InternLM-Math Base 7B on K.CC.C.7
Common Core Standard K.CC.C.7
This standard covers the following:
Compare two numbers between 1 and 10 presented as written numerals.
Problem: Fill in the blank with <, >, or = to compare the numbers in the following: 10 _ 7
InternLM-Math Base 7B:
Reasoning: 7+3=10. 7<10.
Expected answer: >
Correct? No
Problem: Compare the following numbers using <, >, or =. 10 _ 8
InternLM-Math Base 7B:
Reasoning: 10 = 8 ### Answer: 10=8
Expected answer: >
Correct? No
Problem: Determine the relationship between the numbers by filling in the blank with either <, >, or =. Here is your question: 3 _ 7
InternLM-Math Base 7B:
3 = 3 3 = 7 ### Answer: 3=3
Expected answer: <
Correct? No
Problem: In the following problem, fill in the blank with <, >, or = to make a correct statement: 4 _ 1
InternLM-Math Base 7B:
Reasoning: 4 < 1 ### Answer:
Expected answer: >
Correct? No
Problem: Complete the following statement by filling in the blank with <, >, or =. 8 _ 8
InternLM-Math Base 7B:
8 = 8
Expected answer: =
Correct? Yes
Problem: As a follow up to the previous question where you compared value of two identical numbers (8 _ 8), consider now the following: Fill in the blank with <, >, or = to compare two different numbers: 8 _ 7
InternLM-Math Base 7B:
8 > 7
Expected answer: >
Correct? Yes
Problem: In the following question, complete the comparison by filling in the blank with <, >, or =. 8 _ 8
InternLM-Math Base 7B:
Reasoning: 8 = 8 ### Answer: =
Expected answer: =
Correct? Yes
Problem: In a similar manner, consider this follow-up question: 8 _ 2 Complete the comparison by filling in the blank with <, >, or =.
InternLM-Math Base 7B:
Reasoning: 8 > 2 ### Answer: >
Expected answer: >
Correct? Yes
Problem: Compare the values of the following digits by filling in the blank with <, >, or =. 8 _ 4
InternLM-Math Base 7B:
Reasoning: 8 > 4 ### Answer: 8
Expected answer: >
Correct? Yes
Problem: Consider the previous problem where you compared the numbers 8 and 4. Now let's change the second number to 2. Fill in the blank with <, >, or = to compare the two numbers. 8 _ 2
InternLM-Math Base 7B:
Reasoning: 8 > 2 ### Answer: 8
Expected answer: >
Correct? Yes
Problem: Compare these two numbers by filling in the blank with one of these operators: <, >, or =. 8 _ 10
InternLM-Math Base 7B:
8 < 10
Expected answer: <
Correct? Yes
Problem: Following up on our previous comparison, now consider these two numbers and fill in the blank with one of these operators: <, >, or =. 4 _ 10 For instance, if in our previous question we were comparing the heights of two trees (8 feet and 10 feet respectively), this question would now be comparing a shrub of 4 feet to that same 10 feet tree. Which symbol would be appropriate now?
InternLM-Math Base 7B:
4 < 10
Expected answer: <
Correct? Yes
Problem: Fill in the blank with <, >, or = . 2 _ 1
InternLM-Math Base 7B:
2 > 1
Expected answer: >
Correct? Yes
Problem: Now, consider the following: 5 _ 1 How does this comparison change if we change the first number from 2 to 5? Fill in the blank with <, >, or =.
InternLM-Math Base 7B:
5 > 1
Expected answer: >
Correct? Yes
Problem: Fill in the blank in the following with the appropriate symbol (<, >, =): 9 _ 9
InternLM-Math Base 7B:
Reasoning: 9 9 = 9 9. 9 9 9 9. 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9
Expected answer: =
Correct? Yes
Problem: After comparing 9 _ 9 in the previous problem, let's change one number. Now compare the numbers in the following: 9 _ 2
InternLM-Math Base 7B:
Reasoning: 9 2 9 2 9 2 9 2 9 2 9 2 9 2 9 2 9 2 9 2 9 2 9 2 9 2 9 2 9 2 9 2 9 2 9 2 9 2 9 2 9 2 9 2 9 2 9 2 9 2 9 2 9 2 9 2 9 2 9 2 9 2 9 2 9 2 9 2 9 2 9 2 9 2 9 2 9 2 9 2 9 2 9 2 9 2 9 2 9 2 9 2 9 2 9 2 9 2 9 2 9 2 9 2 9 2 9 2 9 2 9 2 9 2 9 2 9 2 9 2 9 2 9 2 9 2 9 2 9 2 9 2 9 2 9 2 9 2 9 2 9 2 9 2 9 2 9 2 9 2 9 2 9 2 9 2 9 2 9 2 9 2 9 2 9 2 9 2 9 2 9 2 9 2 9 2 9 2 9 2 9 2 9 2 9 2 9 2 9 2 9 2 9 2 9 2 9 2 9 2 9 2 9 2 9 2 9 2 9 2 9 2 9 2 9 2 9 2 9 2 9 2 9 2 9 2 9 2 9 2 9 2 9 2 9 2 9 2 9 2 9 2 9 2 9 2 9 2 9 2 9 2 9 2 9 2 9 2 9 2 9 2 9 2 9 2 9 2 9 2 9 2 9 2 9 2 9 2 9 2 9 2 9 2 9 2 9 2 9 2 9 2 9 2 9 2 9 2 9 2 9 2 9 2 9 2 9 2 9 2 9 2 9 2 9 2 9 2 9 2 9 2 9 2 9 2 9 2 9 2 9 2 9 2 9 2 9 2 9 2 9 2 9 2 9 2 9 2 9 2 9 2 9 2 9 2 9 2 9 2 9 2 9 2 9 2 9 2 9 2 9 2 9 2 9 2 9 2 9 2 9 2 9 2 9 2 9 2 9 2 9 2 9 2 9 2 9 2 9 2 9 2 9 2 9 2 9 2 9 2 9 2 9 2 9 2 9 2 9 2 9 2 9 2 9 2 9 2 9 2 9 2 9 2 9 2 9 2 9 2 9 2 9 2 9 2 9 2 9 2 9 2 9 2 9 2 9 2 9 2 9 2 9 2 9 2 9 2 9 2 9 2 9 2 9 2 9 2 9 2 9 2 9 2 9 2 9 2 9 2 9 2 9 2 9 2 9 2
Expected answer: >
Correct? No
Problem: Compare the following numbers and fill in the blank with either <, >, or = to make a true statement: 2 _ 10
InternLM-Math Base 7B:
Reasoning: 2 < 10
Expected answer: <
Correct? Yes
Problem: Now, let's revise the last question. Instead of comparing 2 and 10, we are going to compare 2 and 9. Fill in the blank with either <, >, or = to make a true statement: 2 _ 9
InternLM-Math Base 7B:
Reasoning: 2 < 9
Expected answer: <
Correct? Yes
Problem: Fill in the blank with the correct element, <, >, or =, to compare the numbers in the phrase 7 _ 7
InternLM-Math Base 7B:
Reasoning: 7 = 7 ### Answer: =
Expected answer: =
Correct? Yes
Problem: Considering our previous example, if there were 7 cookies in one jar and 7 cookies in another jar, now suppose there are only 2 cookies in the second jar. Use the symbols <, >, or = to compare the number of cookies in the two jars. Fill in the following statement: 7 _ 2
InternLM-Math Base 7B:
|user|
Expected answer: >
Correct? No
Problem: Fill in the blank to compare these two numbers. Use either <, >, or =. 7 _ 8
InternLM-Math Base 7B:
Reasoning: 7 8 ### Answer: <
Expected answer: <
Correct? Yes
Problem: Earlier, you compared the numbers 7 and 8. Now, consider this change. Fill in the blank to compare these two numbers. Use either <, >, or =. 7 _ 5
InternLM-Math Base 7B:
Reasoning: 7 5 ### Answer: >
Expected answer: >
Correct? Yes
Problem: Please compare the following numbers by inserting the correct symbol (<, >, or =) 8 _ 6
InternLM-Math Base 7B:
8 > 6
Expected answer: >
Correct? Yes
Problem: Reconsider the previous comparison, but now compare the following: 8 _ 10 Insert the correct symbol (<, >, or =) to accurately compare the numbers.
