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

Question

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

Bunuel · Answer

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.

Answer: B.

kinjiGC · Answer

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

AKG1593 · Answer

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

Cosmas · Answer

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.

Answer B

NoHalfMeasures · Answer

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

Bunuel · Answer

__________
Ideally yes.

MathRevolution · Answer

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

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GMAT Data Sufficiency (DS) Questions

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

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