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.
