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

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by Max@Math Revolution » Wed Apr 03, 2019 2:51 am

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[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
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Source: — Data Sufficiency |

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by Brent@GMATPrepNow » Wed Apr 03, 2019 5:38 am
Max@Math Revolution wrote:[GMAT math practice question]

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

1) m² + n² = 5
2) m-n = 1
Given: m and n are positive integers.

Target question: Are m and n consecutive integers?

Statement 1: m² + n² = 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

Answer: D

Cheers,
Brent
Brent Hanneson - Creator of GMATPrepNow.com
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by Max@Math Revolution » Fri Apr 05, 2019 12:36 am
=>

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.

Therefore, D is the answer.
Answer: D
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