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On a certain sight seeing tour. . .

This topic has 1 expert reply and 0 member replies

On a certain sight seeing tour. . .

Post Fri Sep 22, 2017 10:16 am
On a certain sight seeing tour, the ration of the number of women to number of children was 5 to 2, What was the number of men on the sigh seeing tour

(1) On the sight seeing tour, the ratio of 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

The OA is C.

This question is very difficult to me. Can any expert explain me how to solve it?

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Post Fri Sep 22, 2017 2:09 pm
Quote:
On a certain sightseeing 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 sightseeing tour?

(1) On the sightseeing 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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Brent Hanneson – Founder of GMATPrepNow.com
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Thanked by: Vincen, gui_guimaraes
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