InternLM-Math Base 7B:
8 = 8
Expected answer: <
Correct? No
Problem: Compare the values of the following numbers by filling in the blank with <, >, or =. 2 _ 9
InternLM-Math Base 7B:
Reasoning: 2 < 9 ### Answer: <
Expected answer: <
Correct? Yes
Problem: Recall the previous problem where we compared the numbers 2 and 9. Now suppose you replace the number 9 with the number 4. What would the comparison look like now? Fill in the blank with <, >, or =. 2 _ 4
InternLM-Math Base 7B:
Reasoning: 2 = 2 2 < 4 ### Answer: <
Expected answer: <
Correct? Yes
Problem: Fill in the blank in the statement below with <, >, or = to compare the two numbers. 3 _ 4
InternLM-Math Base 7B:
Reasoning: 3 <<3<4>> 4
Expected answer: <
Correct? Yes
Problem: Continuing from the previous comparison, now consider two new numbers: 3 _ 8 Fill in the blank with <, >, or = to complete the comparison. For example, if previously you were comparing the heights of two trees, consider this comparison for a scenario where the first tree is now shorter, standing at 3 meters instead of 4. How does this change your comparison?
InternLM-Math Base 7B:
Reasoning: 3 <<3<8>> 8
Expected answer: <
Correct? Yes
Problem: Compare the following two numbers by filling in the blank with <, >, or =: 3 _ 7
InternLM-Math Base 7B:
Reasoning: 3 <<3<7>>7 ### Answer: <
Expected answer: <
Correct? Yes
Problem: Suppose we now change the numbers in the previous question. Fill in the blank with <, >, or = : 1 _ 7 If the previous question involved comparing 3 apples and 7 oranges, consider this as a follow-up question contemplating what would happen if there were originally only 1 apple instead of 3.
InternLM-Math Base 7B:
Reasoning: 1 <<1<7>>7 ### Answer: <
Expected answer: <
Correct? Yes
Problem: Compare these numbers by filling in the blank with the appropriate symbol (<, >, or =): 2 _ 2
InternLM-Math Base 7B:
2 = 2. The number 2 is not less than 2. The number 2 is not greater than 2. The number 2 is equal to 2.
Expected answer: =
Correct? Yes
Problem: Consider the following change to the previous numbers: 2 _ 5 If before we compared two identical numbers (2 and 2), now let's compare a smaller number with a larger one. Fill in the blank with the appropriate symbol: <, >, or =.
InternLM-Math Base 7B:
2 < 5. The number 2 is less than 5. The number 2 is not greater than 5. The number 2 is not equal to 5.
Expected answer: <
Correct? Yes
Problem: Compare the numbers by filling in the blank with either <, >, or =. 2 _ 10
InternLM-Math Base 7B:
Reasoning: 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2
Expected answer: <
Correct? Yes
Problem: Following the previous comparison, let's consider another one. If in the last problem, 2 represented the number of apples you saw and 10 represented the number of oranges, suppose now the scenario changes. You now observe that the number of apples is the same as the number of oranges. How would you compare these two quantities? Write it in this form: 10 _ 10
InternLM-Math Base 7B:
Reasoning: 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10
Expected answer: =
Correct? No
Problem: Compare these numbers by putting an appropriate symbol (<, >, or =) in the blank: 1 _ 1
InternLM-Math Base 7B:
Reasoning: 1 = 1 ### Answer: =
Expected answer: =
Correct? Yes
Problem: In the previous problem, you compared the numbers 1 and 1. Now, adjust your thinking and compare the numbers 7 and 1. Fill in the gap with the correct symbol (<, >, or =): 7 _ 1
InternLM-Math Base 7B:
Reasoning: 7 > 1 ### Answer: >
Expected answer: >
Correct? Yes
Problem: Complete the following task by choosing the correct comparison symbol (<, >, =): 3 _ 4
InternLM-Math Base 7B:
Reasoning: 3 = <<3=3>>3 3 = 4 ### Answer: <
Expected answer: <
Correct? Yes
Problem: Consider the following situation: In the previous problem, we compared 3 with 4. Now, let's consider a different scenario. How would your answer change if instead of comparing 3 with 4, we compared 3 with itself? So, your task is to fill in the blank with the appropriate symbol (<, >, =): 3 _ 3
InternLM-Math Base 7B:
Reasoning: 3 = <<3=3>>3 3 = 3 ### Answer: =
Expected answer: =
Correct? Yes
Problem: Fill in the blank with one of the following symbols: <, >, or = . 2 _ 10
InternLM-Math Base 7B:
2 < 10
Expected answer: <
Correct? Yes
Problem: Now consider this scenario: Instead of 2, we now have 4. Fill in the blank with one of the following symbols: <, >, or =. 4 _ 10
InternLM-Math Base 7B:
4 < 10
Expected answer: <
Correct? Yes
Problem: Fill in the blank in the following equation with one of the symbols "<", ">", "=" : 3 _ 5 Which expression is correct?
InternLM-Math Base 7B:
Reasoning: 3 < 5 ### Answer: 3<5
Expected answer: <
Correct? Yes
Problem: Using the same concept of comparing numbers, consider this situation: In the previous scenario, we compared 3 objects to 5 objects. Now, let's change it up. We have 3 dollars and 2 dollars. Fill in the blank in the following equation with one of the symbols "<", ">", "=" : 3 _ 2 Which expression is correct?
