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Math Expert V
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If m/n = 5/3, what is the value of m + n ?  [#permalink]

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Difficulty:   5% (low)

Question Stats: 84% (01:08) correct 16% (01:20) wrong based on 507 sessions

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If m/n = 5/3, what is the value of m + n ?

(1) m > 0
(2) 2m + n= 26

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Math Expert V
Joined: 02 Sep 2009
Posts: 61302
Re: If m/n = 5/3, what is the value of m + n ?  [#permalink]

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SOLUTION

If m/n = 5/3, what is the value of m + n ?

(1) m > 0. Clearly insufficient: if m=5, n=3, then m + n = 8 and if m=10, n=6, then m + n = 16.

(2) 2m + n= 26. We have two distinct linear equations with two unknowns (m/n=5/3 and 2m+n=26), hence we can solve for both of them and get the value of m + n. Sufficient.

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Re: If m/n = 5/3, what is the value of m + n ?  [#permalink]

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Bunuel wrote:
The Official Guide For GMAT® Quantitative Review, 2ND Edition

If m/n = 5/3, what is the value of m + n ?

(1) m > 0
(2) 2m + n= 26

Statement 1) We have been given the ratio and multiple values are possible.
For example : m = 5, n = 3 or m = 10, n = 6. Hence Not Sufficient.

Statement 2) 2m + n = 26.
As we have two equation given by premise (3m = 5n) and one given by the statement, we can determine m+n.

Sufficient.

option - B
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Re: If m/n = 5/3, what is the value of m + n ?  [#permalink]

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1
From S1:m>0
m and n could take diff positive values like (5,3) or (25,15).Accordingly,value of m+n will change.Insufficient.
From S2:2m+n=26
As m=5n/3,replacing in the above equation,we get (10n/3)+n=26=>13n/3=26
n=6 and m=10.Therefore,m+n=16.Sufficient.
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Re: If m/n = 5/3, what is the value of m + n ?  [#permalink]

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1
Question stem says 3m=5n.

Statement (1). m>0 gives multiple values of m+n. Insufficient

Statement (2). 2m+n=26. This is sufficient when combined with the relationship of m and n in the stem.

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Re: If m/n = 5/3, what is the value of m + n ?  [#permalink]

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HI Bunuel, If someone wants to score 51/50 on quant, should s/he be able to solve questions like these in less than 30 secs? Thanks
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Math Expert V
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Re: If m/n = 5/3, what is the value of m + n ?  [#permalink]

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MensaNumber wrote:
HI Bunuel, If someone wants to score 51/50 on quant, should s/he be able to solve questions like these in less than 30 secs? Thanks

__________
Ideally yes.
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Re: If m/n = 5/3, what is the value of m + n ?  [#permalink]

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Forget conventional ways of solving math questions. In DS, Variable approach is the easiest and quickest way to find the answer without actually solving the problem. Remember equal number of variables and independent equations ensures a solution.

If m/n = 5/3, what is the value of m + n ?

(1) m > 0
(2) 2m + n= 26

There are 2 variables (m,n), and one equation (m/n=5/3), and 2 more equations from the 2 conditions; there is high chance (D) will be our answer.
For condition 1, m>0. We cannot decide on a value, so this is insufficient
For condition 2, 2m+n=26, 3m=5n. We get m=10, n=6. This is sufficient, and the answer is (B).

For cases where we need 1 more equation, such as original conditions with “1 variable”, or “2 variables and 1 equation”, or “3 variables and 2 equations”, we have 1 equation each in both 1) and 2). Therefore, there is 59 % chance that D is the answer, while A or B has 38% chance and C or E has 3% chance. Since D is most likely to be the answer using 1) and 2) separately according to DS definition. Obviously there may be cases where the answer is A, B, C or E.
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Re: If m/n = 5/3, what is the value of m + n ?  [#permalink]

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Re: If m/n = 5/3, what is the value of m + n? (1) m > 0 (2)  [#permalink]

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Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

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_________________ Re: If m/n = 5/3, what is the value of m + n? (1) m > 0 (2)   [#permalink] 06 Dec 2019, 02:23
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