Question

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.

• A. Statement (1) alone is sufficient, but statement (2) alone is not sufficient.
• B. Statement (2) alone is sufficient, but statement (1) alone is not sufficient.
• C. Both statements together are sufficient, but neither statement alone is sufficient.
• D. Each statement alone is sufficient.
• E. Statements (1) and (2) together are not sufficient.

Answer 1

Answer: (D)

Each statement alone is sufficient.

• Let us consider $C$ to be the number of college graduates and let $N$ be the number who are not college graduates. Then, $C+N=80$, we need to find the value of $C$.
• Since the number who are not college graduates is 3 times the number who are, $N=3C$ . Then , $C+3C=80$, So,$C=20$. Thus, statement 1 is sufficient.
• Since the number who are not college graduates is $40$ more than the number who are college graduates, $N=C+40$. Then , $C+(C+40)=80$. Solving which we get $C=20$. Thus, statement 2 is sufficient.