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

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DanTe02
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Re: A certain salesman's yearly income is determined by a base salary plus [#permalink] New post   04 Jul 2020, 07:35
Should'nt the second statement say the absolute difference between base and commision for us to employ modulus?
I want to know if on gmat the question reads that ..... the difference between a and b is bla bla should i equate a-b = bla bla or should i use |a-b|=bla bla or should i look out for something to tell the difference
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Re: A certain salesman's yearly income is determined by a base salary plus [#permalink] New post   04 Jul 2020, 12:56
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Deeptanshu02 wrote:
Should'nt the second statement say the absolute difference between base and commision for us to employ modulus?
I want to know if on gmat the question reads that ..... the difference between a and b is bla bla should i equate a-b = bla bla or should i use |a-b|=bla bla or should i look out for something to tell the difference


Hi Deeptanshu02,

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 earlier in the sentence in Fact 2. The word "difference" implies that one of them IS bigger, but we don't know which one.

If you find that you are not sure about the exact meaning of a phrase in a Quant question, then it can sometimes help to create a simple example to define whether a pattern exists or not. For example:

The difference between Tom's net worth and Mark Zuckerberg's net worth is approximately 85 billion dollars....

So who has a higher net worth? Tom or Mark Zuckerberg?

Tom appears first in the sentence, but Mark Zuckerberg is the one who has the higher net worth. In simple terms, the modulus is 'implied' (and it does not matter who is first in the sentence).

GMAT assassins aren't born, they're made,
Rich
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Re: A certain salesman's yearly income is determined by a base salary plus [#permalink] New post   05 Jul 2020, 00:41
"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?
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Re: A certain salesman's yearly income is determined by a base salary plus [#permalink] New post   13 Nov 2020, 19:23
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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A certain salesman's yearly income is determined by a base salary plus [#permalink] New post   15 Nov 2020, 06:31
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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.


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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A
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Re: A certain salesman's yearly income is determined by a base salary plus [#permalink] New post   15 Nov 2020, 08:44
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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Re: A certain salesman's yearly income is determined by a base salary plus [#permalink] New post   09 Feb 2021, 06:22
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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Re: A certain salesman's yearly income is determined by a base salary plus [#permalink] New post   09 Feb 2021, 07:36
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WheatyPie wrote:
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.


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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Re: A certain salesman's yearly income is determined by a base salary plus [#permalink] New post   09 Feb 2021, 08:21
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DanTe02 wrote:
"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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Re: A certain salesman's yearly income is determined by a base salary plus [#permalink] New post   25 May 2023, 12:50
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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Re: A certain salesman's yearly income is determined by a base salary plus [#permalink]
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