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# In a certain large company, the ratio of college graduates with a grad

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Math Expert
Joined: 02 Sep 2009
Posts: 55276

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27 Sep 2015, 12:17
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Difficulty:

75% (hard)

Question Stats:

56% (02:22) correct 44% (02:31) wrong based on 191 sessions

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In a certain large company, the ratio of college graduates with a graduate degree to non-college graduates is 1:8, and ratio of college graduates without a graduate degree to non-college graduates is 2:3. If one picks a random college graduate at this large company, what is the probability this college graduate has a graduate degree?

A) 1/11
B) 1/12
C) 1/13
D) 3/19
E) 3/43

Kudos for a correct solution.

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Joined: 12 Sep 2015
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27 Sep 2015, 13:19
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Bunuel wrote:
In a certain large company, the ratio of college graduates with a graduate degree to non-college graduates is 1:8, and ratio of college graduates without a graduate degree to non-college graduates is 2:3. If one picks a random college graduate at this large company, what is the probability this college graduate has a graduate degree?

A) 1/11
B) 1/12
C) 1/13
D) 3/19
E) 3/43

Kudos for a correct solution.

It took me a while to see there are, indeed, 3 types of worker.
Let B = # of non-college graduates

Given: A : B = 1 : 8
Given: C : B = 2 : 3

Since both ratios share B, we need to create equivalent fractions that have the same value for B.
A : B = 1 : 8 = 3 : 24
C : B = 2 : 3 = 16 : 24

So, A : B : C = 3 : 24 : 16
3 + 24 + 16 = 43

So, for every 43 workers, there are:

If one picks a random college graduate at this large company, what is the probability this college graduate has a graduate degree?
We are picking a college graduate.
From the above info, we ignore the number of non-college graduates.
So, for every 19 college graduates, 3 have a graduate degree and 16 do not.

Cheers,
Brent
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##### General Discussion
Manager
Joined: 29 Jul 2015
Posts: 157

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27 Sep 2015, 13:51
Bunuel wrote:
In a certain large company, the ratio of college graduates with a graduate degree to non-college graduates is 1:8, and ratio of college graduates without a graduate degree to non-college graduates is 2:3. If one picks a random college graduate at this large company, what is the probability this college graduate has a graduate degree?

A) 1/11
B) 1/12
C) 1/13
D) 3/19
E) 3/43

Kudos for a correct solution.

Let A be the number of college graduates with degree, B be the number of college graduates without a degree and C be the number of non-college graduates.
It is given that A:C is 1:8 or 3:24 and B:C is 2:3 or 16:24.
Then by scaling, we have A:B:C =3:16:24
Total number of college graduates is A+B = 3+16=19
Probability of choosing a college graduate with degree will be
$$\frac{A}{A+B}=\frac{3}{19}$$

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28 Sep 2015, 12:19
Attachments

Largecompany-Grad.jpg [ 786.15 KiB | Viewed 2282 times ]

Manager
Joined: 23 Aug 2012
Posts: 73
Concentration: Technology
GMAT 1: 710 Q47 V40

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30 Sep 2015, 08:06

0) we are told the following ratios

CGD - College Graduate with Degree
CGN - College Graduate no Degree

CGD NCG CGN
1 8
3 2

In order to make CGD and CGN comparable we need to find the least common multiple of 8 and 3 and that is 24 multiplying the first ratio by 3 and the second ratio by 8 we get

CGD NCG CGN
3 24 16

If one picks a random college graduate at this large company, what is the probability this college graduate has a graduate degree?

Nr of CGD = 3
Nr of CG = 3+ 16 = 19

Probability of CGD / (CG) -> 3/19

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18 Jan 2019, 06:41
Bunuel wrote:
In a certain large company, the ratio of college graduates with a graduate degree to non-college graduates is 1:8, and ratio of college graduates without a graduate degree to non-college graduates is 2:3. If one picks a random college graduate at this large company, what is the probability this college graduate has a graduate degree?

A) 1/11
B) 1/12
C) 1/13
D) 3/19
E) 3/43

Kudos for a correct solution.

Let x be graduates with a degree,
y be " without a degree, and

as the problem says:
$$\frac{x}{NC}=\frac{1}{8}$$; so $$x=(\frac{1}{8})NC$$
$$\frac{y}{NC}=\frac{2}{3}$$; so $$y=(\frac{2}{3})NC$$

and we need to find $$\frac{x}{x+y}$$; so $$(1/8)NC/(1/8+2/3)NC$$
canceling out NC we get: $$\frac{3}{19}$$; answer choice D.
Re: In a certain large company, the ratio of college graduates with a grad   [#permalink] 18 Jan 2019, 06:41
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