Data Sufficiency

Can someone help explain the problem below?

The answer is C.

Is it because the number of women must = 25 in order for the number of children and men to equal whole numbers? (children would = 10 and men would = 22)

Well since it is a DS question lets just evaluate if a definite answer is in store or not.

stmt 1: gives the ration of men to children. This alone will just help me to arrive at a ratio of men : women: children. But I can't calculate a definite number.

stmt 2: this alone just gives a number for women. I don't get any info about men.

If I combine the two stmts:: I have a ratio as well as a cap on number of women. Since women have to be integral, I can sure get a number of total people on the tour.

This in turn will let me get a number of men.

Wow this problem is very tricky..At first even I thought its E

Ok here it goes,

lets set up an equation with the given ratios

we know from the question that W/C=5/2 or C=2W/5

(1) says that C/M=5/11 or C=5M/11 . This is INSUFFICIENT because there might be multiple values though we have all three ratios.

(2) is clearly INSUFFICIENT because it does not mention anythin about men

Combining the two stats we know that C=2W/5 and C=5M/11 and W<30

Just plug in the values for W in C=2W/5 which will only be multiples of 5, you will see that other than 25 there is no other value for W which will satisfy the two conditions C=2W/5 and C=5M/11.

If I would have got this question on the real test I would have surely got it wrong because this problem is very deceptive.

from statement 1 you can deduce common ratio,its given women:children is 5:2 and children:men is 5:11
so common ratio would be women:children:men = 25:10:22

statement 2 says women < 30
so with the common ratio,
25/77 * total = women <30

this can be true only if # of women = 25
so total = (25*77)/25 = 77

now that you know the total no of people , you can find the number of men using the common ratio (22/77)*77 = 22.

so (C) is the correct answer

from statement 1 you can deduce common ratio,its given women:children is 5:2 and children:men is 5:11
so common ratio would be women:children:men = 25:10:22

statement 2 says women < 30
so with the common ratio,
25/77 * total = women <30

this can be true only if # of women = 25
so total = (25*77)/25 = 77

now that you know the total no of people , you can find the number of men using the common ratio (22/77)*77 = 22.

so (C) is the correct answer