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OG #55

by fangtray » Sat Mar 17, 2012 9:29 pm
Guy's net income equals his gross income minus his deductions. By what percent did Guy's net income change on Jan 1st, 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 1st, 1989.

What is a fast way to do this problem? These types take me too long to for me to do. When I plug different scenarios.
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Source: — Data Sufficiency |

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by Anurag@Gurome » Sun Mar 18, 2012 4:22 am
fangtray wrote:Guy's net income equals his gross income minus his deductions. By what percent did Guy's net income change on Jan 1st, 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 1st, 1989.

What is a fast way to do this problem? These types take me too long to for me to do. When I plug different scenarios.
Net Income = Gross Income - Deductions
If we assume net income = n, gross income = g and deductions = d, then n = g - d

(1) Guy's gross income increased by 4 percent on January 1, 1989 gives no info on deductions; NOT sufficient.

(2) Guy's deductions increased by 15 percent on January 1st, 1989 gives no info on gross income; NOT sufficient.

Combining (1) and (2), New net income = (g + 0.04g) - (d + 0.15d) = 1.04g - 1.15d
Therefore, percent change = {[(1.04g - 1.15d) - (n - d)]/(n - d)} * 100 bit we cannot solve this as it has 2 variables; NOT sufficient.

The correct answer is E.
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