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

Question

(1) m/n = 7/10

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

Kudos for a correct  solution .

AmoyV · Answer

m+n=?

1. Not Sufficient
m=7n/10
m+n=7n/10 + n =17n/10

2. Not Sufficient
Tells us that m and n are co primes.

1 and 2.Sufficient
m and n are co primes. So m=7 and n=10 and m+n=17

Answer: C

musunna · Answer

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.

goldfinchmonster · Answer

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.

musunna · Answer

Thanks goldfinchmonster Correct you are. Option (c) is the right answer. I visualized correctly but mess up while explaining :cry:

Now corrected.

GMATinsight · Answer

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

keats · Answer

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.

__________________________

m and n are positive integers. So, m and n can take the values 1,2,3.4.5,...........+infinity

ST 1: m/n = 7/10
Ratio is given. Therefore, a lot of values of m+n are possible. Insufficient.

ST 2: GCF (m,n) = 1 
This means that both m and n are co prime to each other. Again, a lot of possibilities. Insufficient.

ST 1 + 2 :
m = 7 and n = 10 and both have GCF (7,10) = 1
On multiplying it with 2,3,4,5,6,... GCF will not be 1 any more.

So only 1 value is possible. m+n = 17

C should be the answer.

Nunuboy1994 · Answer

This is clearly C

Statement 1

m/n =7/10... could be 14/20 or several other values - as long as it reduces to 7/10

Statement 2

GCF of both is 1

could be 2 primes such as 5 and 7 or 2 other random numbers such 7 and 10

insuff

St 1 and St 2

In order for m/n=7/10 and the gcf to be 1 m and n cannot exceed 7 and 10= any larger that simplifies to that value would have a different gcf

C

TheKingInTheNorth · Answer

silly mistake ..... forgot to use (2) while combining the statement

bumpbot · Answer

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

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