young_gun wrote:
Warehouse W's revenue from the sale of sofas was what percent greater this year than it was last year?
(1) Warehouse W sold 10% more sofas this year than it did last year
(2) Warehouse W's selling price per sofa was $30 greater this year than it was last year
We can begin by defining some variables.
a = quantity of sofas sold last year
b = price per sofa sold last year
c = quantity of sofas sold this year
d = price per sofa sold this year
We need to determine what percentage greater this year’s sofa revenue was than last year’s. To determine the percentage increase, we can use the percent change formula. Recalling that revenue = price x quantity, we see that the revenue from sofas sold last year is ab and the revenue from sofas sold this year is cd.
percent change = (new – old)/old x 100
(cd – ab)/ab x 100 = ?
(cd/ab – 1) x 100 = ?
100cd/ab – 100 = ?
Statement One Alone:
Warehouse W sold 10 percent more sofas this year than it did last year.
Using the information in statement one, we can create the following equation:
c = 1.1a
Without knowing the values of b and d, statement one is not sufficient to answer the question. We can eliminate answer choices A and D.
Statement Two Alone:
Warehouse W’s selling price per sofa was $30 greater this year than it was last year.
Using the information in statement two, we can create the following equation:
d = 30 + b
Without knowing the values of a and c, statement two is not sufficient to answer the question. We can eliminate answer choice B.
Statements One and Two Together:
Using statements one and two together, we still do not have enough information to answer the question. Even if we substitute 1.1a for c and 30 + b for d in the expression 100cd/ab – 100, we are left with:
100(1.1a)(30 + b)/ab – 100
110a(30 + b)/ab – 100
110(30 + b)/b – 100
Since we don’t know the value of b, we can’t determine a unique value for the expression.
Answer: E
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