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.
OA A
Source: Official Guide
The selling price of an article is equal to the cost of the
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\[{\text{sell}} = {\text{cost}} + {\text{mark}}\,\,\,\,\left( * \right)\]BTGmoderatorDC wrote: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.
\[\left[ {{\text{mark}} = \frac{x}{{100}}\left( {{\text{sell}}} \right)\,\,\,\, \Rightarrow } \right]\,\,\,\,\,\,\,?\,\, = \,\,100 \cdot \frac{{{\text{mark}}}}{{{\text{sell}}}}\,\,\,\,\,\,\, \Leftrightarrow \,\,\,\,\,\,\,\boxed{?\,\, = \frac{{{\text{mark}}}}{{{\text{sell}}}}}\,\,\]
\[\left( 1 \right)\,\,\,\frac{1}{4} = \frac{{{\text{mark}}}}{{{\text{cost}}}}\,\,\mathop = \limits^{\left( * \right)} \,\,\frac{{{\text{mark}}}}{{{\text{sell}} - {\text{mark}}}}\,\,\,\,\,\, \Rightarrow \,\,\,\,\,\,\frac{{{\text{sell}} - {\text{mark}}}}{{{\text{mark}}}} = 4\,\,\,\,\,\, \Rightarrow \,\,\,\,\,\,\frac{{{\text{sell}}}}{{{\text{mark}}}} - 1 = 4\,\,\,\,\,\, \Rightarrow \,\,\,\,\,\,?\,\, = \,\,{\left( {\frac{{{\text{sell}}}}{{{\text{mark}}}}} \right)^{ - 1}}\,\,\, = \frac{1}{5}\]\[\left( 2 \right)\,\,\,{\text{sell}} = 250\,\,\,\left\{ \begin{gathered}
\,{\text{If}}\,{\text{cost}} = 200\,\,\,\mathop \Rightarrow \limits^{\left( * \right)} \,\,\,\,{\text{mark}} = 50\,\,\,\,\, \Rightarrow \,\,\,\,\,? = \frac{{50}}{{250}} = \frac{1}{5}\,\, \hfill \\
\,{\text{If}}\,{\text{cost}} = 150\,\,\,\mathop \Rightarrow \limits^{\left( * \right)} \,\,\,\,{\text{mark}} = 100\,\,\,\,\, \Rightarrow \,\,\,\,\,? = \frac{{100}}{{250}} \ne \frac{1}{5}\,\, \hfill \\
\end{gathered} \right.\]
This solution follows the notations and rationale taught in the GMATH method.
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fskilnik.
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Let C = cost of articleBTGmoderatorDC wrote: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.
Target question: The markup on a certain television set is what percent of the selling price?
Statement 1: The markup on the television set is 25 percent of the cost.
If C = cost of article, markup = 0.25C
Selling price = cost + markup
= C + 0.25C
= 1.25C
So, the markup = 0.25C and the selling price = 1.25C
0.25C/1.25C = 0.25/1.25 = 1/5 = 20%
So, the markup on the TV is 20% of the selling price
Since we can answer the target question with certainty, statement 1 is SUFFICIENT
Statement 2: The selling price of the television set is $250
We have no information about the markup. So, consider these two possible cases:
Case a: The cost is $200 and the markup is $50. Here, the markup is $50 and the selling price is $250. So, the markup on the TV is 20% of the selling price
Case b: The cost is $150 and the markup is $100. Here, the markup is $100 and the selling price is $250. So, the markup on the TV is 40% of the selling price
Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT
Answer: A
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Markup = M Selling Price = P Cost = C
P=C+M
(1) M=0.25C
C=4M
Sub back into the equation
P=4M+M
P=5M
We want to find M/P which in this case is M/P = 1/5 or 20% so (1) is sufficient.
(2) 250 = M + C
We cannot solve, so the answer is A.
P=C+M
(1) M=0.25C
C=4M
Sub back into the equation
P=4M+M
P=5M
We want to find M/P which in this case is M/P = 1/5 or 20% so (1) is sufficient.
(2) 250 = M + C
We cannot solve, so the answer is A.