aditiniyer wrote:Jim Broke's only source of income comes from his job as a question writer. In this capacity, Jim earns a flat salary of $200 per week plus a fee of $9 for every question that he writes. Every year Jim takes exactly 2 weeks of unpaid vacation. If a regular year consists of 52 weeks and the number of questions that Jim wrote in each of the past 5 years was an odd number greater than 20, which of the following could be Jim's median annual income over the past 5 years ?
A) $22,474
B) $25,673
C) $27,318
D) $28,423
E) $31,227
Hi aditiniyer,
We have Jim's remuneration = $(500 x 200 + 9 x # of qns)
Remuneration = 10000 + 9 x (an odd number) = Even + Odd = Odd.
This means that Jim's yearly remuneration would be an odd number for each of the 5 years, thus the median would also be an odd number. This way, we can discard option A and C.
Let's test the other three options B, D, and E.
Option B: $25,673
The remuneration through question making = $25,673 - 10000 = 15,673.
Since 15,673 = 9 x (an odd number), 15,673 must be divisible by '9.'
We know the divisibility rule of '9': Sum of the digits of a number must be divisible by 9.
Sum of digits of 15,673 = 1+5+6+7+3 = 22. Since 22 is not divisible by 9, option B cannot be a median value.
Option D: $28,423
The remuneration through question making = $28,423 - 10000 = 18,423.
Since 15,673 = 9 x (an odd number), 15,673 must be divisible by '9.'
We know the divisibility rule of '9': Sum of the digits of a number must be divisible by 9.
Sum of digits of 18,423 = 1+8+4+2+3 = 18. Since 18 is divisible by 9, and 18,423/9 = 2047 (an odd number), option D can be a median value.
Since this is a could be type of question, we need not test option E.
The correct answer:
D
Hope this helps!
Relevant book:
Manhattan Review GMAT Math Essentials Guide
-Jay
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