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Each week we'll be posting several questions from The Official Guide For GMAT® Quantitative Review, 2ND Edition and then after couple of days we'll provide Official Answer (OA) to them along with a slution.

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(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.

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

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26 Jan 2014, 22:13

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. Ans.B

(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.

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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