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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]

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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.
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Re: DS - Percentage [#permalink]

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25 Jan 2012, 03:10
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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.

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

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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]

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01 Aug 2015, 11:34
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Hi stopchange,

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

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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]

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Re: DS - Percentage [#permalink]

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17 Aug 2013, 11:01
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.

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

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, 11:16, edited 2 times in total.

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Re: DS - Percentage [#permalink]

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17 Aug 2013, 11:09
Im2bz2p345 wrote:

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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Re: DS - Percentage [#permalink]

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17 Aug 2013, 11:17
blueseas wrote:
Im2bz2p345 wrote:

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.

Appreciate your quick response.

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

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16 Feb 2015, 11:39
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.

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.

Please correct if I'm wrong.

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

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16 Feb 2015, 13:48
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, 19:37, edited 1 time in total.

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

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16 Feb 2015, 18:30
Hi santorasantu,

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.

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However, the question states only the word difference. So we could have a C-B=(1/2)B scenario as well. In which case, assuming C to be $30, B would be$20 (<50% of the total) which is inconsistent with the 67% above, therefore insufficient and the answer is A.

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

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20 Sep 2017, 15:39
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devinawilliam83 wrote:
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.

Target question: Was the salesman's commission larger than his base salary last year?
This is a good candidate for rephrasing the target question.

Let B = base salary last year
Let C = commission last year
So, B+C = TOTAL income last year
REPHRASED target question: Is C greater than B?

Statement 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.
If we increase the commission by 30% the NEW commission = 1.3C, which means the TOTAL income = 1.3C + B
This NEW income is 10% greater than the actual TOTAL income (B+C)
We can write: 1.3C + B = 1.1(B + C)
Expand: 1.3C + B = 1.1B + 1.1C
Rearrange to get: 0.2C = 0.1B
Make "prettier" by multiplying both sides by 10 to get: 2C = 1B
Since C and B are both POSITIVE, we can see that B must be greater than C (since B is equal to C+C)
Another way say this is, C is NOT greater than B
Since we can answer the REPHRASED target question with certainty, statement 1 is SUFFICIENT

Statement 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.
We can write: |C - B| = 0.5B
This gives us two possible cases:
Case a: C - B = 0.5B. When we solve this for C, we get C = 1.5B, which means C is greater than B
Case b: C - B = -0.5B. When we solve this for C, we get C = 0.5B, which means C is NOT greater than B
Since we cannot answer the REPHRASED target question with certainty, statement 2 is NOT SUFFICIENT

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

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21 Sep 2017, 00:04
Income - I
Commission - C
Base Salary - B

Originally last year - I = B + C

Option 1 -
B + 1.3C = 1.1I
Subtract this from the original equation
We get - 0.1I = 0.3C
Or C = 0.33I
This means that Base was 0.67 of I which is greater than 50%
Sufficient

Option 2 -
Since we are not given whether B > C - we should consider it both ways. First if B was greater than C -

B - C = 0.5B
C = 0.5B
Replacing in original equation
I = B + 0.5B
B = 0.66I

Hence this answers as yes, base salary accounts for more than 50% of the income

Now second if C was greater than B -

C - B = 0.5B
C = 1.5B

Replacing in original equation -

I = B + 1.5B
B = 0.4I

Hence this answers as no, base salary does not account for more than 50% of the income

Hence option 2 does not give us a definite answer. So not sufficient.

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Re: A certain salesman's yearly income is determined by a base   [#permalink] 21 Sep 2017, 00:04
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