BREAKING: Target Test Prep releases Brand New 2026 On Demand GMAT prep course

Redeem

Gmat prep - ratios

This topic has expert replies
Post new topic Post Reply
Previous Topic Next Topic
User avatar
Master | Next Rank: 500 Posts
Posts: 101
Joined: Tue Oct 27, 2009 8:19 am
Thanked: 4 times
Followed by:2 members

Gmat prep - ratios

by g.shankaran » Sun May 29, 2011 3:58 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 the men on the sight-seeing tour?

1.On the sight seeing tour, the ratio of the number of the children to the number of man was 5 to 11.

2. The number of women on the sight seeing tour was less than 30.

The ans is C.

Can you please explain how?
Top
Source: — Data Sufficiency |
User avatar
Legendary Member
Posts: 965
Joined: Thu Jan 28, 2010 12:52 am
Thanked: 156 times
Followed by:34 members
GMAT Score:720

by vineeshp » Sun May 29, 2011 4:40 am
Hey,

I wont get into Stmt 1 alone or Stmt 2 alone since it does not give us any definite numbers.

Combining the statements,
The ratio of women to kids is 5:2 and the ratio of kids to men is 5:11
So we can combine the two ratios. The only way to combine would be to make the childrens number the same. So we can
5:2 is same as 25:10
5:11 is same as 10:22.

So we can say that the ratio between men and women is 25:22.
Which means there are 25x women and 22x men. Right?

At this point, the minimum positive value you can put for x is 1.
At x=1, So there are 25 women and 22 men.
At x=2, there are 50 women and 44 men.
but Stmt 2 says that the number of women is less than 30. So x=1 works and we get the number of men.
Hence C.
--------------------------------------
Just an extra thought for your understanding.
Suppose,
The statement had said the number of children is less than thirty, then the answer would have been E.
at x=1, there would be 10 kids.
at x=2, there would be 20 kids. So not enough Info.
Vineesh,
Just telling you what I know and think. I am not the expert. :)
Top
User avatar
GMAT Instructor
Posts: 905
Joined: Sun Sep 12, 2010 1:38 am
Thanked: 378 times
Followed by:123 members
GMAT Score:760

by Geva@EconomistGMAT » Sun May 29, 2011 4:40 am
First bring all the ratios to the same comparison base:
W:C
5:2

C:M
5:11

Expand the first ratio times 5, and the second ratio times 2, so that both ratios have the same number of ratio units in the common factor "Children"

W:C
25:10

C:M
10:22

so the final ratio of W:C:M is 25:10:22.

this alone does not set the number of women to a single value, as the actual numbers can be 25, 10 and 22, or 50, 20 and 44.

EDIT: Midway through my explanation I realized that Vineesh had beat me to the punchline, so you might as well read the explanation above me. It all stems from the fact that people cannot be broken into fractions. A ratio of 25:10:22 could technically be reduced, were it not for the fact that it represents actual people: if we take 20 women (the original 25 times 4/5), we also need to multiply the other two components times the same 4/5, creating a messy 22*4/5 fraction for the number of men, which cannot be. Thus, the 30 limit fixes the number of women at 25, with no possibility of higher or lower reductions, which also serves to fix the other two components to a single value as well.
Geva
Senior Instructor
Master GMAT
1-888-780-GMAT
https://www.mastergmat.com
Top
Post new topic Post Reply
• Page 1 of 1