InternLM-Math Base 7B:
Reasoning: 3 > 2 ### Answer: 3>2
Expected answer: >
Correct? Yes
Problem: Compare the values of the following numbers by filling in the blank with <, >, or =. 6 _ 10
InternLM-Math Base 7B:
6 = 3 + 3. 10 = 3 + 3 + 4. 3 < 4. 6 < 10.
Expected answer: <
Correct? Yes
Problem: Following the previous problem, now consider the situation where there are 9 tickets for a concert instead of 6. Fill in the blank with <, >, or = to compare this to the total of 10 tickets originally available. 9 _ 10
InternLM-Math Base 7B:
9 = 3 + 3 + 3. 10 = 3 + 3 + 4. 3 < 4. 9 < 10.
Expected answer: <
Correct? Yes
Problem: In the equation below, compare the values of the numbers by filling in the blank with the appropriate symbol (<, >, or =). 8 _ 7
InternLM-Math Base 7B:
8 is __ 7.
Expected answer: >
Correct? No
Problem: Complete the following by choosing from <, >, or =: 7 _ 3
InternLM-Math Base 7B:
7 3 7>3
Expected answer: >
Correct? Yes
Problem: Consider the same scenario as previously mentioned, but this time compare the following numbers instead: 7 _ 2
InternLM-Math Base 7B:
7 2 7>2
Expected answer: >
Correct? Yes
Problem: Consider the following mathematical comparison. Determine whether 3 is less than, equal to, or greater than 9 by filling in the blank with the correct symbol (<, =, >) : 3 _ 9
InternLM-Math Base 7B:
Reasoning: 9 is greater than 3. 9 is 6 more than 3. 9 is <<9>3>>3.
Expected answer: <
Correct? Yes
Problem: Following from the previous question where we compared 3 and 9. Now, adjust the comparison to the new numbers. Determine whether 3 is less than, equal to, or greater than 4 by filling in the blank with the correct symbol (<, =, >): 3 _ 4
InternLM-Math Base 7B:
Reasoning: 4 is greater than 3. 4 is 1 more than 3. 4 is <<4>3>>3.
Expected answer: <
Correct? Yes
Problem: Complete the following comparison between the numbers by using <, >, or =: 7 _ 4
InternLM-Math Base 7B:
Reasoning: 7 is not equal to 4. 7 is greater than 4. So 7 is __ 4.
Expected answer: >
Correct? Yes
Problem: Following up on the previous question comparing 7 and 4, now compare the following two numbers using the symbols <, > or =: 6 _ 4
InternLM-Math Base 7B:
Reasoning: 6 is not equal to 4. 6 is greater than 4. So 6 is __ 4.
Expected answer: >
Correct? Yes
Problem: Fill in the blank with the right symbol (>, <, =) to correctly compare these two numbers: 2 _ 7
InternLM-Math Base 7B:
Reasoning: 2 7 7 2 2 7 2 7 2 7 2 7 2 7 2 7 2 7 2 7 2 7 2 7 2 7 2 7 2 7 2 7 2 7 2 7 2 7 2 7 2 7 2 7 2 7 2 7 2 7 2 7 2 7 2 7 2 7 2 7 2 7 2 7 2 7 2 7 2 7 2 7 2 7 2 7 2 7 2 7 2 7 2 7 2 7 2 7 2 7 2 7 2 7 2 7 2 7 2 7 2 7 2 7 2 7 2 7 2 7 2 7 2 7 2 7 2 7 2 7 2 7 2 7 2 7 2 7 2 7 2 7 2 7 2 7 2 7 2 7 2 7 2 7 2 7 2 7 2 7 2 7 2 7 2 7 2 7 2 7 2 7 2 7 2 7 2 7 2 7 2 7 2 7 2 7 2 7 2 7 2 7 2 7 2 7 2 7 2 7 2 7 2 7 2 7 2 7 2 7 2 7 2 7 2 7 2 7 2 7 2 7 2 7 2 7 2 7 2 7 2 7 2 7 2 7 2 7 2 7 2 7 2 7 2 7 2 7 2 7 2 7 2 7 2 7 2 7 2 7 2 7 2 7 2 7 2 7 2 7 2 7 2 7 2 7 2 7 2 7 2 7 2 7 2 7 2 7 2 7 2 7 2 7 2 7 2 7 2 7 2 7 2 7 2 7 2 7 2 7 2 7 2 7 2 7 2 7 2 7 2 7 2 7 2 7 2 7 2 7 2 7 2 7 2 7 2 7 2 7 2 7 2 7 2 7 2 7 2 7 2 7 2 7 2 7 2 7 2 7 2 7 2 7 2 7 2 7 2 7 2 7 2 7 2 7 2 7 2 7 2 7 2 7 2 7 2 7 2 7 2 7 2 7 2 7 2 7 2 7 2 7 2 7 2 7 2 7 2 7 2 7 2 7 2 7 2 7 2 7 2 7 2 7 2 7 2 7 2 7 2 7 2 7 2 7 2 7 2 7 2 7 2 7 2 7 2 7 2 7 2 7 2 7 2 7 2 7 2 7 2 7 2 7 2 7 2 7 2 7 2 7 2 7 2 7 2 7 2 7 2 7 2 7 2 7 2 7 2 7 2 7 2 7 2 7 2 7 2 7 2 7 2 7 2 7 2 7
Expected answer: <
Correct? Yes
Problem: Following up on our previous question, let's consider a different set of numbers. Use the correct symbol (>, <, =) to compare these two numbers: 2 _ 8
InternLM-Math Base 7B:
Reasoning: 2 8 8 2 2 8 2 8 2 8 2 8 2 8 2 8 2 8 2 8 2 8 2 8 2 8 2 8 2 8 2 8 2 8 2 8 2 8 2 8 2 8 2 8 2 8 2 8 2 8 2 8 2 8 2 8 2 8 2 8 2 8 2 8 2 8 2 8 2 8 2 8 2 8 2 8 2 8 2 8 2 8 2 8 2 8 2 8 2 8 2 8 2 8 2 8 2 8 2 8 2 8 2 8 2 8 2 8 2 8 2 8 2 8 2 8 2 8 2 8 2 8 2 8 2 8 2 8 2 8 2 8 2 8 2 8 2 8 2 8 2 8 2 8 2 8 2 8 2 8 2 8 2 8 2 8 2 8 2 8 2 8 2 8 2 8 2 8 2 8 2 8 2 8 2 8 2 8 2 8 2 8 2 8 2 8 2 8 2 8 2 8 2 8 2 8 2 8 2 8 2 8 2 8 2 8 2 8 2 8 2 8 2 8 2 8 2 8 2 8 2 8 2 8 2 8 2 8 2 8 2 8 2 8 2 8 2 8 2 8 2 8 2 8 2 8 2 8 2 8 2 8 2 8 2 8 2 8 2 8 2 8 2 8 2 8 2 8 2 8 2 8 2 8 2 8 2 8 2 8 2 8 2 8 2 8 2 8 2 8 2 8 2 8 2 8 2 8 2 8 2 8 2 8 2 8 2 8 2 8 2 8 2 8 2 8 2 8 2 8 2 8 2 8 2 8 2 8 2 8 2 8 2 8 2 8 2 8 2 8 2 8 2 8 2 8 2 8 2 8 2 8 2 8 2 8 2 8 2 8 2 8 2 8 2 8 2 8 2 8 2 8 2 8 2 8 2 8 2 8 2 8 2 8 2 8 2 8 2 8 2 8 2 8 2 8 2 8 2 8 2 8 2 8 2 8 2 8 2 8 2 8 2 8 2 8 2 8 2 8 2 8 2 8 2 8 2 8 2 8 2 8 2 8 2 8 2 8 2 8 2 8 2 8 2 8 2 8 2 8 2 8 2 8 2 8 2 8 2 8 2 8 2 8 2 8 2 8 2 8 2 8 2 8 2 8 2 8 2 8 2 8 2 8 2 8 2 8 2 8 2 8 2 8 2 8 2 8
Expected answer: <
Correct? Yes
Problem: Please complete the following comparison. 7 _ 8 Fill in the blank with one of these symbols: <, >, =.
