Ratio Problem......

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phoenix9801: Master | Next Rank: 500 Posts; Posts: 190; Joined: Thu Jan 14, 2010 8:29 pm; Thanked: 2 times

by phoenix9801 » Thu May 31, 2012 10:36 pm

At a family reunion, the ratio of the number of women to the number of children is 3 to 7 and the number of women at the reunion is less than 6. What is the number of men at the reunion if the ratio of the number of children to the number of men is 1 to 2?

A) 13
B) 14
C) 15
D) 16
E) It cannot be determined

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Source: Beat The GMAT — Problem Solving | Thu May 31, 2012 10:36 pm

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by Anurag@Gurome » Thu May 31, 2012 10:51 pm

phoenix9801 wrote:At a family reunion, the ratio of the number of women to the number of children is 3 to 7 and the number of women at the reunion is less than 6. What is the number of men at the reunion if the ratio of the number of children to the number of men is 1 to 2?

As the ration of number of women to the number of children is 3:7, the number of women must be a multiple of 3. As the number of women is less than 6, only possible of number of women is 3.

Hence, number of children is 7.
As the ratio of number of men to the number of children is 2:1, the number of men in the party is 2*7 = 14

The correct answer is B.

Note : I have assumed there is at least some person present at the party as another possible answer would be there is no one in the party.

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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 » Fri Jun 01, 2012 2:14 am

phoenix9801 wrote:At a family reunion, the ratio of the number of women to the number of children is 3 to 7 and the number of women at the reunion is less than 6. What is the number of men at the reunion if the ratio of the number of children to the number of men is 1 to 2?

A) 13
B) 14
C) 15
D) 16
E) It cannot be determined

W/C * C/M = W/M.

Since W/C = 3/7 and C/M = 1/2, we get:
3/7 * 1/2 = W/M
3/14 = W/M.

The resulting ratio implies that the number of women is a multiple of 3.
Since the number of women is less than 6, there must be 3 women, implying that there are 14 men.

The correct answer is B.

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avinashsidha: Newbie | Next Rank: 10 Posts; Posts: 3; Joined: Mon Apr 30, 2012 2:48 am

by avinashsidha » Fri Jun 01, 2012 6:44 am

Hi
I could not understand how to solve it So i used the options to find the answer.

1st choice : 13= no of men
children=26
This option does not fit in the w/c ratio as this is not a multiple of 7.

Looking at other options, 14 is the only multiple.

Correct answer is B) 14

Please update me if i am wrong

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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 » Fri Jun 01, 2012 6:51 am

avinashsidha wrote:Please update me if i am wrong

In general this method is okay and time saving.
But particularly in this case, we have an option It cannot be determined. Hence, we need to do the math whether it can be determined or not.

For example, if the problem said "the number of women at the reunion is less than 10", then possible number of women would have been : 3, 6, and 9. And possible number of men would have been : 14, 28, and 42.

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