Data Sufficiency

AbeNeedsAnswers wrote:If 90 students auditioned for the school musical, how many were accepted?

(1) 2/3 of the boys and 1/3 of the girls who auditioned were accepted.
(2) 26 of the boys who auditioned were accepted.

We are given that 90 students auditioned for a musical, and we need to determine how many were accepted.

Statement One Alone:

2/3 of the boys and 1/3 of the girls who auditioned were accepted.

With statement one, we can set up two equations in which b = the number of the boys who auditioned and g = the number of girls who auditioned:

b + g = 90

(2/3)b + (1/3)g = total accepted

We see we do not have enough information to determine how many students were accepted since we neither know the number of boys nor the number of girls.

Statement one is not sufficient to answer the question.

Statement Two Alone:

26 of the boys who auditioned were accepted.

Without knowing how many girls were accepted, we do not have enough information to determine how many total students were accepted. Statement two is not sufficient to answer the question.

Statements One and Two Together:

From statements one and two we know the following:

b + g = 90

(2/3)b + (1/3)g = total accepted

We also know that 26 boys who auditioned were accepted. Thus we can say:

(2/3)b = 26

b = 26 x 3/2

b = 39

Since there are 39 boys and 90 total students, we know there are 90 - 39 = 51 total girls. We also know that 1/3 of the girls who auditioned were accepted. Thus, we know that 51 x 1/3 = 17 is the number of girls who were accepted. So finally we can say:

A total of 39 boys + 17 girls = 56 students who auditioned were accepted.

Answer: C