The Selling Price of an Article is Equal to the Cost of the Article Plus the Markup GMAT Data Sufficiency

Question: 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.

1. Statement (1) alone is sufficient, but statement (2) alone is not sufficient.
2. Statement (2) alone is sufficient, but statement (1) alone is not sufficient.
3. Both statements together are sufficient, but neither statement alone is sufficient.
4. Each statement alone is sufficient.
5. Statements (1) and (2) together are not sufficient.

Correct Answer: A

Solution and Explanation
Approach Solution 1:
From the first statement, the markup can be derived. This is because it is given that the markup price is 25% of the cost.

Here one can use the formula, Price=Cost+Markup and get the desired ratio of Cost. to find the cost of the article using the formula.

Cost = Markup÷Price= 0.25*cost÷1.25*cost

This implies that to find the cost of the television set, the markup percentage needs to be divided by the price of the television set. The same has been implicated in the above formula which states that the markup of 25% represented as 0.25 is to be multiplied with the cost.
Further, it is to be divided by the price of the television set of 1.25 which needs to be multiplied with cost.
Solving this equation, the answer to the question is obtained in relevance to the first statement where the markup of the television set is found to be 25% of the cost.
The selling price provided in the second statement does not include values of the cost or the markup of the television set. Accordingly, the desired ratio cannot be obtained from the second statement because of the lack of information. This implies that there are no values of information provided for cost and markup in the second statement.

Approach Solution 2:
Based on the 1st statement,
If C = cost of article, markup = 0.25C
Selling price = cost + markup
= C + 0.25C
= 1.25C

Accordingly, 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
Based on the second statement 2, The selling price of the television set is $250

There is particularly no information about the markup. So, these two possible cases can be considered:

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 the answer does not provide any certainty in terms of the target question, statement 2 is not sufficient.

Approach Solution 3:
From statement 1, since it is given that the markup price is 25% of the cost, we can use the formula, Price=Cost+Markup and get the desired ratio of Cost. i.e.. 

The selling price provided in statement 2 is not enough to obtain the desired ratio as there is no information as to the values of Cost and Markup.

“The selling price of an article is equal to the cost of the article plus the markup.”- is a topic of the GMAT Quantitative reasoning section of GMAT. This question has been taken from the book "The Official Guide for GMAT Review". GMAT Quant section consists of a total of 31 questions. GMAT Data Sufficiency questions consist of a problem statement followed by two factual statements. GMAT data sufficiency comprises 15 questions which are two-fifths of the total 31 GMAT quant questions.

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