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

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24 Jan 2012, 23:22

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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.

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.

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}.
_________________

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.

Hi Bunnel, If i do assume that C>S, this will contradict information given in A.

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.

Hi Bunnel, If i do assume that C>S, this will contradict information given in A.

Is this an Official question?

What do you mean by official question? Check the tags. It's MGMAT.
_________________

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

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17 Aug 2013, 02:16

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.
_________________

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.

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.

I don't know how answer choice A can be sufficient. See example below.

Using your statement: 1.1({salary}+{commission})={salary}+1.3{commission}

1.1 s + 1.1 c = s + 1.3 c ; for sake of simplicity, let's say that salary = 100 and commission = 100

1.1 (100) + 1.1 (100) = 100 + 1.3 (100)

110 + 110 = 100 + 130

220 < 230 ; Insufficient

^^ I'm confused, do we have to take a salary that's greater than commission to solve the question "Is salary > commission?"

Another way I thought of it was...

If instead of plugging in values, is you decide isolate salary (s) and commission (c) using your formula in bold, it would be:

.10 s = .02 c

In this case, for all positive values where salary > commission, it holds true. Sufficient.

Can someone please help explain how Bunuel got salary = 2 commission? What am I doing wrong above? Am I missing something?

~ Im2bz2p345

Last edited by Im2bz2p345 on 17 Aug 2013, 10:16, edited 2 times in total.

Using your statement: 1.1({salary}+{commission})={salary}+1.3{commission}

1.1 s + 1.1 c = s + 1.3 c ; for sake of simplicity, let's say that salary = 100 and commission = 100

1.1 (100) + 1.1 (100) = 100 + 1.3 (100)

110 + 110 = 100 + 130

220 < 230

If instead of plugging in values, you decide isolate salary (s) and commission (c) using your formula, it would be:

.10 s = .02 c

In this case, for all positive values salary > commission.

Can someone please help explain how Bunuel got salary = 2 commission? What am I doing wrong above? Am I missing something?

~ Im2bz2p345

hi,

the above highlited part is wrong. in that you are assuming salary = comission = 100 if both are equal how can you compare which one is bigger.

let say salary = \(s\) comission =\(c\)

\(1.1(s + c) = s + 1.3 c\) \(1.1s + 1.1c = s + 1.3 c\) taking s items one side and c item one side \(0.1s = 0.2c\) ok now multiply both sides with 10 \(s = 2c\)

hope its clear now
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Using your statement: 1.1({salary}+{commission})={salary}+1.3{commission}

1.1 s + 1.1 c = s + 1.3 c ; for sake of simplicity, let's say that salary = 100 and commission = 100

1.1 (100) + 1.1 (100) = 100 + 1.3 (100)

110 + 110 = 100 + 130

220 < 230

If instead of plugging in values, you decide isolate salary (s) and commission (c) using your formula, it would be:

.10 s = .02 c

In this case, for all positive values salary > commission.

Can someone please help explain how Bunuel got salary = 2 commission? What am I doing wrong above? Am I missing something?

~ Im2bz2p345

hi,

the above highlited part is wrong. in that you are assuming salary = comission = 100 if both are equal how can you compare which one is bigger.

let say salary = \(s\) comission =\(c\)

\(1.1(s + c) = s + 1.3 c\) \(1.1s + 1.1c = s + 1.3 c\) taking s items one side and c item one side \(0.1s = 0.2c\) ok now multiply both sides with 10 \(s = 2c\)

hope its clear now

Thank you blueseas! I missed that last step of multiplying both sides by 10, shoot - should have realized it before I posted.

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

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19 Aug 2014, 01:25

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

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16 Feb 2015, 10:39

Bunuel wrote:

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.

Dear Bunuel,

I'm not sure if you need to consider two cases here based on the question's second statement. It is like stating " if the difference between A and B is 4, I would consider A-B = 4 and not |A-B| =4.

The similar question, which you used to merge the topic clearly specifies that the absolute difference between the base salary and the commission is..., there I can understand the two cases but not for the question above, where it does not state anything about the absolute difference.

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

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16 Feb 2015, 12:48

My 2 cents from question stem: commission + base = 1

for statement 1, -> 1.3base + commission = 1.1 plus 1base + commission = 1 -> 0.3 base = 0.1 -> base = 33% -> sufficient

for statement 2, -> base - commission = 0.5base or -> commission - base = 0.5base -> base is equal 50% or 33% -> not greater than 50% -> not suffificent

-> Correct Answer is A

JMO, please correct me if there is any logical flaw. Thanks very much!

Last edited by cherryli2015 on 16 Feb 2015, 18:37, edited 1 time in total.

The prompt never stated whether the base salary was larger than the commission or the commission was larger than the base salary, so we CANNOT assume that the base salary is bigger just because it was mentioned first in the sentence. The word "difference" implies that one of them IS bigger, but we don't know which one. THAT is why Bunuel addressed it.

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

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31 Jul 2015, 16:38

For statement 1, why can we assume that the base salary stays the same? i.e no percent change associated with base salary. If only the commission had been 30% higher, then the answer would be A, but what if the base salary could be, for example, 20% lower? Wouldn't the answer then be E?

The specific question that is asked refers to a base salary and a commission LAST YEAR, so we're dealing with 2 unknowns, NOT 2 variables. This means that the two numbers are constants, but we do NOT know what they are (and thus, we don't know which one is bigger).

Fact 1 uses a 'hypothetical' that points out that increasing JUST the commission (by 30%) would have led to an increase in income (of 10%). By extension, this assumes that the other pieces (in this case, the base salary) stay the same.

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