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
OA D.
5-Day Free Trial
5-day free, full-access trial TTP
Available with Beat the GMAT members only code
MORE DETAILS
For each month of a given year except December, a worker
This topic has expert replies
GMAT/MBA Expert
-
Jeff@TargetTestPrep
- GMAT Instructor
- Posts: 1462
- Joined: Thu Apr 09, 2015 9:34 am
- Location: New York, NY
- Thanked: 39 times
- Followed by:22 members
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.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
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]
See why Target Test Prep is rated 5 out of 5 stars on BEAT the GMAT. Read our reviews
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.
$$11x*\frac{1}{10}+Nx*\frac{1}{5}=\frac{1}{8}(11x+Nx);$$
$$\frac{11}{10}+\frac{N}{5}=\frac{1}{8}(11+N)$$
$$N=\frac{11}{13}$$
Hence, D is the correct answer.
