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Jim Broke’s only source of income comes from his job as a qu [#permalink]

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20 Nov 2011, 05:44

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00:00

A

B

C

D

E

Difficulty:

75% (hard)

Question Stats:

65% (02:23) correct
35% (02:41) wrong based on 246 sessions

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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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Re: Jim Broke’s only source of income comes from his job as a qu [#permalink]

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20 Nov 2014, 09:29

Hello from the GMAT Club BumpBot!

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Jim Broke’s only source of income comes from his job as a qu [#permalink]

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02 May 2015, 05:36

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Okay u just need less than one min to answer this question. any odd number greater than 20 means that that last digit must be 1,3,5,7, or 9. 9$ per week for every question. So (odd)(odd) will give odd digit. A and C out. (50 weeks) (200) = 10,000. subtract this amount from option A, D and E and u will find that only option D is divisible by 9 (once 10,000 is subtracted from 28423) so its the right choice..No mathematics..
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Jim Broke’s only source of income comes from his job as a qu [#permalink]

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25 Sep 2015, 06:27

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Not so calculation intensive if we just invest a few seconds in planning:

Step 1: We will get following equation: Total Salary = 52 * $200 - 2*$200 + 9 * (some odd number > 20)

With little simplification we got Total Salary = $10,000 + 9 * (some odd number > 20)

Step 2 (planning): We can deduce from above equation and available answer choices that calculation is going to be stingy so let's try backtrack from given options.

Now let's eliminate.

Trick 1: For a number to be divisible by 9, sum of all the digits must be equal to 9. Trick 2: 9 (odd) * some odd number => Last digit must be an odd number

Step 3 (Elimination): To apply trick 1, we have to decrease ten thousands place number with 1 (Total salary - 10,000) and then do divisibility test. This will eliminate B,C and E.

Trick 2 will eliminate A and C.

Only option that we are left with is D.
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Re: Jim Broke’s only source of income comes from his job as a qu [#permalink]

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25 Sep 2015, 11:17

Thought this question is not that calculation intensive, figuring out the tricks might take sometime. To increase up speed for such questions, in my opinion, try to solve MGMAT Quant Advanced Strategy Guide.

bdw this question took 2:17 for me.

vinnisatija wrote:

it took me more than 4 minutes to solve this question.Is it too long ?

Re: Jim Broke’s only source of income comes from his job as a qu [#permalink]

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10 Dec 2016, 13:00

Hello from the GMAT Club BumpBot!

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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Re: Jim Broke’s only source of income comes from his job as a qu [#permalink]

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10 Dec 2016, 13:02

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Below one is an amazing solution but I think you misses "+" sign.

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.
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