InternLM-Math Base 7B:
Reasoning: 7 8 7 is less than 8, so 7 < 8.
Expected answer: <
Correct? Yes
Problem: Let's consider a variation of the previous problem. This time, compare: 7 _ 2 Again, fill in the blank with one of these symbols: <, >, =. Think about how this is similar to, and different from, the previous comparison between 7 and 8.
InternLM-Math Base 7B:
Reasoning: 7 2 7 is greater than 2, so 7 > 2.
Expected answer: >
Correct? Yes
Problem: Compare the values of the following two numbers by filling in the blank with either <, >, or =. 9 _ 7
InternLM-Math Base 7B:
Reasoning: 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9
Expected answer: >
Correct? No
Problem: Consider the following two numbers: 8 _ 5 Compare the two numbers by filling in the blank with <, >, or =.
InternLM-Math Base 7B:
Reasoning: 8_5 = <<8_5=13>>13 8_5 = 8_5 ### Answer: =
Expected answer: >
Correct? No
Problem: Compare the following numbers by filling in the blank with either <, >, or =: 2 _ 5
InternLM-Math Base 7B:
Reasoning: 2 <<2>5>>5 ### Answer: 2>5
Expected answer: <
Correct? No
Problem: Fill in the blank in the following comparison with either a <, >, or =. 10 _ 3
InternLM-Math Base 7B:
Reasoning: 10>3.
Expected answer: >
Correct? Yes
Problem: In the last question, you compared the numbers 10 and 3. Now, let's compare 10 to a different number. Fill in the blank to make the comparison accurate: 10 _ 6
InternLM-Math Base 7B:
Reasoning: 10>6.
Expected answer: >
Correct? Yes
Problem: Place the correct symbol in the blank to compare these two numbers. 7 _ 9 Is it a <, >, or = ?
InternLM-Math Base 7B:
Reasoning: 7<9, so the correct symbol is <. ### Answer: <
Expected answer: <
Correct? Yes
Problem: Building on the previous question, consider this scenario: Instead of having 7 toys to compare, let's say a child only has 3 toys. Now compare this number with 9 using the appropriate symbol. So, complete this: 3 _ 9 with one of the symbols <, >, or =.
InternLM-Math Base 7B:
Reasoning: 3<9, so the correct symbol is <. ### Answer: <
Expected answer: <
Correct? Yes
Problem: Complete the following problem using <, >, or =: 6 _ 10
InternLM-Math Base 7B:
You are correct.
Expected answer: <
Correct? No
Problem: Complete the comparison between the two numbers by filling in the missing symbol: less than (<), greater than (>), or equals (=). 7 _ 10
InternLM-Math Base 7B:
7 is <<7<10>>less than 10.
Expected answer: <
Correct? Yes
Problem: Let's consider a modification to the previous question. Instead of comparing 7 and 10, now compare these two numbers: 1 _ 10 Remember, you should fill in the blank with either a lower than (<), greater than (>), or equals (=) to complete the comparison.
InternLM-Math Base 7B:
1 is <<1<10>>less than 10.
Expected answer: <
Correct? Yes
Problem: Check the following statement and complete it with the correct sign (<, >, or =): 3 _ 9
InternLM-Math Base 7B:
3 < 9
Expected answer: <
Correct? Yes
Problem: Let's consider a new pair of numbers. Again, complete the comparison by filling in the appropriate symbol (<, >, or =): 3 _ 10
InternLM-Math Base 7B:
3 < 10
Expected answer: <
Correct? Yes
Problem: Compare the following numbers by filling in the blank with <, >, or =. 5 _ 2
InternLM-Math Base 7B:
Reasoning: 5 > 2 5 is greater than 2.
Expected answer: >
Correct? Yes
Problem: Given the change from the previous problem, now compare the following numbers by filling in the blank with <, >, or =. 5 _ 4 Does the sign change when the number changes from 2 to 4?
InternLM-Math Base 7B:
Reasoning: 5 > 4 5 is greater than 4.
Expected answer: >
Correct? Yes
Problem: Compare the values of the following numbers by inserting the appropriate sign (<, >, or =) in the blank: 5 _ 2
InternLM-Math Base 7B:
Reasoning: 2 < 5 ### Answer:
Expected answer: >
Correct? No
Problem: Compare the values of the following numbers by filling in the blank with <, >, or =. 9 _ 1
InternLM-Math Base 7B:
9>1
Expected answer: >
Correct? Yes
Problem: Continuing from the previous comparison problem where we compared 9 and 1, let's consider a new scenario. Now instead of considering a value of 9, we are considering a value of 3. Please fill in the blank with <, >, or = in the following: 3 _ 1
InternLM-Math Base 7B:
3>1
Expected answer: >
Correct? Yes
Problem: Determine the relationship between the following numbers: 7 _ 5 Fill in the blank space with one of the following symbols: <, > or =.
InternLM-Math Base 7B:
Reasoning: 7 5 7 5 ### Answer:
Expected answer: >
Correct? No
Problem: Fill in the blank with one of these symbols: <, >, or =. 2 _ 8. Compare these two numbers based on their values.
InternLM-Math Base 7B:
Reasoning: 2 < 8. The value of 2 is less than the value of 8. ### Answer: <
Expected answer: <
Correct? Yes
Problem: Imagine using the same two numbers instead of different numbers in the previous problem. Now consider this: 2 _ 2 Fill in the blank with one of these symbols: <, >, or =. Compare these two numbers based on their values.
InternLM-Math Base 7B:
Reasoning: 2 = 2. The value of 2 is equal to the value of 2. ### Answer: =
Expected answer: =
Correct? Yes
Problem: Fill in the blank in the question 6 _ 7 with either a <, >, or = to compare the two numbers.
