The selling price of an article is equal to the cost of the article

SOLUTION

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?

Given: Price=Cost+Markup.
Question: \(\frac{Markup}{Price}=?\)

(1) The markup on the television set is 25 percent of the cost. \(Markup=0.25*Cost\) --> \(Price=Cost+Markup=Cost+0.25*Cost=1.25*Cost\) --> \(\frac{Markup}{Price}=\frac{0.25*Cost}{1.25*Cost}=0.2\). Sufficient.

(2) The selling price of the television set is $250. Not sufficient to get the ratio required.

Answer: A.
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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.

Markup = M Selling Price = P Cost = C
P=C+M

(1) M=0.25C
C=4M
Sub back into 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 suff

(2) 250 = M + C
We cannot solve, so answer is A

From Question Stem => SP = CP + M. (M/SP) = ?? %
St 1: Sufficient: M=.25CP, So, SP=CP + .25CP = 1.25CP, Therefore M/SP x 100% = .25/1.25 x 100% = 20%

St 2: Insufficient: SP=$250= CP + M, Two variables with one equation. Hence cannot be solved.

Hence Answer is A.

The question can be reduced to "What is the ratio of Markup to Selling Price"
Let Cost Price = 100P
Markup = M
Thus Selling price (SP) = 100P +M...........(1)
Statement 1 - M=25P ----> & SP =125P ------> Sufficient
Statement 2 - SP=250---> No relative amount is given for M----> Thus insufficient

Answer A

SOLUTION

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?

Given: Price=Cost+Markup.
Question: \frac{Markup}{Price}=?

(1) The markup on the television set is 25 percent of the cost. Markup=0.25*Cost --> Price=Cost+Markup=Cost+0.25*Cost=1.25*Cost --> \frac{Markup}{Price}=\frac{0.25*Cost}{1.25*Cost}=0.2. Sufficient.

(2) The selling price of the television set is $250. Not sufficient to get the ratio required.[quote][/quote]

Hi Bunuel,

I understand why statement A is correct, but I don't understand why in this case the answer can't be C. If we use both the statements together, we have Selling Price = 1.25*Cost and the 2nd statement tells us the price.

If Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked, then the answer is A.

The data sufficiency problem consists of a question and two statements, labeled (1) and (2), in which certain data are given. You have to decide whether the data given in the statements are sufficient for answering the question. Using the data given in the statements, plus your knowledge of mathematics and everyday facts (such as the number of days in July or the meaning of the word counterclockwise), you must indicate whether—

A. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked.
B. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked.
C. BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficient to answer the question asked.
D. EACH statement ALONE is sufficient to answer the question asked.
E. Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data specific to the problem are needed.

I suggest you to go through the following post ALL YOU NEED FOR QUANT.

Hope this helps.
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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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Let C = cost of article

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

Cheers,
Brent
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\({\text{sell}} = {\text{cost}} + {\text{mark}}\,\,\,\,\left( * \right)\)

\(\left[ {{\text{mark}} = \frac{x}{{100}}\left( {{\text{sell}}} \right)\,\,\,\, \Rightarrow } \right]\,\,\,\,\,\,\,?\,\, = \,\,100 \cdot \frac{{{\text{mark}}}}{{{\text{sell}}}}\,\,\,\,\,\,\, \Leftrightarrow \,\,\,\,\,\,\,\boxed{?\,\, = \frac{{{\text{mark}}}}{{{\text{sell}}}}}\,\,\)

\(\left( 1 \right)\,\,\,\frac{1}{4} = \frac{{{\text{mark}}}}{{{\text{cost}}}}\,\,\mathop = \limits^{\left( * \right)} \,\,\frac{{{\text{mark}}}}{{{\text{sell}} - {\text{mark}}}}\,\,\,\,\,\, \Rightarrow \,\,\,\,\,\,\frac{{{\text{sell}} - {\text{mark}}}}{{{\text{mark}}}} = 4\,\,\,\,\,\, \Rightarrow \,\,\,\,\,\,\frac{{{\text{sell}}}}{{{\text{mark}}}} - 1 = 4\,\,\,\,\,\, \Rightarrow \,\,\,\,\,\,?\,\, = \,\,{\left( {\frac{{{\text{sell}}}}{{{\text{mark}}}}} \right)^{ - 1}}\,\,\, = \frac{1}{5}\)

\(\left( 2 \right)\,\,\,{\text{sell}} = 250\,\,\,\left\{ \begin{gathered}\\
\,{\text{If}}\,{\text{cost}} = 200\,\,\,\mathop \Rightarrow \limits^{\left( * \right)} \,\,\,\,{\text{mark}} = 50\,\,\,\,\, \Rightarrow \,\,\,\,\,? = \frac{{50}}{{250}} = \frac{1}{5}\,\, \hfill \\\\
\,{\text{If}}\,{\text{cost}} = 150\,\,\,\mathop \Rightarrow \limits^{\left( * \right)} \,\,\,\,{\text{mark}} = 100\,\,\,\,\, \Rightarrow \,\,\,\,\,? = \frac{{100}}{{250}} \ne \frac{1}{5}\,\, \hfill \\ \\
\end{gathered} \right.\)


This solution follows the notations and rationale taught in the GMATH method.

Regards,
fskilnik.
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fskilnik
Hello sir,
In statement 2, how do someone convinced that \(\frac{markup}{selling price}\) has to be \(\frac{1}{5}\) by your method?
Note: We're going to ignore statement 1 for some moments where \(\frac{markup}{selling price}\) is \(\frac{1}{5}\).
Thanks__
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