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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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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
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Question Stats:

57% (02:04) correct 43% (02:08) wrong based on 135 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
[Reveal] Spoiler: OA

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Director
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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, 06:14
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.

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Kudos [?]: 1074 [0], given: 43

Manager
Joined: 03 Jul 2012
Posts: 129

Kudos [?]: 107 [0], given: 16

GMAT 1: 710 Q50 V36
GPA: 3.9
WE: Programming (Computer Software)
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.

Kudos [?]: 107 [0], given: 16

Manager
Joined: 05 Jul 2012
Posts: 76

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Location: India
Concentration: Finance, Strategy
GMAT Date: 09-30-2012
GPA: 3.08
WE: Engineering (Energy and Utilities)
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.

Kudos [?]: 52 [0], given: 8

Director
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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.

If there are twice as many women as men - you should have 20 men and 40 women. Then continue.
_________________

PhD in Applied Mathematics
Love GMAT Quant questions and running.

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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, 18:13
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

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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
KUDOS
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 1338 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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15 Nov 2015, 12:31
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

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Re: If there are twice as many women as men in a group and an eq   [#permalink] 15 Nov 2015, 12:31
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