InternLM-Math Base 7B:
6 7
Expected answer: <
Correct? No
Problem: Compare the values of the following numbers by filling in the blank with either <, >, or =. 2 _ 8
InternLM-Math Base 7B:
2 = 8
Expected answer: <
Correct? No
Problem: Fill in the blank in the following equation to compare the values of the numbers: 6 _ 6
InternLM-Math Base 7B:
Reasoning: 6 _ 6 6-6 = 0 ### Answer: 0
Expected answer: =
Correct? No
Problem: Fill in the blank with <, >, or = to compare the numbers in the following: 8 _ 7
InternLM-Math Base 7B:
Reasoning: 8 7 ### Answer: >
Expected answer: >
Correct? Yes
Problem: In a follow-up to the previous question, consider the same comparison but with different numbers. Fill in the blank with <, >, or = to complete the comparison: 8 _ 2
InternLM-Math Base 7B:
Reasoning: 8 2 ### Answer: >
Expected answer: >
Correct? Yes
Problem: Compare the values of the following numbers by filling in the blank with <, >, or =. 1 _ 8
InternLM-Math Base 7B:
1 < 8
Expected answer: <
Correct? Yes
Problem: Remember the previous comparison where you had to compare the numbers 1 and 8. Now consider a different set of numbers. Fill in the blank with <, >, or = to make the comparison accurate: 2 _ 8
InternLM-Math Base 7B:
2 < 8
Expected answer: <
Correct? Yes
Problem: Compare the values of the following numbers by filling in the blank with <, >, or =. 2 _ 6
InternLM-Math Base 7B:
Reasoning: 2 < 6 ### Answer: <
Expected answer: <
Correct? Yes
Problem: In our previous comparison, we compared 2 and 6. Now consider a new scenario: Compare the values of the following numbers by filling in the blank with <, >, or =. 2 _ 1
InternLM-Math Base 7B:
Reasoning: 1 < 2 ### Answer: <
Expected answer: >
Correct? No
Problem: Compare the values of the following numbers by supplying the appropriate symbol (<, >, or =) 9 _ 4
InternLM-Math Base 7B:
Reasoning: 9 > 4 ### Answer: 9 > 4
Expected answer: >
Correct? Yes
Problem: Consider the following situation: Now, instead of comparing 9 and 4 as in the previous exercise, you are asked to compare these two different numbers. Fill in the blank with the correct symbol (<, >, or =): 3 _ 4
InternLM-Math Base 7B:
Reasoning: 3 < 4 ### Answer: 3 < 4
Expected answer: <
Correct? Yes
Problem: Fill in the blank with <, >, or = to compare these two numbers: 9 _ 3
InternLM-Math Base 7B:
9>3
Expected answer: >
Correct? Yes
Problem: Consider the quantities from the last problem again. This time, let's compare different numbers. Fill in the blank with <, >, or = to compare these two numbers: 8 _ 3
InternLM-Math Base 7B:
8>3
Expected answer: >
Correct? Yes
Problem: Fill the blank in the following with <, >, or = to correctly compare the numbers. 4 _ 7
InternLM-Math Base 7B:
Reasoning: 4 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224 225 226 227 228 229 230 231 232 233 234 235 236 237 238 239 240 241 242 243 244 245 246 247 248 249 250 251 252 253 254 255 256 257 258 259 260 261 262 263 264 265 266 267 268 269 270 271 272 273 274 275 276 277 278 279 280 281 282 283 284 285 286 287 288 289 290 291 292 293 294 295 296 297 298 299 300 301 302 303 304 305 306 307 308 309 310 311 312 313 314 315 316 317 318 319 320 321 322 323 324 325 326 327 328 329 330 331 332 333 334 335 336 337 338 339 340 341 342 343 344 345 346 347 348 349 350 351 352 353 354 355 356 357 358 359 360 361 362 363 364 365 366 367 368 369 370 371 372 373 374 375 376 377 378 379 380 381 382 383 384 385 386 387 388 389 390 391 392 393 394 395 396 397 398 399 400 401 402 403 404 405 406 407 408 409 410 411 412 413 414 415 416 417 418 419 420 421 422 423 424 425 426 427 428 429 430 431 432 433 434 435 436 437 438 439 440 441 442 443 444 445 446 447 448 449 450 451 452 453 454 455 456 457 458 459 460 461 462 463 464 465 466 467 468 469 470 471 472 473 474 475 476 477 478 479 480 481 482 483 484 485 486 487 488 489 490 491 492 493 494 495 496 497 498 499 500
Expected answer: <
Correct? Yes
Problem: Consider the following scenario: In the previous question, we compared the numbers 4 and 7. Now let's change the second number. Compare the following two numbers again by filling the blank with <, > or = 4 _ 1
InternLM-Math Base 7B:
Reasoning: 4 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224 225 226 227 228 229 230 231 232 233 234 235 236 237 238 239 240 241 242 243 244 245 246 247 248 249 250 251 252 253 254 255 256 257 258 259 260 261 262 263 264 265 266 267 268 269 270 271 272 273 274 275 276 277 278 279 280 281 282 283 284 285 286 287 288 289 290 291 292 293 294 295 296 297 298 299 300 301 302 303 304 305 306 307 308 309 310 311 312 313 314 315 316 317 318 319 320 321 322 323 324 325 326 327 328 329 330 331 332 333 334 335 336 337 338 339 340 341 342 343 344 345 346 347 348 349 350 351 352 353 354 355 356 357 358 359 360 361 362 363 364 365 366 367 368 369 370 371 372 373 374 375 376 377 378 379 380 381 382 383 384 385 386 387 388 389 390 391 392 393 394 395 396 397 398 399 400 401 402 403 404 405 406 407 408 409 410 411 412 413 414 415 416 417 418 419 420 421 422 423 424 425 426 427 428 429 430 431 432 433 434 435 436 437 438 439 440 441 442 443 444 445 446 447 448 449 450 451 452 453 454 455 456 457 458 459 460 461 462 463 464 465 466 467 468 469 470 471 472 473 474 475 476 477 478 479 480 481 482 483 484 485 486 487 488 489 490 491 492 493 494 495 496 497 498 499 500
Expected answer: >
Correct? No
Problem: Fill in the blank with <, >, or = to compare the two numbers. Here is the problem: 10 _ 8
InternLM-Math Base 7B:
Reasoning: 8+2=10, so 8<10. ### Answer: <
Expected answer: >
Correct? No
Problem: Fill in the blank with <, >, or = to compare these two numbers: 1 _ 10
InternLM-Math Base 7B:
Reasoning: 1 < 10 ### Answer:
Expected answer: <
Correct? Yes
Problem: Considering the previous comparison between 1 and 10, let's now compare the following two numbers: 9 _ 10 Fill in the blank with <, >, or = to compare these numbers.
