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

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by Max@Math Revolution » Thu Mar 21, 2019 11:17 pm

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[GMAT math practice question]

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

1) 15 ≤ m < n ≤ 20
2) mn = 323
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Source: — Data Sufficiency |

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by Brent@GMATPrepNow » Fri Mar 22, 2019 11:04 am
Max@Math Revolution wrote:[GMAT math practice question]

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

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

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

Statement 1: 15 ≤ m < n ≤ 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

Answer: D

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Brent
Brent Hanneson - Creator of GMATPrepNow.com
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by Max@Math Revolution » Sun Mar 24, 2019 5:04 pm
=>

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 ≤ m < n ≤ 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.

Therefore, D is the answer.
Answer: D
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