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

Great explanation Kostyan. Much appreciated.

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.

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

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.



Hope it helps

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.

There are 5 salaries in the Set for which we need to find the Median

median = 3rd salary in set when the salaries are listed in ascending order from least to greatest

A salary for any given year =

(50)(200) + (9) * (Odd No. of Questions written)

= 10,000 + (9) * (ODD #)

One of the answer choices = Median = must be one of the Salaries he made so

(Answer Choice value) -10,000 = (9) * (ODD #)


Subtracting 10,000 will remove -(1) digit from the Sum of Digits for each answer choice.

Thus, to be Divisible by 9 (since Questions written is an Integer) ———>

(Sum of Answer’s Digits) - (1) = Multiple of 9


(D)
$28,423

(2 + 8 + 4 + 2 + 3) - (1) =

(19) - (1) = 18——> multiple or 9

Only answer D is a possible Median salary

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smart question which requires options elimination combined with number theory.