The selling price of an article is equal to the cost of the article plus the markup. The markup on a certain television set is what percent of the selling price?
(1) The markup on the television set is 25 percent of the cost.
(2) The selling price of the television set is $250.
We are given that the selling price of an article is equal to the cost of the article plus the markup. We define some variables so that we can translate the given information into an expression.
c = cost of the article
m = the markup
Thus, we know that the selling price of the article (with the markup) is c + m.
We need to determine the percent of the selling price represented by the markup. Translating the question into an expression gives us:
m/(c + m) x 100 = ?Statement One Alone:
The markup on the television set is 25 percent of the cost.
From statement one we can create the following equation:
m = 0.25c
We now substitute 0.25c for m into our original expression. So we have:
m/(c + m) x 100 = ?
0.25c/(c + 0.25c) x 100 = ?
0.25c/(1.25c) x 100 = ?
0.25/1.25 x 100 = 20%
Statement one alone is sufficient to answer the question. We can eliminate answer choices B, C, and E.
(Note: We were able to determine m/(c + m) x 100 because we were able to get variable m in terms of variable c
and thus, when we plugged 0.25c in for m into our expression, all the variables canceled, allowing us to determine the percentage.)Statement Two Alone:
The selling price of the television set is $250.
With the information in statement two we can create the following equation:
c + m = 250
With the equation c + m = 250, we can simplify m/(c + m) x 100 as m/250 x 100. However, since we don’t know the value of m, we can’t determine the value of m/(c + m) x 100. Thus, statement two alone is not sufficient to answer the question.
The answer is A.
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