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If there are twice as many women as men in a group and an eq

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If there are twice as many women as men in a group and an eq [#permalink] New post 08 Sep 2012, 05:01
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Question Stats:

56% (02:52) correct 44% (01:39) wrong based on 84 sessions
If there are twice as many women as men in a group and an equal number of men and women do not own cars - a group that is 30% of the total. What fraction of the total is men who own cars?

A) 3⁄20
B) 11⁄60
C) 9⁄40
D) 1⁄3
E) 11⁄20
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Re: If there are twice as many women as men in a group and an eq [#permalink] New post 08 Sep 2012, 05:14
mehulsayani wrote:
If there are twice as many women as men in a group and an equal number of men and women do not own cars - a group that is 30% of the total. What fraction of the total is men who own cars?

A) 3⁄20
B) 11⁄60
C) 9⁄40
D) 1⁄3
E) 11⁄20


Consider a group of 100 men and 200 women, a total of 300 people. 30% of them, which is 90, form a group of people who don't own a car.
Half of them are men, and the other half are women, more precisely 45.
It means that there are 100 - 45 = 55 men who own a car, and this represents 55/300 = 11/60 of the total.

Answer B
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Re: If there are twice as many women as men in a group and an eq [#permalink] New post 08 Sep 2012, 05:33
EvaJager wrote:
mehulsayani wrote:
If there are twice as many women as men in a group and an equal number of men and women do not own cars - a group that is 30% of the total. What fraction of the total is men who own cars?

A) 3⁄20
B) 11⁄60
C) 9⁄40
D) 1⁄3
E) 11⁄20


Consider a group of 100 men and 200 women, a total of 300 people. 30% of them, which is 90, form a group of people who don't own a car.
Half of them are men, and the other half are women, more precisely 45.
It means that there are 100 - 45 = 55 men who own a car, and this represents 55/300 = 11/60 of the total.

Answer B


Now consider a group of 20 women and 40 men, 30% of ppl can't drive i.e. 18, half of them are men, so 9 men don't own a car. So, no. of men who own a car is 40-9 = 31.

SO, the required ratio is 31/60. which is what I was getting. Correct me if I am wrong somewhere.
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Re: If there are twice as many women as men in a group and an eq [#permalink] New post 08 Sep 2012, 05:38
mehulsayani wrote:
EvaJager wrote:
mehulsayani wrote:
If there are twice as many women as men in a group and an equal number of men and women do not own cars - a group that is 30% of the total. What fraction of the total is men who own cars?

A) 3⁄20
B) 11⁄60
C) 9⁄40
D) 1⁄3
E) 11⁄20


Consider a group of 100 men and 200 women, a total of 300 people. 30% of them, which is 90, form a group of people who don't own a car.
Half of them are men, and the other half are women, more precisely 45.
It means that there are 100 - 45 = 55 men who own a car, and this represents 55/300 = 11/60 of the total.

Answer B


Now consider a group of 20 women and 40 men, 30% of ppl can't drive i.e. 18, half of them are men, so 9 men don't own a car. So, no. of men who own a car is 40-9 = 31.

SO, the required ratio is 31/60. which is what I was getting. Correct me if I am wrong somewhere.



Men 20, Women 40 !
Twice women not men.
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Re: If there are twice as many women as men in a group and an eq [#permalink] New post 08 Sep 2012, 05:38
mehulsayani wrote:
EvaJager wrote:
mehulsayani wrote:
If there are twice as many women as men in a group and an equal number of men and women do not own cars - a group that is 30% of the total. What fraction of the total is men who own cars?

A) 3⁄20
B) 11⁄60
C) 9⁄40
D) 1⁄3
E) 11⁄20


Consider a group of 100 men and 200 women, a total of 300 people. 30% of them, which is 90, form a group of people who don't own a car.
Half of them are men, and the other half are women, more precisely 45.
It means that there are 100 - 45 = 55 men who own a car, and this represents 55/300 = 11/60 of the total.

Answer B


Now consider a group of 20 women and 40 men, 30% of ppl can't drive i.e. 18, half of them are men, so 9 men don't own a car. So, no. of men who own a car is 40-9 = 31.

SO, the required ratio is 31/60. which is what I was getting. Correct me if I am wrong somewhere.


If there are twice as many women as men - you should have 20 men and 40 women. Then continue.
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Re: If there are twice as many women as men in a group and an eq [#permalink] New post 02 Sep 2014, 17:13
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Re: If there are twice as many women as men in a group and an eq [#permalink] New post 02 Sep 2014, 22:50
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Women .................. Men ....................... Total

2x ............................ x ................................. 3x

y .............................. y .............................. 2y (Do not have cars)

30% of total men & women do not have cars

\frac{30}{100} * 3x = 2y

y = \frac{9x}{20}

Men owing cars= x - \frac{9x}{20} = \frac{11x}{20}

Fraction = \frac{\frac{11x}{20}}{3x} = \frac{11}{60}

Answer = B
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Re: If there are twice as many women as men in a group and an eq [#permalink] New post 21 Sep 2014, 20:52
Using Double matrix (Single variable)

Attachment:
frac.png
frac.png [ 6.36 KiB | Viewed 282 times ]


1. Let Total Men = x

2. So, total Women = 2x

3. Total People = x+2x = 3x

4. 30% People are without cars = \frac{30}{100} * 3x = \frac{9x}{10}

5. Equal number of Women are without cars = \frac{9x}{10} * \frac{1}{2} = \frac{9x}{20}

6. Equal number of Men are without cars = \frac{9x}{10} * \frac{1}{2} = \frac{9x}{20}

7. Number of Men with Car = x - \frac{9x}{20} = \frac{11x}{20}

Fraction = \frac{(7)}{(3)} = \frac{\frac{11x}{20}}{3x} = \frac{11}{60}
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Re: If there are twice as many women as men in a group and an eq   [#permalink] 21 Sep 2014, 20:52
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