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

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GMATD11
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A certain salesman's yearly income is determined by a base [#permalink] New post  03 Oct 2011, 19:02
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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.

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Guys i marked B

Another simple question if 50/100 = 1/2
50/100 = .5
which one to consider used 1/2 but explanation use .5
can we ignore last zero on R.H.S of decimal
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bobfirth
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Re: A certain salesman's yearly income is determined by a base [#permalink] New post  26 Nov 2011, 05:10
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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  Updated on: 04 Oct 2011, 10:22
The absolute difference of two real numbers x, y is given by |x − y|, the absolute value of their difference.

Statement 2
The difference may be positive or negative... you don't know what.
Eliminate B &D

Statement 1
1 is sufficient
Hence A

Yes you can use both... use what you're more comfortable with more- fraction or decimal. Yes, you can ignore the zero

Originally posted by blink005 on 04 Oct 2011, 07:34.
Last edited by blink005 on 04 Oct 2011, 10:22, edited 1 time in total.
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Re: A certain salesman's yearly income is determined by a base [#permalink] New post  04 Oct 2011, 09:42
blink005 wrote:
The absolute difference of two real numbers x, y is given by |x − y|, the absolute value of their difference.

Statement 2
The difference may be positive or negative... you don't know what.
Eliminate B &D

Statement 1
GMATD11 are you familiar with weighted averages?
You can evaluate this statement by using that concept.
1 is sufficient
Hence A

Yes you can use both... use what you're more comfortable with more- fraction or decimal. Yes, you can ignore the zero


Hi Blink,

Can you explain your approach in detail for lesser mortals like me :)
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Re: A certain salesman's yearly income is determined by a base [#permalink] New post  04 Oct 2011, 10:22
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sorry my bad, simple equations will do

S+1.3C=1.1(S+C);
which simplifies to:
S=2C
Since both S, and C are positive;
S>C.
Sufficient.
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Re: A certain salesman's yearly income is determined by a base [#permalink] New post  26 Nov 2011, 01:53
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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  17 Apr 2021, 01:43
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Regarding statement 1 , could somebody verify whether the following approach is ok? Bunuel nick1816

so x=base salary
(a/100)y = commission on sales

so is (ay/100)>x ?

x+1.3(ay/100)= 1.1 (x+ay/100) after some calculations we get y=50x/a and if we substitute it in the inequality we get that is x/2>x ? the answer is a definite no so A is sufficient .
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Re: A certain salesman's yearly income is determined by a base [#permalink] New post  17 Apr 2021, 06:36
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UNSTOPPABLE12 wrote:
Regarding statement 1 , could somebody verify whether the following approach is ok? Bunuel nick1816

so x=base salary
(a/100)y = commission on sales

so is (ay/100)>x ?

x+1.3(ay/100)= 1.1 (x+ay/100) after some calculations we get y=50x/a and if we substitute it in the inequality we get that is x/2>x ? the answer is a definite no so A is sufficient .

Hi UNSTOPPABLE12
Your approach is time consuming. There is no need to bring in % of sales and sales variables for calculations as this will impact on your time consumption to get the right answer.

You can simply use B (base salary) & C (commission) with B+C total salary. For this only 2 variables to deal with.
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Re: A certain salesman's yearly income is determined by a base [#permalink] New post  25 Nov 2023, 07:50
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Re: A certain salesman's yearly income is determined by a base [#permalink]
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