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

[jjjinapinch]

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
Answer: D

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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

Final Answer: D

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

[Jay@ManhattanReview]

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
Answer: D

Statement 1:

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

the number of adults who are not college graduates = 3x

=> The number of adults who are college graduates + The number of adults who are not college graduates = Total number of adults

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

=> The number of adults who are college graduates + The number of adults who are not college graduates = Total number of adults

x + (x + 40) = 80

2x = 40

=> x = 20. Sufficient.

The correct answer: D

Hope this helps!

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-Jay
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[Scott@TargetTestPrep]

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.

We need to determine the number of college graduates in a sample of 80 adults. Because some of the 80 adults are college graduates, while others are not, let's define two variables:

c = the number of adults who are college graduates

n = the number of adults who are not college graduates

Since there are 80 adults in the random sample, we can create the following equation:

c + n = 80

Statement One Alone:

In the sample, the number of adults who are not college graduates is 3 times the number who are college graduates.

Thus:

n = 3c

Since n = 3c, we can plug 3c for n into the equation c + n = 80.

c + 3c = 80

4c = 80

c = 20

Thus, there are 20 college graduates. Statement one is sufficient to answer the question.

Statement Two Alone:

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

Thus:

n = 40 + c

Since 40 + c = n, we can substitute 40 + c for n into the equation c + n = 80.

c + 40 + c = 80

2c = 40

c = 20

There are 20 college graduates.

Statement two is also sufficient to answer the question.

Answer: D

[rishab0507]

total : 80

Statement 1 :
NG =3x, G = x
So equation can be made: x+3 x = 80 , solve for X : Sufficient

Statement 2:
NG : x+40 , G : X
Add both : 2x +40 =80
Solve for X
sufficient

D is answer

[SampathKp]

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
Answer: D

Total no: adults in the sample is 80

Let number of college graduates be X. No: of students who are not college graduates = 80-X

From (1) x +3x =80 x = 20. This information is sufficient to answer the question

From (2) X+ X+40 = 80 = 2X= 80. X = 40 . This information is sufficient to answer the question.

Hence Answer is D