloud loses water droplets at an equal rate and becomes entirely dry after every 289 droplets, how many droplets will be left when the cloud is dry after the final cycle?
Gemini-1.5 Pro:
Reasoning: Since the cloud becomes entirely dry, there will be no droplets left after the final cycle of losing water droplets. ### Answer: 0
Expected answer: 227
Correct? No
Problem: A transport company needs to load 330 boxes into trucks. Each truck can hold exactly 4 boxes. After filling each truck to its full capacity, how many boxes will be left unloaded?
Gemini-1.5 Pro:
Reasoning: We need to find the remainder when 330 is divided by 4. 330 divided by 4 is 82 with a remainder of 2. ### Answer: 2
Expected answer: 2
Correct? Yes
Problem: The transport company now needs to load a new batch of 274 boxes into trucks. Again, each truck can hold exactly 4 boxes. After filling each truck to its full capacity, how many boxes will be left unloaded this time?
Gemini-1.5 Pro:
Reasoning: We need to find the remainder when 274 is divided by 4. 274 divided by 4 is 68 with a remainder of 2. ### Answer: 2
Expected answer: 2
Correct? Yes
Problem: A farmer harvested 649 potatoes this season. He decides to pack them into crates each containing 183 potatoes. How many potatoes will be left after all crates are filled to their maximum capacity?
Gemini-1.5 Pro:
Reasoning: We need to find the remainder when 649 potatoes are divided into crates of 183. This is the same as finding the remainder when 649 is divided by 183. 649 divided by 183 is 3 with a remainder of 100. ### Answer: 100
Expected answer: 100
Correct? Yes
Problem: The farmer realized that he actually only harvested 238 potatoes this season instead of 649. If he still packs them into crates each holding 183 potatoes, how many potatoes will be left after all crates are filled to their maximum capacity?
Gemini-1.5 Pro:
Reasoning: Since the farmer only has 238 potatoes, and each crate holds 183, he can only fill one crate completely. This will leave some potatoes leftover. To find out how many are left, we subtract the number of potatoes in a full crate from the total number of potatoes: 238 - 183 = 55 ### Answer: 55
Expected answer: 55
Correct? Yes
Problem: A t-shirt company has a batch of 258 shirts in production. Each box can pack 67 shirts. If all the shirts are evenly distributed in the boxes, how many shirts would be left outside the boxes?
Gemini-1.5 Pro:
Reasoning: We need to find the remainder when 258 shirts are divided into boxes of 67. This is the same as finding the modulo of 258 by 67. 258 divided by 67 is 3 with a remainder of 57 (258 = 67 * 3 + 57). ### Answer: 57
Expected answer: 57
Correct? Yes
Problem: Suppose the t-shirt company actually had a batch of 258 shirts, but this time each box can pack 828 shirts. If all the shirts are evenly distributed in the boxes, how many shirts would be left outside the boxes?
Gemini-1.5 Pro:
Reasoning: Since each box can pack 828 shirts, and the company only has 258 shirts, all the shirts can fit in one box. Therefore, there would be no shirts left outside the boxes. ### Answer: 0
Expected answer: 258
Correct? No
Problem: On a pirate ship, there are 995 gold coins that need to be evenly divided among the 267 pirates. If they split the gold up as evenly as possible, how many gold coins will be left over?
Gemini-1.5 Pro:
Reasoning: To find out how many gold coins are left over, we can calculate the remainder after dividing the total gold coins by the number of pirates: 995 divided by 267. 995 divided by 267 is 3 with a remainder of 184. ### Answer: 184
Expected answer: 194
Correct? No
Problem: There are 776 snails all lined up in a row. If you group them in bunches of 375 snails, how many snails will be left in the final group?
Gemini-1.5 Pro:
Reasoning: We need to divide the total number of snails (776) by the number of snails in each group (375) to find out how many groups we can make: 776 / 375 = 2 with a remainder. The remainder represents the snails in the final group. To find the remainder, we can multiply the number of groups (2) by the size of each group (375) and then subtract that from the total number of snails: (2 * 375 = 750), (776-750=26) ### Answer: 26
Expected answer: 26
Correct? Yes
Problem: Originally, you had grouped the snails in bunches of 375 snails each. Now, think about what would happen if each bunch had 18 snails instead. How many snails would be left in the final group then?
