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For each month of a given year except December, a worker

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by AAPL » Wed Aug 29, 2018 4:51 am

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B

C

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For each month of a given year except December, a worker earned the same monthly salary and donated one-tenth of that salary to charity. In December, the worker earned N times his usual monthly salary and donated one-fifth of his earnings to charity. If the worker's charitable contributions totaled one-eighth of his earnings for the entire year, what is the value of N?

A. 8/5
B. 5/2
C. 3
D. 11/3
E. 4

OA D.
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by Jeff@TargetTestPrep » Wed Sep 05, 2018 9:44 am
AAPL wrote:Manhattan Prep

For each month of a given year except December, a worker earned the same monthly salary and donated one-tenth of that salary to charity. In December, the worker earned N times his usual monthly salary and donated one-fifth of his earnings to charity. If the worker's charitable contributions totaled one-eighth of his earnings for the entire year, what is the value of N?

A. 8/5
B. 5/2
C. 3
D. 11/3
E. 4
We can let the normal salary = k, so his total salary for the first 11 months was 11k. Each month k/10 went to charity, so for the first 11 months, his total charitable contribution was 11k/10.

The December salary was kN, and kN/5 was donated to charity.

Since the worker's charitable contributions totaled one-eighth of his earnings for the entire year:

kN/5 + 11k/10 = (kN + 11k)/8

Multiplying the equation by 40, we have:

8kN + 44k = 5kN + 55k

Dividing the equation by k, we have:

8N + 44 = 5N + 55

3N = 11

N = 11/3

Answer: D

Jeffrey Miller
Head of GMAT Instruction
[email protected]

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by swerve » Thu Sep 06, 2018 11:00 am
Let monthly salary for each of the 11 months except December was x, then

$$11x*\frac{1}{10}+Nx*\frac{1}{5}=\frac{1}{8}(11x+Nx);$$
$$\frac{11}{10}+\frac{N}{5}=\frac{1}{8}(11+N)$$
$$N=\frac{11}{13}$$

Hence, D is the correct answer.
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