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

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Manager
Joined: 03 Jul 2012
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GMAT 1: 710 Q50 V36
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If there are twice as many women as men in a group and an eq  [#permalink]

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08 Sep 2012, 06:01
1
5
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Difficulty:

65% (hard)

Question Stats:

61% (02:26) correct 39% (02:30) wrong based on 127 sessions

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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
Director
Joined: 22 Mar 2011
Posts: 588
WE: Science (Education)
Re: If there are twice as many women as men in a group and an eq  [#permalink]

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08 Sep 2012, 06:14
1
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.

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Re: If there are twice as many women as men in a group and an eq  [#permalink]

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08 Sep 2012, 06:33
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.

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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Posts: 58
Location: India
Concentration: Finance, Strategy
GMAT Date: 09-30-2012
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Re: If there are twice as many women as men in a group and an eq  [#permalink]

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08 Sep 2012, 06:38
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.

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.
Director
Joined: 22 Mar 2011
Posts: 588
WE: Science (Education)
Re: If there are twice as many women as men in a group and an eq  [#permalink]

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08 Sep 2012, 06:38
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.

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]

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02 Sep 2014, 23:50
1
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 $$= \frac{\frac{11x}{20}}{3x} = \frac{11}{60}$$

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Re: If there are twice as many women as men in a group and an eq  [#permalink]

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21 Sep 2014, 21:52
Using Double matrix (Single variable)

Attachment:

frac.png [ 6.36 KiB | Viewed 1882 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]

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27 Feb 2019, 12:12
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Re: If there are twice as many women as men in a group and an eq   [#permalink] 27 Feb 2019, 12:12
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