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In a survey of 200 people, 20% of the men and 10% of the women are ath

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Joined: 28 Feb 2018

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In a survey of 200 people, 20% of the men and 10% of the women are ath [#permalink]

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28 Feb 2018, 09:34

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18% (02:45) wrong

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In a survey of 200 people, 20% of the men and 10% of the women are athletes. If 29 people are athletes in total, how many women were in the survey?

a) 29
b) 90
c) 100
d) 110
e) 200

Spoiler: OA

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Re: In a survey of 200 people, 20% of the men and 10% of the women are ath [#permalink]

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28 Feb 2018, 10:55

swong1503 wrote:

In a survey of 200 people, 20% of the men and 10% of the women are athletes. If 29 people are athletes in total, how many women were in the survey?

a) 29
b) 90
c) 100
d) 110
e) 200

Good Question!

Let Number of women be x.

(200-x)*0.2 + 0.1x = 29

Solving the above for x will give us x = 110.
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Re: In a survey of 200 people, 20% of the men and 10% of the women are ath [#permalink]

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28 Feb 2018, 11:27

swong1503 wrote:

In a survey of 200 people, 20% of the men and 10% of the women are athletes. If 29 people are athletes in total, how many women were in the survey?

a) 29
b) 90
c) 100
d) 110
e) 200

Process of elimination is the quickest way to solve

Rule out A and E for obvious reasons

Try for B

if Num of women = b = 90, 10% of 90 = 9
and Num of men = 110, 20% of 110 = 22
adding them 22+9 =/= 29

Rule out B

Try for C

Similarly, 10% of 100 = 10
20% of 100 = 20
20+10 =/= 29

Rule out C

D.
{Test : 10% of 110 = 11; 20% of 90 = 18; 18+11 = 29!}

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Re: In a survey of 200 people, 20% of the men and 10% of the women are ath [#permalink]

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02 Mar 2018, 11:51

swong1503 wrote:

In a survey of 200 people, 20% of the men and 10% of the women are athletes. If 29 people are athletes in total, how many women were in the survey?

a) 29
b) 90
c) 100
d) 110
e) 200

We are given the following information
1. 20% of the men are athletes
2. 10% of the women are athletes
3. Total number of athletes is 29

Let the total number of women be x.
Therefore, the total number of men is 200-x

The equation formed is 0.2(200 - x) + 0.1x = 29
40 - 0.2x + 0.1x = 29 -> 0.1x = 11 -> x = 110

Therefore, the total number of women in the survey are 110(Option D)
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Re: In a survey of 200 people, 20% of the men and 10% of the women are ath [#permalink]

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08 Mar 2018, 16:45

swong1503 wrote:

In a survey of 200 people, 20% of the men and 10% of the women are athletes. If 29 people are athletes in total, how many women were in the survey?

a) 29
b) 90
c) 100
d) 110
e) 200

We can let m = the number of men and w = the number of women and create the equation:

m + w = 200

m = 200 - w

and

0.2m + 0.1w = 29

2m + w = 290

Substituting 200 - w for m, we have:

2(200 - w) + w = 290

400 - 2w + w = 290

400 - w = 290

110 = w

Answer: D
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