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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