Gemini-1.5 Pro:
Reasoning: We need to divide the total number of snails (776) by the new number of snails in each group (18) to find out how many groups we can make: 776 / 18 = 43 with a remainder. The remainder represents the snails left in the final group. To find the remainder, we can multiply the number of full groups (43) by the size of each group (18) and subtract that from the total number of snails: (43 * 18 = 774), (776 - 774 = 2) ### Answer: 2
Expected answer: 2
Correct? Yes
Problem: A pillow factory produces 589 pillows per day. They package these pillows in boxes, and each box holds 198 pillows. If they pack as many full boxes as possible, how many pillows will be left outside the boxes at the end of the day?
Gemini-1.5 Pro:
Reasoning: To find the number of pillows left over, we need to find the remainder when the total number of pillows is divided by the number of pillows per box. We can calculate this as follows: 589 pillows ÷ 198 pillows/box = 2 remainder 193 pillows. ### Answer: 193 pillows.
Expected answer: 193
Correct? Yes
Problem: The pillow factory has made an adjustment to the packaging process and recently upgraded their boxes so that each can now hold 810 pillows. If they still produce 589 pillows per day and pack as many full boxes as possible, how many pillows will be left outside the boxes at the end of the day?
Gemini-1.5 Pro:
Reasoning: Since each box now holds more pillows than the factory produces in a day (810 pillows/box > 589 pillows), they won't be able to fill a single box. ### Answer: 589 pillows.
Expected answer: 589
Correct? Yes
Problem: A jewelry maker has 633 beads. If she uses beads to make necklaces, with each necklace using exactly 30 beads, how many beads will she have left after making as many necklaces as she can?
Gemini-1.5 Pro:
Reasoning: The jewelry maker can make 633 / 30 = <<633/30=21.1>> 21 necklaces. Since she can't make .1 necklaces, we only consider the whole number, 21. That means she used 21 * 30 = <<21*30=630>> 630 beads for the necklaces. Therefore, she has 633 - 630 = <<633-630=3>> 3 beads left over. ### Answer: 3
Expected answer: 3
Correct? Yes
Problem: The jewelry maker found an additional box of beads in her storage, increasing her total number of beads to 588. Now, if she uses these beads to make necklaces, with each necklace using exactly 30 beads, how many beads will she have left after making as many necklaces as she can?
Gemini-1.5 Pro:
Reasoning: The jewelry maker can make 588 / 30 = <<588/30=19.6>> 19.6 necklaces. Since she can't make .6 necklaces, we only consider the whole number, 19. That means she used 19 * 30 = <<19*30=570>> 570 beads for the necklaces. Therefore, she has 588 - 570 = <<588-570=18>> 18 beads left over. ### Answer: 18
Expected answer: 18
Correct? Yes
Problem: John has collected 365 coins. He decided to put equal numbers of them in his 140 wallets. However, he found out he would still have some coins left after evenly distributing them into these wallets. How many coins will John have left?
Gemini-1.5 Pro:
Reasoning: We can find the number of coins left by finding the remainder when 365 is divided by 140. 365 divided by 140 is 2 remainder 85. ### Answer: 85
Expected answer: 85
Correct? Yes
Problem: Now, suppose John comes across additional coins and his collection increases to 739 coins. He again tries to evenly distribute these coins among his 140 wallets. How many coins will John have left after this distribution?
Gemini-1.5 Pro:
Reasoning: We need to find the remainder when 739 is divided by 140. 739 divided by 140 is 5 remainder 39. ### Answer: 39
Expected answer: 39
Correct? Yes
Problem: A sock manufacturer produces 743 socks in a single production run. The socks are packed into cartons, each containing 451 socks. After filling up as many cartons as possible, how many socks are left unpacked?
Gemini-1.5 Pro:
Reasoning: We need to find out how many times 451 fits into 743, which is the same as finding the quotient of 743 divided by 451. 743 divided by 451 is 1 with a remainder. To find the remainder, we subtract 451 from 743: 743 - 451 = 292 This means 1 carton can be filled completely, and 292 socks will be left unpacked. ### Answer: 292
Expected answer: 292
Correct? Yes
Problem: Now suppose the sock manufacturer changes their packaging method and each carton contains 179 socks instead of 451 socks. After filling up as many cartons as possible with 743 socks, how many socks are left unpacked?
Gemini-1.5 Pro:
Reasoning: We need to find out how many times 179 fits into 743, which is the same as finding the quotient of 743 divided by 179. 743 divided by 179 is 4 with a remainder. To find the remainder, we can multiply 179 by 4 (which equals 716) and then subtract that from 743: 743 - 716 = 27 This means 4 cartons can be filled completely, and 27 socks will be left unpacked. ### Answer: 27
Expected answer: 27
Correct? Yes
Problem: A total of 923 children want to slide down a slide at an amusement park. If 771 children can go down the slide without rest, how many children will be left waiting for their turn?
