# GMAT OFFICIAL GUIDE DS – Guy’s net income equals his gross…

## Solution:

We are given that Guy’s net income is equal to his gross income minus his deductions and we want to determine by what percent did his net income change on January 1, 1989, when both his gross income and his deductions increased.

Statement One Alone:

Guy’s gross income increased by 4 percent on January 1, 1989.

Since we don’t know anything about his deductions, statement one does not have sufficient information for us to determine the percent change in his net income. We can eliminate answer choices A and D.

Statement Two Alone:

Guy’s deductions increased by 15 percent on January 1, 1989.

Since we don’t know anything about his gross income, statement two does not have sufficient information for us to determine the percent change in his net income. We can eliminate answer choice B.

Statements One and Two Together:

Let g = his old gross income and d = his old deductions. Using the information from statements one and two we can express his new gross income as 1.04g and his new deductions as 1.15d.

The percent change in his net income is

(new net income)/(old net income) x 100.

In other words, the percent change is

(new gross income – new deductions)/(old gross income – old deductions) x 100.

Thus, the percent change is

(1.04g – 1.15d)/(g – d) x 100.

However, we see that we still do not have enough information to determine the percent change in his net income since we still don’t know the values of g and d.