GMAT Prep : Ratios Problem

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nandy1984: Master | Next Rank: 500 Posts; Posts: 105; Joined: Fri Nov 05, 2010 8:29 pm; Thanked: 4 times

by nandy1984 » Tue Mar 27, 2012 9:20 pm

On a certain sight seeing tour, the ratio of the number of women to 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.

My approach:

Given: w : c = 5 : 2
Statement 1: c : m = 5 : 11
therefore w : c : m = 25 : 10 : 22
there we get the ratio of number of men to the overall population as m : (m + w + c) = 22 : 57 .... from this we cannot calculate the number of men as we don't know how many people in total went for the tour. INSUFFICIENT.

Statement2: number of women < 30
this doesn't give any info of other people so INSUFFICIENT

Statement 1 & 2: from 1 w = 25:57
therefore lets say T be the total people . (25/57) * T < 30....

I am stuck here... can anyone help me how to solve this further?.....

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Source: Beat The GMAT — Data Sufficiency | Tue Mar 27, 2012 9:20 pm

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Anurag@Gurome: GMAT Instructor; Posts: 3835; Joined: Fri Apr 02, 2010 10:00 pmFollowed by: 523 members; Location: Milpitas, CA; Thanked: 1854 times; GMAT Score:770

by Anurag@Gurome » Tue Mar 27, 2012 10:28 pm

Given: w : c = 5 : 2
Let us assume that number of women, w = 5x and number of children, c = 2x for some integer x.
If m = number of males, we have to find the value of m.

(1) c : m = 5 : 11
Let us assume that number of children, c = 5y and number of men, m = 11y, but this is NOT sufficient to find m.

(2) w < 30; NOT sufficient to find m.

Combining (1) and (2), w = 5x and w < 30 implies 5x < 30 or x < 6
c = 5y implies c is a multiple of 5 and c = 2x implies x = 5 (as x < 6)
So, c = 2 * 5 = 10 = 5y implies y = 2
So, m = 11 * 2 = 22; SUFFICIENT.

The correct answer is C.

Anurag Mairal, Ph.D., MBA
GMAT Expert, Admissions and Career Guidance
Gurome, Inc.
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GMATGuruNY: GMAT Instructor; Posts: 15539; Joined: Tue May 25, 2010 12:04 pmFollowed by: 1906 members; Location: New York, NY; Thanked: 13060 times; GMAT Score:790

by GMATGuruNY » Wed Mar 28, 2012 4:13 am

nandy1984 wrote:On a certain sight seeing tour, the ratio of the number of women to 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.

My approach:

Given: w : c = 5 : 2
Statement 1: c : m = 5 : 11
therefore w : c : m = 25 : 10 : 22
there we get the ratio of number of men to the overall population as m : (m + w + c) = 22 : 57 .... from this we cannot calculate the number of men as we don't know how many people in total went for the tour. INSUFFICIENT.

Statement2: number of women < 30
this doesn't give any info of other people so INSUFFICIENT

Statement 1 & 2: from 1 w = 25:57
therefore lets say T be the total people . (25/57) * T < 30....

I am stuck here... can anyone help me how to solve this further?.....

I used a similar approach. Check my solution here:

https://www.beatthegmat.com/ratio-proportion-t82796.html

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nandy1984: Master | Next Rank: 500 Posts; Posts: 105; Joined: Fri Nov 05, 2010 8:29 pm; Thanked: 4 times

by nandy1984 » Wed Mar 28, 2012 4:30 am

GMATGuruNY wrote:
nandy1984 wrote:On a certain sight seeing tour, the ratio of the number of women to 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.

My approach:

Given: w : c = 5 : 2
Statement 1: c : m = 5 : 11
therefore w : c : m = 25 : 10 : 22
there we get the ratio of number of men to the overall population as m : (m + w + c) = 22 : 57 .... from this we cannot calculate the number of men as we don't know how many people in total went for the tour. INSUFFICIENT.

Statement2: number of women < 30
this doesn't give any info of other people so INSUFFICIENT

Statement 1 & 2: from 1 w = 25:57
therefore lets say T be the total people . (25/57) * T < 30....

I am stuck here... can anyone help me how to solve this further?.....
I used a similar approach. Check my solution here:

https://www.beatthegmat.com/ratio-proportion-t82796.html

Super ..... its a small twist we need to know " The ratios can be written in their multiples"..... Got it... Super Likes....

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nandy1984: Master | Next Rank: 500 Posts; Posts: 105; Joined: Fri Nov 05, 2010 8:29 pm; Thanked: 4 times

by nandy1984 » Wed Mar 28, 2012 4:34 am

GMATGuruNY wrote:
nandy1984 wrote:On a certain sight seeing tour, the ratio of the number of women to 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.

My approach:

Given: w : c = 5 : 2
Statement 1: c : m = 5 : 11
therefore w : c : m = 25 : 10 : 22
there we get the ratio of number of men to the overall population as m : (m + w + c) = 22 : 57 .... from this we cannot calculate the number of men as we don't know how many people in total went for the tour. INSUFFICIENT.

Statement2: number of women < 30
this doesn't give any info of other people so INSUFFICIENT

Statement 1 & 2: from 1 w = 25:57
therefore lets say T be the total people . (25/57) * T < 30....

I am stuck here... can anyone help me how to solve this further?.....
I used a similar approach. Check my solution here:

https://www.beatthegmat.com/ratio-proportion-t82796.html

Please help me on this Problem too : https://www.beatthegmat.com/gmat-prep-pe ... 09151.html

Thanks...

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