Ratio Problem......

Question

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

Anurag@Gurome · Answer

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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GMATGuruNY · Answer

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.

avinashsidha · Answer

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

Anurag@Gurome · Answer

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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