Hi aditiniyer,

This question can be solved by TESTing THE ANSWERS.

Here, we're given Jim"s pay rate ($200/week + $9 per question), we're told that he works for 50 weeks out of the year and that he writes an ODD number of questions greater than 20. As an example, I'm going to calculate the LEAST amount of money that he could have earned....

IF... he wrote just 21 questions for the year, he would have made...

$200(50) + $9(21) = 10,000 + 189 = $10,189

Now we have the 'framework' to figure out what his MEDIAN income COULD have been: $10,000 + $9(ODD number). We can use the 'rule of 9' to eliminate answers that aren't possible:

Answer A: $22,474 - $10,000 = $12,474 IS divisible by 9, BUT is it an ODD multiple of 9.... 12474/9 = 1386 NOT ODD. Eliminate A
Answer B: $25,673 - $10,000 = $15,673 NOT divisible by 9. Eliminate B
Answer C: $27,318 - $10,000 = $17,318 NOT divisible by 9. Eliminate C
Answer D: $28,423 - $10,000 = $18,423 IS divisible by 9, BUT is it an ODD multiple of 9.... 18423/9 = 2047 IT'S ODD.

Since we can easily add or subtract $18 increments to this total, this COULD be the median value for the 5-year period.

Final Answer: D

GMAT assassins aren't born, they're made,
Rich

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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