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.
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
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