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Jim Broke’s only source of income comes from his job as a qu

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Director
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Status: Preparing for the 4th time -:(
Joined: 25 Jun 2011
Posts: 563
Location: United Kingdom
Concentration: International Business, Strategy
GMAT Date: 06-22-2012
GPA: 2.9
WE: Information Technology (Consulting)
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Jim Broke’s only source of income comes from his job as a qu [#permalink] New post 20 Nov 2011, 04:44
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A
B
C
D
E

Difficulty:

  55% (medium)

Question Stats:

55% (03:29) correct 45% (03:20) wrong based on 41 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?

(A) $22,474
(B) $25,673
(C) $27,318
(D) $28,423
(E) $31,227

[Reveal] Spoiler:
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?
[Reveal] Spoiler: OA

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Joined: 29 Oct 2011
Posts: 189
Concentration: General Management, Technology
Schools: Sloan '16 (D)
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Re: Jim's Income [#permalink] New post 20 Nov 2011, 10:39
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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.
Director
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Status: Preparing for the 4th time -:(
Joined: 25 Jun 2011
Posts: 563
Location: United Kingdom
Concentration: International Business, Strategy
GMAT Date: 06-22-2012
GPA: 2.9
WE: Information Technology (Consulting)
Followers: 13

Kudos [?]: 374 [0], given: 217

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Re: Jim's Income [#permalink] New post 20 Nov 2011, 21:18
Great explanation Kostyan. Much appreciated.
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E.

MGMAT 1 --> 530
MGMAT 2--> 640
MGMAT 3 ---> 610 :-(

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Re: Jim's Income [#permalink] New post 18 Sep 2013, 23:51
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Re: Jim's Income   [#permalink] 18 Sep 2013, 23:51
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