DS - GMAT PREP - practise test

[ata]

on a certain tour, ratio of number of women to number of children was 10 to 4. what was the no of men on the tour?

(1) ratio of children to men was 10 to 22
(2) no of women on the tour was less than 30

got it right on a fluke but could someone pls explain. ans both together are sufficient.

[djjamal]

Ratio of women (W) to children (C) is 10:4 or 5:2

(1) this only gives a ratio, and the prompt only provides a ratio. With only ratios, there is no way to determine the actual # of men. INSUFFICIENT.

(2) this provides the actual number of women on the tour, but combined with the prompt provides no info on the # of men. INSUFFICIENT.

(1) && (2) since we know that the ratio of W:C is 5:2, W must be a multiple of 5, and C must be even. Let's try the first number under 30 that's a multiple of 5: 25.
W=25, then C=10, then M=22
Let's try another
W=20, then C=8, then M=not a whole number. From this we can tell that M must be a multiple of 22 and C must be a multiple of 10. We can't reduce C:M to 5:11 because the prompt states that C must be even. W=25, C=10, and M=22 is the only combination that works for W<30. SUFFICIENT.

[Joey Z.]

W:C:M = 100:40:88, among which the greatest common divisor is 4. Divide through by 4, you get:

W:C:M = 25:10:22.

[RonPurewal]

W:C:M = 100:40:88, among which the greatest common divisor is 4. Divide through by 4, you get:

W:C:M = 25:10:22.

yeah, whoa, those are some awfully big numbers. your statement is of course correct, but there's no good reason to use numbers that big.

takeaway:
when you combine 2 ratios to make a larger ratio, use the LEAST COMMON MULTIPLE of the two numbers you're trying to merge.

in this case, you're trying to merge the numbers for "children". the original numbers for children are 2 (because 10:4 reduces to 5:2) and 10, and therefore have a least common multiple of 10.
all you have to do is multiply 5:2 by 5 to give 25:10, whereupon it combines instantly with the other given ratio.

i find it interesting that these ratios were apparently given in non-reduced form; that's somewhat uncharacteristic of the gmat writers. are you sure that statement (2) wasn't given as 5:11?

[tomslawsky]

Ron,
your takeaway is succinct and applicable across a few "different" types of questions, and it's easy once you "get it". Thank you.
Tom