girindra wrote:

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.

A. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.

B. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.

C. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.

D. EACH statement ALONE is sufficient.

E. Statements (1) and (2) TOGETHER are NOT sufficient.

I find it helps to write down the given relation:

Net Income = Gross Income - Deductions

Ques: By what % did Net Income increase if both Gross Income and Deductions increase?

First up, what comes to mind is that if both Gross Income and Deductions increase by the same percentage, Net Income will increase by the same % too.

Say, both increase by 10%,

New Net Income = (110/100)Gross Income - (110/100)Deductions

New Net Income = (110/100)(Gross Income - Deductions) = (110/100) Net Income

But here, even if we consider both statements together, we get

New Net Income = (104/100)Gross Income - (115/100)Deductions

There is no way we can find how New Net Income is related to Net Income. It will depend on the values of Gross Income and Deductions. (Take Gross Income as 100 and Deductions as 50 in one case and Deductions as 25 in another to see that Net Income changes by a different % in the two cases.)

Answer (E).

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