# In a random sample of 80 adults…

## Solution:

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.

**Answer: D**