Ratio Question

Question

Veritas Prep Book 2 - page 228 - Q# 81 Answer is D - but not sure how to get answer

81)

The ratio of men to women at a picnic is 7:5 and the ratio of men to children at that picnic is 3:4. What is the smallest total number of men and women and children that could be at the picnic?

a) 18
b) 36
c) 54
d) 64
e) 128

ind23 · Answer

Hi,

As m:w = 7:5, lets say m = 7x & w = 5x
AS m:c = 3:4, lets say m = 3y & c = 4y

Now 7x = 3y => x/y = 3/7

the min value which x can take is 3 and minimum which y can take is 7

so m = 7*3 = 21
w = 5*3 = 15
c = 4*7 = 28

m+w+c = 64

Answer is D.

dainovu3 · Answer

A slightly faster way (and I think easier).

M:W = 7:5
M:C = 3:4

Somewhat becomes simultaneous equation where
# children = 4/3 * Men

M:W:C = 7:5:(4/3 * 7) => 7:5:(28/3) => 7x3 : 5x3 : 28
M:W:C = 21:15:28
total = 21 + 15 + 28 = 64 (D)

EMPOWERgmatRichC · Answer

Hi All,

The 'key' to these types of questions is to look for the variables that 'overlap' and deal with them first. In this question, 'men' appear in both ratios. In the first ratio, M:W = 7:5 means that the number of men MUST be a multiple of 7 and the number of women MUST be an equivalent multiple of 5. In the second ratio, M:C = 3:4 means that the number of men MUST be a multiple of 3 and the number of children MUST be an equivalent multiple of 4.

Since the number of men MUST be a multiple of 7 AND MUST be a multiple of 3, the smallest number of men in the room will be 21. From there, you can multiply the two ratios out (the first ratio gets multiplied by 3 and the second ratio gets multiplied by 7) to get the smallest number of women and the smallest number of children.

GMAT assassins aren't born, they're made,
Rich

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