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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] New post 25 Nov 2011, 14:19
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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. Was the salesman's commission larger than his base salary last year?

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

(2) The absolute 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.

OPEN DISCUSSION OF THIS QUESTION IS HERE: a-certain-salesman-s-yearly-income-is-determined-by-a-base-126533.html
[Reveal] Spoiler: OA

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Re: A certain salesman's yearly income is determined by a base [#permalink] New post 26 Nov 2011, 00:53
Clearly (A).

Using (1), if a 30 percent change in the commission only creates a 10 percent change overall, it is clear that the commission is smaller than the base. Sufficient.

Using (2), we can't conclude anything because we are given the absolute difference, so either of the quantities may be bigger.
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Re: A certain salesman's yearly income is determined by a base [#permalink] New post 26 Nov 2011, 04:10
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Yes A.

if income is i, base salary is b and commission is c we know that i = b + c

the information in 1. can be expressed as 1.1i = b + 1.3c

substituting i = b +c gives:
1.1(b + c) = b + 1.3c

this resolves to b = 2c (the base is twice the size of the commission).

SUFFICIENT

2. can be expressed as |c - b| = b/2

This can be solved two ways:
if the commission is larger we get
c - b = b/2
2/3c = b (the base is two thirds of the commission - i.e. the commission is larger)

if the base is larger we get
b -c = b/2
b = 2c (the base is twice the commission - i.e. the base is larger)

INSUFFICIENT.

therefore it is A.
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Re: A certain salesman's yearly income is determined by a base [#permalink] New post 26 Aug 2014, 20:56
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Re: A certain salesman's yearly income is determined by a base [#permalink] New post 27 Aug 2014, 03:25
Expert's post
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.

OPEN DISCUSSION OF THIS QUESTION IS HERE: a-certain-salesman-s-yearly-income-is-determined-by-a-base-126533.html
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Re: A certain salesman's yearly income is determined by a base   [#permalink] 27 Aug 2014, 03:25
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