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

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.

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

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

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!

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.

GMAT assassins aren't born, they're made,
Rich

Contact Rich at: [email protected]

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