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Ratios and Inequalities

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Ratios and Inequalities

by cratos » Wed Oct 21, 2015 2:36 am
Hi

Wondering if anyone can help explain. Here's a DS question but I am not sure why the inequality helps us answer it.

Ratio of women to children is 5:2. How many men are there?

(1) Children to Men ratio is 5:11

(2) Women < 30

Doing a few workings based on statement one, we find that the ration of women to children to men (W:C:M) is 25:10:22

How is it that statement (2) allows us to find out the number of men? How about if we have 26 women, wouldn't that generate a different number of men?

Thanks in advance.
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by GMATGuruNY » Wed Oct 21, 2015 2:48 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.
This question is restricted to POSITIVE INTEGERS..

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 cratos » Wed Oct 21, 2015 3:23 am
Thanks for that.

Statement 2: W<30.
No way to determine M.
Insufficient.
If statement two said

(2) The number of women is more than 30

Would that make both statements together insufficient?
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by GMATGuruNY » Wed Oct 21, 2015 3:43 am
cratos wrote:Thanks for that.

Statement 2: W<30.
No way to determine M.
Insufficient.
If statement two said

(2) The number of women is more than 30

Would that make it insufficient then?
Correct.
Here are two cases such that W:C:M = 25:10:22 and W>30:
W=50, C=20, M=44
W=75, C=30, M=66.
Since M can be different values, INSUFFICIENT.
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by Brent@GMATPrepNow » Wed Oct 21, 2015 7:17 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
Brent Hanneson - Creator of GMATPrepNow.com
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