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In Company X, 30 percent of the employees live over ten miles from wor

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Bunuel
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In Company X, 30 percent of the employees live over ten miles from wor [#permalink] New post   28 Jun 2017, 03:34
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In Company X, 30 percent of the employees live over ten miles from work and 60 percent of the employees who live over ten miles from work use car pools. If 40 percent of the employees of Company X use car pools, what percent of the employees of Company X live ten miles or less from work and use car pools?

(A) 12%
(B) 20%
(C) 22%
(D) 28%
(E) 32%
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C
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sashiim20
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Re: In Company X, 30 percent of the employees live over ten miles from wor [#permalink] New post   28 Jun 2017, 05:13
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Bunuel wrote:
In Company X, 30 percent of the employees live over ten miles from work and 60 percent of the employees who live over ten miles from work use car pools. If 40 percent of the employees of Company X use car pools, what percent of the employees of Company X live ten miles or less from work and use car pools?

(A) 12%
(B) 20%
(C) 22%
(D) 28%
(E) 32%


Let the total number of employee \(= 100\)

\(30\)% of employee live over \(10\) miles = 30% of 100 \(= \frac{30}{100} * 100 = 30\)

\(60\)% of \(30\)% of employee living over \(10\) miles use car pools \(= \frac{60}{100} * 30 = 18\)

\(40\)% of total employee use car pools = 40% of 100 \(= \frac{40}{100} * 100 = 40\)

Therefore total number employee living under \(10\) miles or less using car pools \(= 40 - 18 = 22\).

Required percent = Number of employee living under 10 miles or less using car pools / Total employee \(= \frac{22}{100} * 100 = 22\)%. Answer (C)...
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Re: In Company X, 30 percent of the employees live over ten miles from wor [#permalink] New post   28 Jun 2017, 05:58
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Total number can be assumed as 100 as the question is gives only percents and no concrete numbers

Number of employees who live more than 10 miles away, and carpool = 30*\(\frac{60}{100}\) = 18
Total number of employees who car pool is given as 40% = 40

Number of employees who car live 10 miles or less and carpool = 40-18 = 22 or 22%
Answer C
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Re: In Company X, 30 percent of the employees live over ten miles from wor [#permalink] New post   30 Jun 2017, 09:19
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Bunuel wrote:
In Company X, 30 percent of the employees live over ten miles from work and 60 percent of the employees who live over ten miles from work use car pools. If 40 percent of the employees of Company X use car pools, what percent of the employees of Company X live ten miles or less from work and use car pools?

(A) 12%
(B) 20%
(C) 22%
(D) 28%
(E) 32%


We can let the total number of people in Company X = 100.

Thus, since 30% of the employees lives more than ten miles from work and 60% of those employees use car pools:

100 x 0.3 x 0.6 = 18 employees live more than ten miles from work and use car pools.

We are also given that 0.4 x 100 = 40 employees use car pools.

Thus, 40 - 18 = 22 employees or 22% of the employees live 10 miles or less from work and use car pools.

Answer: C
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Re: In Company X, 30 percent of the employees live over ten miles from wor [#permalink] New post   30 Jun 2017, 14:10
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I hope it helps.
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Re: In Company X, 30 percent of the employees live over ten miles from wor [#permalink] New post   12 Feb 2020, 07:45
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Bunuel wrote:
In Company X, 30 percent of the employees live over ten miles from work and 60 percent of the employees who live over ten miles from work use car pools. If 40 percent of the employees of Company X use car pools, what percent of the employees of Company X live ten miles or less from work and use car pools?

(A) 12%
(B) 20%
(C) 22%
(D) 28%
(E) 32%


One approach is to use the Double Matrix Method. This technique can be used for most questions featuring a population in which each member has two characteristics associated with it (aka overlapping sets questions).

Here, we have a population of employees , and the two characteristics are:
- lives over ten miles from work or doesn't live over ten miles from work
- uses carpool or doesn't use carpool

Here's how we can set up the Matrix:


I'll let you complete the diagram.

Please note that this question type is VERY COMMON on the GMAT, so be sure to master the technique.

Here's a video covering the technique:


Here's an extra practice question:


Cheers,
Brent
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In Company X, 30 percent of the employees live over ten miles from wor [#permalink] New post   14 Feb 2020, 14:08
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Bunuel wrote:
In Company X, 30 percent of the employees live over ten miles from work and 60 percent of the employees who live over ten miles from work use car pools. If 40 percent of the employees of Company X use car pools, what percent of the employees of Company X live ten miles or less from work and use car pools?

(A) 12%
(B) 20%
(C) 22%
(D) 28%
(E) 32%
 


If there are 100 employees, then 30 employees live more than 10 miles from work, 0.6 x 30 = 18 employees live more than 10 miles from work and use car pools, and 40 employees use car pools. Therefore, 40 - 18 = 22, or 22%, of the employees live ten miles or less from work and use car pools.

Answer: C­
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Re: In Company X, 30 percent of the employees live over ten miles from wor [#permalink] New post   03 Mar 2024, 13:54
Isn't 22 out of 70 will be the percentage of people who live in less than 10 miles and use carpool? I could see we have said 22% is the answer. shouldnt it be (22/70) * 100?
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Re: In Company X, 30 percent of the employees live over ten miles from wor [#permalink] New post   04 Mar 2024, 00:24
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anikpait17 wrote:
Isn't 22 out of 70 will be the percentage of people who live in less than 10 miles and use carpool? I could see we have said 22% is the answer. shouldnt it be (22/70) * 100?

­Your question is addresses in the solutions above. I suggest reviewing them more carefully. Hopefully, they could help pinpoint the error in your logic.
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Re: In Company X, 30 percent of the employees live over ten miles from wor [#permalink]
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