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100 points for $49 worth of Veritas practice GMATs FREE VERITAS PRACTICE GMAT EXAMS Earn 10 Points Per Post Earn 10 Points Per Thanks Earn 10 Points Per Upvote ## m and n are positive integers. Are m and n consecutive integ tagged by: Max@Math Revolution ##### This topic has 2 expert replies and 0 member replies ### GMAT/MBA Expert ## m and n are positive integers. Are m and n consecutive integ ## Timer 00:00 ## Your Answer A B C D E ## Global Stats Difficult [GMAT math practice question] m and n are positive integers. Are m and n consecutive integers? 1) m^2+n^2 = 5 2) m-n = 1 _________________ Math Revolution Finish GMAT Quant Section with 10 minutes to spare. The one-and-only Worldâ€™s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy. Only$149 for 3 month Online Course
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### GMAT/MBA Expert

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Max@Math Revolution wrote:
[GMAT math practice question]

m and n are positive integers. Are m and n consecutive integers?

1) mÂ² + nÂ² = 5
2) m-n = 1
Given: m and n are positive integers.

Target question: Are m and n consecutive integers?

Statement 1: mÂ² + nÂ² = 5
Since m and n are positive integers, there are only two possible solutions:
Solution #1: m = 1 and n = 2
Solution #2: m = 2 and n = 1
In BOTH possible cases, the answer to the target question is the same: YES, m and n ARE consecutive integers
Since we can answer the target question with certainty, statement 1 is SUFFICIENT

Statement 2: m-n = 1
Rewrite as: m = n+1
In other words, m is 1 greater than n
Since m and n are integers, we can see that m and n ARE consecutive integers
Since we can answer the target question with certainty, statement 2 is SUFFICIENT

Cheers,
Brent

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Forget conventional ways of solving math questions. For DS problems, the VA (Variable Approach) method is the quickest and easiest way to find the answer without actually solving the problem. Remember that equal numbers of variables and independent equations ensure a solution.

The first step of the VA (Variable Approach) method is to modify the original condition and the question. We then recheck the question.

Condition 1)
The only positive integers satisfying m^2+n^2 = 5 are m = 1 and n = 2, or m=2 and n = 1.
These are consecutive integers, so condition 1) is sufficient.

Condition 2)
Since the difference between m and n is 1, they are consecutive integers. Condition 2) is sufficient.

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