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by GMATGuruNY » Fri Jun 20, 2014 5:15 am
Akansha wrote:On a certain sight-seeing tour, the ratio of the number of women to the number of children is 5 to 2. What was the number of men on the sight seeing tour?

1) On the sight-seeing tour , the ratio of the number of children to the number of men was 5 to 11.
2) The number of women on the sight seeing tour was less than 30.
This problem is constrained to POSITIVE INTEGERS because it is about PEOPLE.
We can't have 2/3 of a child.

Given info:
W:C = 5:2.

Question: What is the value of M?

Statement 1: C:M = 5:11.
To combine this ratio with the first ratio, the common element (C) must be represented by the same value in each ratio.
W:C = 5:2 = 25:10
C:M = 5:11 = 10:22
Thus, W:C:M = 25:10:22.
Since we know only the ratio, no way to determine the actual value of M.
Insufficient.

Statement 2: W<30.
No way to determine M.
Insufficient.

Statements 1 and 2 together:
Given that W:C:M = 25:10:22 and W<30, we know that W=25 (because if we use a multiple of the ratio, the number of women will be at least 2*25 = 50).
Since W=25 and W:C:M = 25:10:22, M=22.
Sufficient.

The correct answer is C.
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by Brent@GMATPrepNow » Fri Jun 20, 2014 5:28 am
On a certain sight-seeing tour, the ratio of the number of women to the number of
children was 5 to 2. What was the number of men on the sight-seeing tour?

(1) On the sight-seeing tour, the ratio of the number of children to the number of men was 5 to 11.
(2) The number of women on the sight-seeing tour was less than 30.
Let W = # of women
Let M = # of men
Let C = # of children

Target question: What is the value of M?

Given: The ratio of the number of women to the number of children was 5 to 2
In other words, W : C = 5 : 2

Statement 1: On the sight-seeing tour, the ratio of the number of children to the number of men was 5 to 11.
In other words, C : M = 5 : 11

Let's combine this ratio with the given ratio (W : C = 5 : 2)
To do so, we'll find some EQUIVALENT RATIOS such that they both share a term.

Take 5 : 2 and multiply both terms by 5 to get 25 : 10
So, W : C = 25 : 10

Now take 5 : 11 and multiply both terms by 2 to get 10 : 22
So, C : M = 10 : 22

At this point, we can combine the ratios to get W : C : M = 25 : 10 : 22
As you can see this just tells us the ratios of the variables, it does not provide enough information to find the exact value of M
Consider these three conflicting possibilities:
Case a: W : C : M = 25 : 10 : 22
Case b: W : C : M = 50 : 20 : 44
Case c: W : C : M = 75 : 30 : 66
etc.
Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT

Statement 2: The number of women on the sight-seeing tour was less than 30.
There's no information at all about the men so statement 2 is NOT SUFFICIENT

Statements 1 and 2 combined
Statement 1 essentially tells us that W : C : M = 25 : 10 : 22, so with each ratio that's equivalent to 25 : 10 : 22, we can a different value of M
So, we could have W : C : M = 25 : 10 : 22
or W : C : M = 50 : 20 : 44
or W : C : M = 75 : 30 : 66
etc.
Statement 2 reduces the possible number of women (W).
If W < 30, then there's only ONE possible ratio that works. That is W : C : M = 25 : 10 : 22
This means that there MUST be 22 men
Since we can answer the target question with certainty, the combined statements are SUFFICIENT

Answer = C

Cheers,
Brent
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by kartikc11 » Fri Jun 20, 2014 5:41 am
Thank you Brent and Mitch, that explains it well!
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