Gmat_mission wrote: ↑

Sun Aug 08, 2021 10:35 am

Guy's net income equals his gross income minus his deductions. By what percent did Guy's net income change on January 1, 1989, when both his gross income and his deductions increased?

(1) Guy's gross income increased by 4 percent on January 1, 1989.
(2) Guy's deductions increased by 15 percent on January 1, 1989.

Answer: E

Source: Official Guide

Given: Guy's net income equals his gross income minus his deductions.

Target question: By what percent did Guy's net income change on January 1, 1989, when both his gross income and his deductions increased?

When I SCAN the two statements, they both feel insufficient, AND I’m pretty sure I can identify some cases with conflicting answers to the target question. So, I’m going to head straight to……

Statements 1 and 2 combined
Statement 1 tells us that Guy's gross income increased by 4 percent on January 1, 1989
Statement 2 tells us that Guy's deductions increased by 15 percent on January 1, 1989.
Let's examine two possible cases:

Case a: Guy's gross income WAS $200 and his deductions WERE $100.
So, his PREVIOUS net income = $200 - $100 = $100

AFTER the increases, Guy's gross income is $208 and his deductions are $115.
So, his CURRENT net income = $208 - $115 = $93

Guy's net income went from $100 to $93, which represents a 7% DECREASE in net income


Case b: Guy's gross income WAS $1000 and his deductions WERE $20.
So, his PREVIOUS net income = $1000 - $20 = $980

AFTER the increases, Guy's gross income is $1040 and his deductions are $23
So, his CURRENT net income = $1040 - $23 = $1017

Guy's net income went from $980 to $1017, which represents some INCREASE in net income

Since we cannot answer the target question with certainty, the combined statements are NOT SUFFICIENT

Answer: E

Cheers,
Brent