Gemini-1.5 Pro:
Reasoning: 923-771 = <<923-771=152>>152 children will be left waiting. ### Answer: 152
Expected answer: 152
Correct? Yes
Problem: After the first 771 children go down the slide, another wave of children arrives and now there are 923 children in total waiting again. If 881 children can go down the slide without any break this time, how many children will be left waiting for their turn?
Gemini-1.5 Pro:
Reasoning: 923 - 881 = <<923-881=42>>42 children will be left waiting. ### Answer: 42
Expected answer: 42
Correct? Yes
Problem: Superhero Iron Punch has to save 442 people from a collapsing building. He can teleport a maximum of 104 people at a time to safety. After teleporting as many full groups as he can, how many people will be left in the building for his last round of rescue?
Gemini-1.5 Pro:
Reasoning: Iron Punch can teleport 442/104 = <<442/104=4.25>>4 full groups of people to safety. This means he saves 4*104 = <<4*104=416>>416 people in his first four trips. Therefore, there will be 442-416 = <<442-416=26>>26 people left for his last rescue. ### Answer: 26
Expected answer: 26
Correct? Yes
Problem: What if there were actually 512 people in the collapsing building instead of 442? After Superhero Iron Punch teleports as many full groups of 104 people as he can to safety, how many people will be left in the building for his last round of rescue now?
Gemini-1.5 Pro:
Reasoning: With 512 people, Iron Punch can teleport 512/104 = <<512/104=4.92>>4 full groups of people to safety. This means he saves 4*104 = <<4*104=416>>416 people in his first four trips. Therefore, there will be 512-416 = <<512-416=96>>96 people left for his last rescue. ### Answer: 96
Expected answer: 96
Correct? Yes
Problem: A card game manufacturer creates a deck of cards with 569 cards. Each card pack has 68 cards. After creating as many packs as possible, how many cards will the manufacturer have left over?
Gemini-1.5 Pro:
Reasoning: To find the number of cards left over, we'll use the concept of remainders. Divide the total number of cards by the number of cards per pack: 569 ÷ 68 = 8 with a remainder of 25. ### Answer: 25
Expected answer: 25
Correct? Yes
Problem: After realizing the popularity of the game, the card manufacturer decides to produce another deck of cards, this time with 205 cards. Once again, each card pack can hold 68 cards. After creating as many full packs as possible, how many cards will the manufacturer have left over this time around?
Gemini-1.5 Pro:
Reasoning: We'll divide the total number of cards in the new deck by the number of cards per pack: 205 ÷ 68 = 3 with a remainder of 1. ### Answer: 1
Expected answer: 1
Correct? Yes
Problem: A stationery store received a shipment of 842 erasers. The store owner wants to display them in boxes, with each box containing 719 erasers. After filling as many boxes as possible, how many erasers will be left over?
Gemini-1.5 Pro:
Reasoning: To find out how many boxes can be filled, we perform the division: 842 erasers / 719 erasers/box = <<842/719=1.17107090403338>>1.17 boxes. This means the store owner can completely fill 1 box. To find the number of leftover erasers, we multiply the decimal part of the result above by the number of erasers per box: 0.17107090403338 * 719 erasers/box ≈ <<0.17107090403338*719= 123>> 123 erasers. ### Answer: 123
Expected answer: 123
Correct? Yes
Problem: Suppose the stationery store owner later decided to display the erasers in smaller boxes, with each box containing 420 erasers instead. After filling as many boxes as possible, how many erasers will be left over now?
Gemini-1.5 Pro:
Reasoning: We can use the same process as before. Dividing the total erasers by the new number of erasers per box: 842 erasers / 420 erasers/box = <<842/420=2.004761904761905>> 2.004761904761905 boxes. The store owner can now completely fill 2 boxes. Multiplying the decimal part of the result by the new number of erasers per box, we find the number of leftover erasers: 0.004761904761905 * 420 erasers/box ≈ <<0.004761904761905*420=2>> 2 erasers. ### Answer: 2
Expected answer: 2
Correct? Yes
Problem: A farmer harvested 461 carrots from his garden. He packs them into boxes, each box can hold up to 244 carrots. After packing as many full boxes as possible, how many carrots will be left unpacked?
Gemini-1.5 Pro:
Reasoning: The farmer can pack 461 / 244 = <<461/244=1>>1 full box of carrots. That leaves 461 - 244 = <<461-244=217>>217 carrots unpacked. ### Answer: 217
Expected answer: 217
Correct? Yes
Problem: The farmer found out that he had initially miscounted and he actually only harvested 11 carrots. After he tries to pack these into the boxes which each can hold up to 244 carrots, how many carrots will be left unpacked now?
