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20 Nov 2011, 05:44
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Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
75%
(hard)
Question Stats:
64% (03:22) correct
36%
(03:17)
wrong
based on 676
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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?
(A) $22,474
(B) $25,673
(C) $27,318
(D) $28,423
(E) $31,227
(A) $22,474
(B) $25,673
(C) $27,318
(D) $28,423
(E) $31,227
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?
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?
20 Nov 2011, 11:39
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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.
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.
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..