InternLM-Math Base 7B:
Reasoning: 9 < 10 ### Answer:
Expected answer: <
Correct? Yes
Problem: Complete the following expression with the appropriate symbol (<, >, or =): 8 _ 7
InternLM-Math Base 7B:
Reasoning: 8 is not equal to 7.
Expected answer: >
Correct? No
Problem: Compare the following numbers by placing <, >, or = in the blank space. 10 _ 3
InternLM-Math Base 7B:
3
Expected answer: >
Correct? No
Problem: Compare the values of the following numbers by filling in the blank with <, >, or =. 2 _ 7
InternLM-Math Base 7B:
2 < 7
Expected answer: <
Correct? Yes
Problem: Now, imagine if instead of 2, you had 10 items to start with. Compare that to the originally given 7 items by filling in the blank with <, >, or =. 10 _ 7
InternLM-Math Base 7B:
10 > 7
Expected answer: >
Correct? Yes
Problem: Determine how the values of the following numbers compare. Fill in the blank with <, >, or =: 3 _ 2
InternLM-Math Base 7B:
Reasoning: <<3>2>>3 is greater than 2. ### Answer: 3>2
Expected answer: >
Correct? Yes
Problem: Imagine you had 3 apples instead of 2 from the previous problem. With this change, how do the numbers compare now? Fill in the blank with <, >, or =. 3 _ 3
InternLM-Math Base 7B:
Reasoning: 3 = 3 ### Answer: 3=3
Expected answer: =
Correct? Yes
Problem: Fill in the blank in the following statement using <, >, or = to compare the two numbers: 10 _ 5
InternLM-Math Base 7B:
5
Expected answer: >
Correct? No
Problem: Compare the values of the two numbers by filling in the blank with <, >, or =. 3 _ 6
InternLM-Math Base 7B:
Reasoning: 3 <<3>6>>6 ### Answer: >
Expected answer: <
Correct? No
Problem: Fill in the blank in the following comparison with <, >, or =: 7 _ 2
InternLM-Math Base 7B:
Answer: 7>2
Expected answer: >
Correct? Yes
Problem: Consider the previous comparison between 7 and 2. How would the comparison change if we now compare 7 and 1 instead? Please fill in the blank with <, >, or =: 7 _ 1
InternLM-Math Base 7B:
Answer: 7>1
Expected answer: >
Correct? Yes
Problem: Compare the following pair of numbers by inserting <, >, or = in the gap. 5 _ 4
InternLM-Math Base 7B:
Reasoning: 5 is <<5>4>>more than 4. ### Answer: >
Expected answer: >
Correct? Yes
Problem: Remember the previous situation where we compared 5 and 4. Now, let's consider a situation where we only have 1 instead of 5. So, compare the following pair of numbers by inserting <, >, or = in the gap. 1 _ 4
InternLM-Math Base 7B:
Reasoning: 1 is <<1<4>>less than 4. ### Answer: <
Expected answer: <
Correct? Yes
Problem: Compare the numbers by filling in the blank with <, >, or =: 1 _ 3
InternLM-Math Base 7B:
Reasoning: 1 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3
Expected answer: <
Correct? Yes
Problem: Continuing from the previous exercise where you compared 1 and 3, modify the comparison. This time, compare the following numbers by filling in the blank with <, >, or =: 10 _ 3
InternLM-Math Base 7B:
Reasoning: 10 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3
Expected answer: >
Correct? No
Problem: Determine the relationship between the following two numbers by filling in the blank with <, >, or =. 7 _ 6
InternLM-Math Base 7B:
Reasoning: 7 6 ### Answer: 6
Expected answer: >
Correct? No
Problem: Compare the following numbers by placing <, > or = in the blank. 6 _ 3
InternLM-Math Base 7B:
Reasoning: 3<6. The correct sign is <.
Expected answer: >
Correct? No
Problem: Determine which symbol (<, >, or =) should be used to accurately compare these you numbers: 1 _ 7
InternLM-Math Base 7B:
Reasoning: 1 < 7 ### Answer:
Expected answer: <
Correct? Yes
Problem: Continuing from the previous problem, adjust the first number and now decide which symbol (<, >, or =) should be used to compare these two numbers: 6 _ 7
InternLM-Math Base 7B:
Reasoning: 6 < 7 ### Answer:
Expected answer: <
Correct? Yes
Problem: Fill in the blank in the following comparison: 8 _ 3 Use either <, >, or = to correctly compare the two numbers.
InternLM-Math Base 7B:
Reasoning: 8 3 8 3 8 3 8 3 8 3 8 3 8 3 8 3 8 3 8 3 8 3 8 3 8 3 8 3 8 3 8 3 8 3 8 3 8 3 8 3 8 3 8 3 8 3 8 3 8 3 8 3 8 3 8 3 8 3 8 3 8 3 8 3 8 3 8 3 8 3 8 3 8 3 8 3 8 3 8 3 8 3 8 3 8 3 8 3 8 3 8 3 8 3 8 3 8 3 8 3 8 3 8 3 8 3 8 3 8 3 8 3 8 3 8 3 8 3 8 3 8 3 8 3 8 3 8 3 8 3 8 3 8 3 8 3 8 3 8 3 8 3 8 3 8 3 8 3 8 3 8 3 8 3 8 3 8 3 8 3 8 3 8 3 8 3 8 3 8 3 8 3 8 3 8 3 8 3 8 3 8 3 8 3 8 3 8 3 8 3 8 3 8 3 8 3 8 3 8 3 8 3 8 3 8 3 8 3 8 3 8 3 8 3 8 3 8 3 8 3 8 3 8 3 8 3 8 3 8 3 8 3 8 3 8 3 8 3 8 3 8 3 8 3 8 3 8 3 8 3 8 3 8 3 8 3 8 3 8 3 8 3 8 3 8 3 8 3 8 3 8 3 8 3 8 3 8 3 8 3 8 3 8 3 8 3 8 3 8 3 8 3 8 3 8 3 8 3 8 3 8 3 8 3 8 3 8 3 8 3 8 3 8 3 8 3 8 3 8 3 8 3 8 3 8 3 8 3 8 3 8 3 8 3 8 3 8 3 8 3 8 3 8 3 8 3 8 3 8 3 8 3 8 3 8 3 8 3 8 3 8 3 8 3 8 3 8 3 8 3 8 3 8 3 8 3 8 3 8 3 8 3 8 3 8 3 8 3 8 3 8 3 8 3 8 3 8 3 8 3 8 3 8 3 8 3 8 3 8 3 8 3 8 3 8 3 8 3 8 3 8 3 8 3 8 3 8 3 8 3 8 3 8 3 8 3 8 3 8 3 8 3 8 3 8 3 8 3 8 3 8 3 8 3 8 3 8 3 8 3 8 3 8 3 8 3 8 3 8 3 8 3 8 3 8 3 8 3 8 3 8 3 8 3 8 3 8 3 8 3 8 3 8 3 8 3 8 3
Expected answer: >
Correct? No
Problem: Fill in the blank with <, >, or = to complete the comparison: 3 _ 7
InternLM-Math Base 7B:
Reasoning: 3 <<3<7>> 7, so the answer is "less than".
