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Jim Broke’s only source of income comes from his job as a qu [#permalink]
20 Nov 2011, 04:44

1

This post was BOOKMARKED

00:00

A

B

C

D

E

Difficulty:

85% (hard)

Question Stats:

58% (03:48) correct
42% (03:09) wrong based on 46 sessions

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 two weeks of unpaid vacation to visit his uncle, a monk in Tibet, and get inspired for the next year. 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?

Ok - as the OA is not provided for this questions this is how I tried to solve it, but got stuck and didn't complete.

Regular year has 52 weeks, so total number of weeks = 260 Total week's that Jim takes off = 10 Total number of weeks he worked = 250

Let's say Jim wrote 21 questions per year, so in total he wrote = 105 questions. Therefore, income from questions = 105 * 9 = 945 Normal income = 200 * 250 = 50, 000

I am struggling to solve after this. Can someone please help?

Jim works 50 weeks per year (52-2). Therefore, he's income in a particular year is 50*200+9*(# of questions) = 10,000 + 9*(# of questions) and # of questions is odd.

Since they are asking for a median (as opposed to mean), the answer must be one of the actual incomes.

9 * odd number of questions is odd. So you can immediately cross out A and C.

Out of the remaining choices:

Income = 10,000 9 * # of questions Income - 10,000 = 9 * # of questions

Since # of questions is an integer, (Income - 10,000) must be divisible by 9. Divisibility by 9 is easy to test, so you subtract 10,000 from B, D, and E, and see which result is divisible by 9.

The answer is D. (28,423-10,000) = 18,423 is the only one divisible by 9.

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

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