GMAT Challenge Series (700+): Q26

Cars.jpg

Question:

In a group of 80 college students, how many own a car? 

(1) Of the students who do not own a car, 14 are male. 
(2) Of the students who own a car, 42% are female.

(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.

MBA Wisdom's Answer:

$$\text{Statement 1:}$$ $$\text{Clearly not sufficent as we do not know how many female students do not own a car}$$ $$\text{Statement 1 is NOT SUFFICIENT}$$ $$$$ $$\text{Statement 2:}$$ $$\text{Let the number of students who own a car be: } \textit{x}$$ $$\text{Female students who own a car} = {0.42}\textit{x} = \frac{21}{50} \textit{x} \text{ (in lowest terms)}$$ $$\text{We know that } \frac{21}{50} \textit{x} \text{ is an integer}$$ $$\text{Therefore, } \textit{x} \text{ must be a multiple of 50: 50, 100, 150...}$$ $$\text{As } \textit{x} \leq {80} \textit{, x} \text{ must equal 50}$$ $$\text{Statement 2 is SUFFICIENT}$$

(B) Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.