Expected answer: <
Correct? Yes
Problem: Consider the previous comparison where you compared 3 to 7. Now, instead of 3, let's use 5. Fill in the blank with <, >, or = to complete the new comparison: 5 _ 7
InternLM-Math Base 7B:
Reasoning: 5 <<5>7>> 7, so the answer is "greater than".
Expected answer: <
Correct? Yes
Problem: Compare the numerical values in the next question and fill in the blank with <, >, or =. 9 _ 1
InternLM-Math Base 7B:
9>1.
Expected answer: >
Correct? Yes
Problem: Consider the previous comparison of numbers, 9 and 1. Now, instead of 1, consider another 9. Make the comparison again by filling in the blank with <, >, or =. 9 _ 9
InternLM-Math Base 7B:
9=9.
Expected answer: =
Correct? Yes
Problem: In the following math problem, compare two numbers and fill in the blank with either <, > or =. 5 _ 1
InternLM-Math Base 7B:
1. 5 is <<5>1?>> greater than 1.
Expected answer: >
Correct? Yes
Problem: Earlier, we compared 5 and 1. Now, consider this comparison instead: 9 _ 1 Using the symbols <, >, or =, determine the relationship between these two numbers.
InternLM-Math Base 7B:
9 is <<9>1?>> greater than 1.
Expected answer: >
Correct? Yes
Problem: Compare the following numbers by filling in the blank with <, >, or =. 4 _ 8
InternLM-Math Base 7B:
8 is greater than 4.
Expected answer: <
Correct? No
Problem: Fill in the blank with one of the following signs: <, >, = to compare the two numbers: 4 _ 10
InternLM-Math Base 7B:
Reasoning: 4 < 10 ### Answer: <
Expected answer: <
Correct? Yes
Problem: As a follow up to the previous comparison, let's consider another pair of numbers. Fill the blank with one of the following signs: <, >, = to compare these two numbers: 4 _ 2
InternLM-Math Base 7B:
Reasoning: 2 < 4 ### Answer: <
Expected answer: >
Correct? No
Problem: Compare the following numbers by filling in the blank with <, >, or =: 5 _ 5
InternLM-Math Base 7B:
Reasoning: 5 = 5 ### Answer: =
Expected answer: =
Correct? Yes
Problem: Now consider the following comparison: 5 _ 10 Just as before, fill in the blank with <, >, or =. This time, think about how your conclusion would change if you compared 5 to 10 instead of comparing 5 to 5.
InternLM-Math Base 7B:
Reasoning: 5 < 10 ### Answer: <
Expected answer: <
Correct? Yes
Problem: Compare the following two numbers by filling in the blank with either <, >, or =. 4 _ 8
InternLM-Math Base 7B:
Reasoning: 4 8 ### Answer: 4<8
Expected answer: <
Correct? Yes
Problem: Considering the earlier problem where you compared 4 and 8, now let's compare a new set of numbers. Fill in the blank in the following problem statement with <, >, or =: 6 _ 8
InternLM-Math Base 7B:
Reasoning: 6 8 ### Answer: 6<8
Expected answer: <
Correct? Yes
Problem: Fill in the blank to compare the two numbers: 8 _ 3 You can use <, >, or =.
InternLM-Math Base 7B:
8 3 8 is _____ 3. 8 3 8 is <<8 3 8 is 8>>greater than 3.
Expected answer: >
Correct? Yes
Problem: Consider the following: Instead of 8, you now only have 2 items. Fill in the blank to compare the two quantities: 2 _ 3 You can use <, >, or =.
InternLM-Math Base 7B:
2 3 2 is _____ 3. 2 3 2 is <<2 3 2 is 3>>less than 3.
Expected answer: <
Correct? Yes
Problem: Compare the following numbers by filling in the blank with <, >, or =. 1 _ 5
InternLM-Math Base 7B:
Reasoning: 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
Expected answer: <
Correct? No
Problem: Fill in the operation in the expression 4 _ 5 Choose from the operations <, >, or = to compare these two numbers accurately.
InternLM-Math Base 7B:
Reasoning: 4 _ 5 4 = 5 ### Answer: =
Expected answer: <
Correct? No
Problem: Compare the following two numbers by filling in the blank with <, >, or =. 7 _ 8
InternLM-Math Base 7B:
Reasoning: 8 is greater than 7.
Expected answer: <
Correct? No
Problem: Compare the following two numbers by putting either <, >, or = in between: 3 _ 5
InternLM-Math Base 7B:
Reasoning: 3 < 5 ### Answer: <
Expected answer: <
Correct? Yes
Problem: Consider the same scenario as before, but now the number has changed. Compare the following two numbers by putting either <, >, or = in between: 3 _ 6
InternLM-Math Base 7B:
Reasoning: 3 < 6 ### Answer: <
Expected answer: <
Correct? Yes
Problem: Determine whether 10 is less than, greater than, or equal to 4. Use the symbols <, >, or = to fill in the blank: 10 _ 4
InternLM-Math Base 7B:
Reasoning: 10 is a <<10>4>>4. ### Answer: >
Expected answer: >
Correct? Yes
Problem: In continuation to the previous problem where you compared 10 with 4, now determine whether 10 is less than, greater than, or equal to 6. Use the symbols <, >, or = to fill in the blank: 10 _ 6
InternLM-Math Base 7B:
Reasoning: 10 is a <<10>6>>6. ### Answer: >
Expected answer: >
Correct? Yes
Problem: Decide whether the following inequality is true or false by filling in the blank space with <, >, or =. 9 _ 6
InternLM-Math Base 7B:
Reasoning: 9 is <<9>6>>6.
Expected answer: >
Correct? No
Problem: Fill in the blank with <, >, or = to compare the numbers: 1 _ 7
InternLM-Math Base 7B:
Reasoning: 1 <<1>7>>7 ### Answer: 1>7
Expected answer: <
Correct? No
Problem: Fill in the blank with '<', '>', or '=' to make a correct comparison between these two numbers: 9 _ 5
InternLM-Math Base 7B:
Reasoning: 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9
Expected answer: >
Correct? No
Problem: Determine the relationship between the two numbers by filling in the blank with <, >, or =. 10 _ 2
InternLM-Math Base 7B:
Reasoning: 10 is 8 more than 2. 10 is 8 more than 2, so 10 is <<10 2>>more than 2.
Expected answer: >
Correct? Yes
Problem: Consider the same scenario as before but this time compare these two numbers. 10 _ 6
InternLM-Math Base 7B:
Reasoning: 10 is 4 more than 6. 10 is 4 more than 6, so 10 is <<10 6>>more than 6.
Expected answer: >
Correct? Yes
Problem: Determine which symbol to place between the following two numbers to accurately compare them: 3 _ 8 The symbol can either be <, >, or =.
