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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 ## If m and n are prime numbers, what is the value of m+n? tagged by: Max@Math Revolution ##### This topic has 2 expert replies and 0 member replies ### GMAT/MBA Expert ## If m and n are prime numbers, what is the value of m+n? ## Timer 00:00 ## Your Answer A B C D E ## Global Stats Difficult [GMAT math practice question] If m and n are prime numbers, what is the value of m+n? 1) 15 â‰¤ m < n â‰¤ 20 2) mn = 323 _________________ 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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Max@Math Revolution wrote:
[GMAT math practice question]

If m and n are prime numbers, what is the value of m+n?

1) 15 â‰¤ m < n â‰¤ 20
2) mn = 323
Given: m and n are prime numbers

Target question: What is the value of m+n?

Statement 1: 15 â‰¤ m < n â‰¤ 20
17 and 19 are the only PRIME numbers from 15 to 20 inclusive
So, it must be the case that m = 17 and n = 19
So, the answer to the target question is m+n = 17 + 19 = 33
Since we can answer the target question with certainty, statement 1 is SUFFICIENT

Statement 2: mn = 323
Find the prime factorization of 323 to get: 323 = (17)(19)
So, there are two possible cases:
Case a: m = 17 and n = 19,in which case, the answer to the target question is m + n = 17 + 19 = 33
Case b: m = 19 and n = 17,in which case, the answer to the target question is m + n = 19 + 17 = 33
In both cases, the answer to the target question is the same: m + n = 33
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)
15 â‰¤ m < n â‰¤ 20 tells us that m = 17 and n = 19. So, m + n = 17 + 19 = 36.
Condition 1) is sufficient since it yields a unique solution.

Condition 2)
mn=323 tells us that m = 17 and n = 19, or m = 19 and n = 17.
In both cases, m + n is 36.
Condition 2) is sufficient since it yields a unique solution.

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