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If m and n are positive integers, what is the value of m + n? [#permalink]

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28 Oct 2015, 08:27

Quote:

If m and n are positive integers, what is the value of m + n? (1) m/n = 7/10 (2) The greatest common factor of m and n is 1.

Kudos for a correct solution.

Statement 1 says m/n = 7/10. There are multiple values of m & n e.g. m/n = 14/20 = 7/10 OR 21/30 = 7/10 etc. NOT sufficient. Statement 2 says m & n have no common factor except 1. However, no specific value of m & n is provided. NOT sufficient.

Combining 1 & 2 As there is no common factor except 1, the only possible values for m & n are 7 & 10 respectively. So m+n = 17. Sufficient.

Option (C) wins.
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Re: If m and n are positive integers, what is the value of m + n? [#permalink]

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28 Oct 2015, 08:37

1

This post received KUDOS

Ans should be C.

The question does not asks the exact values of M & N, It asks their sum.what is M + N = ...? ( certainly some +ve Integer as M & N are +ve Integers )

Statement 1-> M / N = 7 / 10 , As this is a ratio, exact values of M & N tend to vary accordingly...

If M = 7, N would be 10. If M = 14, N would be 20. If M = 70, N would be 100. Similarlly infinite values exists for M & N.

Hence Insufficient.

Statement 2-> The GCD of M & N is 1. This signifies that M & N have no common divisor apart from 1. That is M & N could be a combination of different primes such as 2 & 3, 3 & 5 or 7 & 11 and so on.

Hence insufficient.

Combining both Statements,7 and 10 are the only values of M & N that satisfies both conditions. Hence suficcient.

Note:- If the question would have asked M - N ( a potential trap ), then the answer would have been E, as in that case exact values of Both M & N would have been required.

If m and n are positive integers, what is the value of m + n?

(1) m/n = 7/10

(2) The greatest common factor of m and n is 1.

Kudos for a correct solution.

Question : m + n = ?

Statement 1: m/n = 7/10 Case 1: m = 7, n = 10 and m+n = 17 Case 2: m = 14, n = 20 and m+n = 34 Hence, NOT SUFFICIENT

Statement 2: The greatest common factor of m and n is 1. Case 1: m = 7, n = 10 and m+n = 17 Case 2: m = 4, n = 3 and m+n = 7 Hence, NOT SUFFICIENT

Combining the two statements m/n = 7/10 and GCD of m and n is 1 i.e. they must be co-prime to each other which is possible only when m = 7 and n = 10 i.e. m+n = 17 SUFFICIENT

Answer: option C
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