InternLM-Math Base 7B:
Reasoning: 8 is greater than 3, so 8 is the greater number. The correct symbol to place between 3 and 8 is <.
Expected answer: <
Correct? Yes
Problem: Determine which symbol to place between the following two numbers to accurately compare them: 9 _ 8 The symbol can either be <, >, or =. Recall the previous question where we were comparing 3 and 8. Now consider what happens if the first number changes to 9 instead of 3. How would you compare 9 and 8?
InternLM-Math Base 7B:
Reasoning: 8 is less than 9, so 9 is the greater number. The correct symbol to place between 9 and 8 is >.
Expected answer: >
Correct? Yes
Problem: Compare the following numbers: 3 _ 8 Fill in the blank with either <, >, or =.
InternLM-Math Base 7B:
Reasoning: 3 < 8. ### Answer: <
Expected answer: <
Correct? Yes
Problem: Continuing from the previous question where you compared 3 and 8, now let's consider a slight change. Compare the following numbers: 3 _ 4 Fill in the blank with either <, >, or =. What changes when 8 is replaced by 4?
InternLM-Math Base 7B:
Reasoning: 3 < 4. ### Answer: <
Expected answer: <
Correct? Yes
Problem: Compare the values of the following numbers by filling in the blank with <, >, or =. 6 _ 1
InternLM-Math Base 7B:
Reasoning: 6 _ 1 6 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
Expected answer: >
Correct? No
Problem: In the following comparison, fill in the blank with either <, >, or =: 10 _ 2
InternLM-Math Base 7B:
Reasoning: 10>2 ### Answer:
Expected answer: >
Correct? Yes
Problem: Consider the same comparison as before, but this time replace the number 2 with 1. What would the comparison be between 10 _ 1? Fill in the blank with either <, >, or =.
InternLM-Math Base 7B:
Reasoning: 10>1 ### Answer:
Expected answer: >
Correct? Yes
Problem: Compare the following numbers by filling in the blank with <, >, or =: 5 _ 1
InternLM-Math Base 7B:
Reasoning: 5 > 1 5 is to the right of 1 on the number line, so 5 > 1.
Expected answer: >
Correct? Yes
Problem: Now consider a similar comparison, but this time with different numbers 10 _ 1 How does this comparison change compared to the previous comparison (5 _ 1)? Fill in the blank with <, >, or = to complete the comparison.
InternLM-Math Base 7B:
Reasoning: 10 > 1 10 is to the right of 1 on the number line, so 10 > 1.
Expected answer: >
Correct? Yes
Problem: Fill in the blank in the following question with either <, >, or = to compare the two numbers: 8 _ 3
InternLM-Math Base 7B:
Reasoning: 8 3 ### Answer: 8>3
Expected answer: >
Correct? Yes
Problem: Consider the original challenge where you compared 8 and 3. Now, think about what would happen if you were to compare 8 to a different number. Fill in the blank with <, >, or = in the following: 8 _ 10
InternLM-Math Base 7B:
Reasoning: 8 10 ### Answer: 8<10
Expected answer: <
Correct? Yes
Problem: Determine the relationship between the two numbers by filling in the blank with <, >, or =. 4 _ 6
InternLM-Math Base 7B:
4 = 3+1. 3= 6/2. 1= 3-2. 3-2= 6/2-1. 6/2-1= 6/2-3/2. 6/2-3/2= 3/2-3/2. 3/2-3/2= 0. 0<4. 4<6.
Expected answer: <
Correct? No
Problem: Compare the following numbers by filling in the blank with <, >, or =. 6 _ 1
InternLM-Math Base 7B:
Reasoning: 6 1 = <<6 1=6>>6 ### Answer: =
Expected answer: >
Correct? No
Problem: Fill in the blank in the equation below with <, >, or = to compare the two numbers: 7 _ 3
InternLM-Math Base 7B:
Reasoning: 3<7, so 3<<3<7>>7.
Expected answer: >
Correct? No
Problem: Complete the following statement by substituting the blank with <, > or =. 8 _ 8
InternLM-Math Base 7B:
Reasoning: 8 = 8 ### Answer: =
Expected answer: =
Correct? Yes
Problem: Following the previous comparison, let's consider a new pair of numbers. Fill in the blank in the question: 9 _ 8 with either a <, >, or = to compare these two numbers.
InternLM-Math Base 7B:
Reasoning: 9 > 8 ### Answer: >
Expected answer: >
Correct? Yes
Problem: Compare the following numbers by filling in the blank with the correct symbol (>, <, or =): 3 _ 1
InternLM-Math Base 7B:
Reasoning: 3 is greater than 1, so 3>1. ### Answer: 3>1
Expected answer: >
Correct? Yes
Problem: Continuing from the previous problem, now consider these two numbers: 2 _ 1 Just like before, fill in the blank with the correct symbol (>, <, or =) to compare the two numbers.
InternLM-Math Base 7B:
Reasoning: 2 is less than 3, and 1 is less than 2, so 2<3, and 1<2. ### Answer: 2<3, 1<2
Expected answer: >
Correct? No
Problem: Compare the following two numbers by using either <, >, or =: 7 _ 2
InternLM-Math Base 7B:
2 is less than 7.
Expected answer: >
Correct? No
Problem: Please compare the following numbers by filling in the blank with <, >, or =: 4 _ 10
InternLM-Math Base 7B:
Reasoning: 4 < 10 ### Answer: <
Expected answer: <
Correct? Yes
Problem: Following up from the previous question where we compared 4 with 10, let's make a slight change. Please compare the following numbers by filling in the blank with <, >, or =: 2 _ 10 Consider the scenario where we only had two items instead of four. Could your comparison from the earlier problem help you in this situation?
InternLM-Math Base 7B:
Reasoning: 2 < 4 < 10 ### Answer: <
Expected answer: <
Correct? Yes
Problem: Please compare these two numbers 2 and 9 using the symbols <, >, or =. Complete the following equation: 2 _ 9
InternLM-Math Base 7B:
Reasoning: 9 is <<9=9>>9. 9 is greater than 2.
Expected answer: <
Correct? Yes
Problem: In the above comparison you made between 2 and 9, now let's change the second number. Suppose we change the number 9 to 4. Compare them using the symbols <, >, or =. So, the new equation to solve will be: 2 _ 4
InternLM-Math Base 7B:
Reasoning: 2 is <<2=2>>2. 2 is less than 4.
Expected answer: <
Correct? Yes
Problem: Compare these two numbers by filling in the blank with <, >, or =: 6 _ 8
InternLM-Math Base 7B:
Reasoning: 8 is the greater number.
Expected answer: <
Correct? No
Problem: Fill in the blank in the question 8 _ 7 with either a <, >, or = sign to compare the numbers.
InternLM-Math Base 7B:
Reasoning: 8 7 ### Answer:
Expected answer: >
Correct? No