# GMAT Challenge Series (700+): Q24

Question:

A certain salesman's yearly income is determined by a base salary plus a commission on the sales he makes during the year. Did the salesman's base salary account for more than half of the salesman's yearly income last year?

(1) If the amount of the commission had been 30 percent higher, the salesman's income would have been 10 percent higher last year.
(2) The difference between the amount of the salesman's base salary and the amount of the commission was equal to 50 percent of the salesman's base salary last year.

(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.

$$\text{Income} = \text{Salary} + \text{Commission}$$ $$\text{The question is effectively asking if: } \text{Salary} > \text{Commission?}$$  $$\text{Statement 1:}$$ $${1.1}{\left( {\text{Salary} + \text{Commission}} \right)} = \text{Salary} + {1.3}{\left( \text{Commission} \right)}$$ $${0.1}\left( \text{Salary} \right) = {0.2}\left( \text{Commission} \right)$$ $$\text{Salary} = {2}\left( \text{Commission} \right)$$ $$\text{Therfore, } \text{Salary} > \text{Commission}$$ $$\text{Statement 1 is SUFFICIENT}$$  $$\text{Statement 2:}$$ $$\left|\text{Salary} - \text{Commission} \right| = {0.5}\left( \text{Salary} \right)$$  $$\text{Case 1: } {\text{Salary} - \text{Commission}} > {0}$$ $$\text{Salary} - \text{Commission} = {0.5}\left( \text{Salary} \right)$$ $${0.5}\left( \text{Salary} \right) = \text{Commission}$$ $$\text{Salary} = {2}\left( \text{Commission} \right)$$ $$\text{In this case, } \text{Salary} > \text{Commission}$$  $$\text{Case 2: } \text{Salary} - \text{Commission} < {0}$$ $$\text{Commission} - \text{Salary} = {0.5}\left( \text{Salary} \right)$$ $$\text{Commission} = {1.5}\left( \text{Salary} \right)$$ $$\text{In this case, } \text{Salary} < \text{Commission}$$  $$\text{Different answers in each case}$$ $$\text{Statement 2 is NOT SUFFICIENT}$$