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.

Answer 1

Given: {Income} = {salary} + {commission}. Question basically asks: is {salary} > {commission}?

(1) If the amount of the commission had been 30 percent higher, the salesman's income would have been 10 percent higher last year:

1.1({salary} + {commission}) = {salary} + 1.3{commission};

{salary} = 2{commission};

Therefore, {salary} > {commission}. Sufficient.

(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:

|{salary} - {commission}| = 0.5{salary}, notice that {salary} - {commission} is in absolute value sign ||, meaning that we can have two cases:

A. {salary} - {commission} = 0.5{salary};

0.5{salary} = {commission};

{salary} > {commission}, thus the answer would be YES;

Or:

B. {commission} - {salary} = 0.5{salary};

1.5{salary} = {commission};

{salary} < {commission}, thus the answer would be No.

Two different answers. Not sufficient.

Answer: A.

Hope it's clear.