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## In a random sample of 80 adults, how many are college gradua

This topic has 2 expert replies and 0 member replies
jjjinapinch Senior | Next Rank: 100 Posts
Joined
24 Jul 2017
Posted:
83 messages

#### In a random sample of 80 adults, how many are college gradua

Thu Aug 03, 2017 12:18 pm
In a random sample of 80 adults, how many are college graduates?

(1) In the sample, the number of adults who are not college graduates is 3 times the number who are college graduates.
(2) In the sample, the number of adults who are not college graduates is 40 more than the number who are college graduates.

Official Guide question

### GMAT/MBA Expert

Jay@ManhattanReview GMAT Instructor
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Thu Aug 03, 2017 8:41 pm
jjjinapinch wrote:
In a random sample of 80 adults, how many are college graduates?

(1) In the sample, the number of adults who are not college graduates is 3 times the number who are college graduates.
(2) In the sample, the number of adults who are not college graduates is 40 more than the number who are college graduates.

Official Guide question
Statement 1:

Say the number of adults who are college graduates = x, thus,

x + 3x = 80

=> x = 20. Sufficient.

Statement 2:

Say the number of adults who are college graduates = x, thus,

the number of adults who are not college graduates = x + 40

x + (x + 40) = 80

2x = 40

=> x = 20. Sufficient.

Hope this helps!

-Jay
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### GMAT/MBA Expert

Rich.C@EMPOWERgmat.com Elite Legendary Member
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GMAT Score:
800
Thu Aug 03, 2017 8:37 pm
Hi jjjinapinch,

We're told that there is a random sample of 80 adults. We're asked how many are college graduates. This prompt has a built-in Algebra shortcut that we can use to avoid doing some of the math. To start, using the information in the prompt, we can create the following equation:

G + N = 80 where G is the number of college graduates and N is the number of NON-graduates

1) In the sample, the number of adults who are NOT college graduates is 3 times the number who are college graduates.

Using the variables from above, we can use the information in Fact 1 to create the following equation:
N = 3G

Combined with the equation that we initially created (G+N = 80), we now have a 2-variable 'system' of equations. This system will have just ONE solution, so we can figure out the number of college graduates (and we don't have to do the math). IF you wanted to solve it though, here's one way that you could do it using 'substitution'...

N = 3G
G + N = 80
G + (3G) = 80
4G = 80
G = 20
Fact 1 is SUFFICIENT

2) In the sample, the number of adults who are not college graduates is 40 more than the number who are college graduates.

With the information in Fact 2, we can create a new equation using the same 2 variables...
N = G+40

And again, we could solve this system of equations (and we would end up with the same results that we did in Fact 1).
Fact 1 is SUFFICIENT

GMAT assassins aren't born, they're made,
Rich

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Contact Rich at Rich.C@empowergmat.com

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