A certain salesman's yearly income is determined by a base

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A certain salesman's yearly income is determined by a base [#permalink]

25 Jan 2012, 00:22

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A certain salesman's yearly income is determined by a base salary plus a commission on the sales he makes during the year. Did the salesman's base salary account for more than half of the salesman's yearly income last year?

(1) If the amount of the commission had been 30 percent higher, the salesman's income would have been 10 percent higher last year.

(2) The difference between the amount of the salesman's base salary and the amount of the commission was equal to 50 percent of the salesman's base salary last year.

[Reveal] Spoiler: OA

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Re: DS - Percentage [#permalink]

25 Jan 2012, 03:10

devinawilliam83 wrote:

Why is the answer to this A and not D?

A certain salesman's yearly income is determined by a base salary plus a commission on the sales he makes during the year. Did the salesman's base salary account for more than half of the salesman's yearly income last year?

Given: {Income}={salary}+{commission}. Question basically asks: is {salary}>{commission}?

(1) If the amount of the commission had been 30 percent higher, the salesman's income would have been 10 percent higher last year --> 1.1({salary}+{commission})={salary}+1.3{commission} --> {salary}=2{commission} --> {salary}>{commission}. Sufficient.

(2) The difference between the amount of the salesman's base salary and the amount of the commission was equal to 50 percent of the salesman's base salary last year --> |{salary}-{commission}|=0.5{salary}, notice that {salary}-{commission} is in absolute value sign ||, meaning that we can have two cases:

A. {salary}-{commission}=0.5{salary} --> 0.5{salary}={commission} --> {salary}>{commission}, thus the answer would be YES;
Or:
A. {commission}-{salary}=0.5{salary} --> 1.5{salary}={commission} --> {salary}<{commission}, thus the answer would be No.
Not sufficient.

Answer: A.

Hope it's clear.
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Re: A certain salesman's yearly income is determined by a base [#permalink]

21 Jun 2012, 03:54

please explain why salary - commission is in absoulute value sign?

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Re: A certain salesman's yearly income is determined by a base [#permalink]

21 Jun 2012, 04:04

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jaswinder46 wrote:

please explain why salary - commission is in absoulute value sign?

Because if {salary}>{commission} then {salary}-{commission}=0.5{salary}, since 0.5{salary}>0.

But if {salary}<{commission} then {commission}-{salary}=0.5{salary}.

So, the second statement, which says that "the difference between the amount of the salesman's base salary and the amount of the commission was equal to 50 percent of the salesman's base salary last year" should be expressed as |{salary}-{commission}|=0.5{salary}.
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Re: A certain salesman's yearly income is determined by a base [#permalink] 21 Jun 2012, 04:04

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A certain salesman's yearly income is determined by a base

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