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

SOLUTION

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. Say the number of college graduates is \(x\), then the number of not college graduates is \(3x\). Thus, \(x+3x=80\). We can find \(x\). Sufficient.

(2) In the sample, the number of adults who are not college graduates is 40 more than the number who are college graduates. Say the number of college graduates is \(x\), then the number of not college graduates is \((x+40)\). Thus, \(x+(x+40)=80\). We can find \(x\). Sufficient.

Answer: D.
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Let the number of adults who are college graduates = x
& number of adults who are not college graduates = y
x+y = 80 ...(1)

1) y = 3x
Putting in equation (1), we get 4x= 80-----Sufficient
2) y = x + 40
Putting in equation (1), we get 2x + 40= 80-----Sufficient

Answer D

Since there are 80 adults we don't need to consider non-adults number here. Otherwise, we would have to solve this by 2X2 matrix.
Either adults are college graduates (X) or not (Y)
Stmt 1) X + Y = 80
Y = 3X
these 2 eq can be solved to get the value of X

Stmt 2) Similar way
X + Y = 80
Y = 40 + X
these 2 eqns can also be solved for value of X

Both statements are sufficient, Hence D

Lets say college going graduate is X
and college not going graduate is Y

form question X + Y = 80.
Option 1: Y = 3X
so, X + 3X = 80 leads to X = 20. Therefore option 1 is sufficient to answer the question.
Option 2: Y - X = 40.
so, 2Y = 120, leads to Y = 60 and X = 20. therefore option 2 is sufficient to anser the question.

Therefor from above both the options are individually sufficient to answer the question => "D" is the correct choice.

Total of 80 adults.
Let C be the college graduates.
let N be the non college grads.

What is C?

(1) N = 3C
3C + C = 80, SUFFICIENT.
(2) N = 40 + C
40 + C + C = 80, SUFFICIENT

answer: D

Basically, we need to solve for x + y = 80, so we need to solve for 2 unknowns, either by solving for one of them or for both at the same time.

1) This statement tells us that x + 3x = 80, we have one equation and one unknown, so it's sufficient.
2) This tells us that (y + 40) + y = 80, so again we have 1 unknown and 1 equation, so we can solve it. Sufficient.

So we go with D.

Rephrase the question
College = 80 - Non College
C = 80 - NC

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

3C + C = 80
4C = 80
C = 20

or

Part 1 3
Part 2 1
Ratio 4

80 = Ratio x 20

Non College = 60
College = 20

Sufficient - Linear equation with one variable

Statement II

NC = C + 40

C = 80 - C + 40
2C = 40
C = 20

Sufficient

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.

From statement one we can say:

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. We can eliminate answer choices B, C, and E.

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.

From statement two, we can say:

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.

The answer is D.
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