Gemini-1.5 Pro:
Reasoning: Since the farmer only has 11 carrots, which is less than the capacity of a single box, he won't be able to fill any boxes. Therefore, all 11 carrots will be left unpacked. ### Answer: 11
Expected answer: 11
Correct? Yes
Problem: A penguin scientist counts 309 penguins in a colony. She decides to tag them in groups of 293 for easier tracking. How many penguins will be in the final, possibly incomplete, group?
Gemini-1.5 Pro:
Reasoning: We need to find the remainder when 309 penguins are divided into groups of 293. This is the same as finding the remainder when 309 is divided by 293. 309 divided by 293 is 1 with a remainder of 16. ### Answer: 16
Expected answer: 16
Correct? Yes
Problem: The penguin scientist realizes she made a mistake and there were actually only 262 penguins in each group. How many penguins will be in the final, possibly incomplete, group now?
Gemini-1.5 Pro:
Reasoning: We need to find the remainder when 309 penguins are divided into groups of 262. This is the same as finding the remainder when 309 is divided by 262. 309 divided by 262 is 1 with a remainder of 47. ### Answer: 47
Expected answer: 47
Correct? Yes
Problem: A sandwich shop has 580 slices of bread. They use 18 slices of bread for each sandwich-making batch. After using up the bread in these batches, how many slices will they have left?
Gemini-1.5 Pro:
Reasoning: We calculate the total number of batches they can make: 580 slices / 18 slices/batch = <<580/18=32.22>>32.22 batches. Since they can't make a fraction of a batch, they can make 32 full batches. They use 32 batches * 18 slices/batch = <<32*18=576>> 576 slices of bread. They will have 580 slices - 576 slices = <<580-576=4>> 4 slices left. ### Answer: 4
Expected answer: 4
Correct? Yes
Problem: The sandwich shop's supplier delivered an additional batch of bread, bringing their total to 580 slices. If the shop still makes sandwiches using 477 slices of bread per batch, how many slices will they have left after the latest batch of sandwiches is made?
Gemini-1.5 Pro:
Reasoning: They can make 580 total slices / 477 slices/batch = <<580/477=1.2159>> 1.2159 batches. Since they can't make a fraction of a batch, they can only make 1 full batch. That batch will use 477 slices, leaving 580 slices - 477 slices = <<580-477=103>> 103 slices. ### Answer: 103
Expected answer: 103
Correct? Yes
Problem: A tailor has 925 meters of fabric. The tailor uses 529 meters of fabric to make each dress. If the tailor uses the fabric evenly for each dress, how many meters of fabric will be left over after completing the dresses?
Gemini-1.5 Pro:
Reasoning: The tailor can make 925/529 = <<925/529=1.75>>1.75 dresses. Since the tailor can only make whole dresses, this means the tailor can make 1 dress. The tailor will use 1*529 = <<1*529=529>>529 meters of fabric on the dress. The tailor will have 925-529 = <<925-529=396>>396 meters of fabric left over. ### Answer: 396
Expected answer: 396
Correct? Yes
Problem: After making some dresses, the tailor now only has 62 meters of fabric left. If the tailor continues to use 529 meters of fabric to make each dress, how many meters of fabric will be left over after making the dresses?
Gemini-1.5 Pro:
Reasoning: Since the tailor only has 62 meters of fabric left, which is less than the 529 meters needed to make a dress, the tailor cannot make any more dresses. ### Answer: 62
Expected answer: 62
Correct? Yes
Problem: There are 976 tourists wanting to explore a castle. Each tour group throughout the day accommodates up to 530 people. After all the groups have taken off, how many tourists will be left for the last group of the day?
Gemini-1.5 Pro:
Reasoning: We need to find the remainder when 976 tourists are divided into groups of 530. This is the same as finding the remainder of 976 divided by 530. 976 divided by 530 is 1 with a remainder of 446. ### Answer: 446
Expected answer: 446
Correct? Yes
Problem: What would happen if the number of tourists wanting to explore the castle was still 976, but this time each group could accommodate up to 726 people? How many tourists would be left for the last group of the day now?
Gemini-1.5 Pro:
Reasoning: With a larger group size, it's possible that all 976 tourists could fit in the first group, leaving no one for a second group. Let's check: * Since 726 (the group size) is larger than 976 (the number of tourists), all the tourists can fit in one group. * This means there would be no tourists left for a last group. ### Answer: 0
Expected answer: 250
Correct? No