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

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EMPOWERgmatRichC

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05 Jul 2020, 15:16

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Hi Deeptanshu02,

When a GMAT Quant question uses the phrase "the difference between (one value and another)", it is implied that it's the 'absolute difference' (so the larger number might be the first or the second in the sentence).

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13 Nov 2020, 19:23

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Dear Expert
How do we infer that the base salary and commission remains constant for both the years, as it is not mentioned.

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14 Nov 2020, 21:46

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Hi GRS,

This prompt ONLY refers to "last year", so there's no comparison over time - there's just a base salary and a commission for that year-long period.

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15 Nov 2020, 06:31

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devinawilliam83

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.

Question stem, rephrased:
Is the base salary greater than the commission?

Statement 1:
In other words, a 30% increase in the commission is equal to a 10% increase in the total salary, as follows:
$0.3C = 0.1T$
$3C = T$
$C = \frac{1}{3}T$
Since the commission is equal to 1/3 of the total income, the base salary must be equal to 2/3 of the total income.
Thus, the answer to the question stem is YES.
SUFFICIENT.

Statement 2:
In other words, the commission is either 50% LESS THAN the base salary (in which case the answer to the question stem is YES) or 50% GREATER THAN the base salary (in which case the answer to the question stem is NO).
INSUFFICIENT.

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15 Nov 2020, 08:44

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

Yearly Income (i) = Base Salary (b) + Commission on the sales (c)
i = b + c

(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 * i = b + 1.3c
.1 i = .3c
i = 3c
b = 2c = (2/3) i = 66.66% I
Salesman's base salary account for more than half (66.66%>50%) of the salesman's yearly income last year.
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.
b - c = .5 b
b = 2c = (2/3)i = 66.66%i
or
c - b = .5b
c = 1.5b = (3/2)b
b = 2c/3 = (2/5)I = 40%i
NOT SUFFICIENT

IMO A

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09 Feb 2021, 06:22

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The second statement in this problem is not as written in the original Manhattan problem.

The correct second statement is: (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.

The question as written is incorrect. Statement 2, as written, implies that the information given is about Base Salary - Commission, and NOT the other way around. The explanations given to justify why statement 2 is not sufficient are incorrect.

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09 Feb 2021, 07:36

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WheatyPie

There are two versions of this question. You are talking about the second version which is discussed here: https://gmatclub.com/forum/a-certain-sa ... 21474.html

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09 Feb 2021, 08:21

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DanTe02

"The difference between Tom's net worth and Mark Zuckerberg's net worth is approximately 85 billion dollars....
" Well the statement implies its T-M=85billion dollar if we dont know whose net worth is bigger shouldnt we say that the absolute difference between Tom's net worth and Mark Zuckerberg's net worth is approximately 85 billion dollars.... or if we know whose bigger it should be difference between mark and toms net worth either way my opinion does'nt matter on GMAT What matter is how GMAC thinks so does GMAC Cosnider the sentence construction in red and in green the same?

The word difference implies "absolute difference"
Hence, we have:
Difference between 5 and 2 = 3
Also: Difference between 2 and 5 = 3

Hope that helps!

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25 May 2023, 12:50

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So if a question says "the difference between 'a' and 'b' is 5", does that mean we always take this to be: |a-b|=5 ?

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25 May 2023, 15:34

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Cav

So if a question says "the difference between 'a' and 'b' is 5", does that mean we always take this to be: |a-b|=5 ?

Hi Cav,

Yes - in Algebraic terms, that's how you should interpret that type of language.

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