‘A Store Sells One Particular Type of Widget’ is the topic for GMAT Quantitative Reasoning. GMAT quantitative reasoning section analyses the candidates' ability to solve mathematical, and quantitative problems and interpret graphic data. This section of the GMAT exam comprises 31 questions. ‘A Store Sells One Particular Type of Widget’ is the GMAT Quantitative Reasoning question that includes five optional answers and candidates need to choose one of them. Candidates are given 62 minutes to complete this section. GMAT Quant syllabus has mainly the two categories-
- Problem Solving: This question type in GMAT Quantitative analysis candidates logical and analytical reasoning skills. In this section, candidates indicate the best five answer choices.
- Data Sufficiency: Candidates' ability to analyze quantitative problems and identify relevance with the data given.
Topic: A Store Sells One Particular Type of Widget
Question: A store sells one particular type of widget. This month, the store raised the price of each widget to X % of the original price but sold only Y % as many widgets as last month. As a result, the total revenue from the sale of widgets was the same for both months.
In the table, identify the values of X and Y that are consistent with the information provided. Make only two selections, one in each column.
| Options | X (%) | Y (%) | Values |
|---|---|---|---|
| A. | - | - | 25 |
| B. | - | - | 50 |
| C. | - | - | 80 |
| D. | - | - | 125 |
| E. | - | - | 160 |
| F. | - | - | 250 |
Hint:
| X(%) | Y (%) | Values |
|---|---|---|
| - | - | 25 |
| - | - | 50 |
| - | Tick | 80 |
| Tick | - | 125 |
| - | - | 160 |
| - | - | 250 |
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Answer: X = D; Y = C
Model Answer 1
Explanation:
The given situation states that the store raised the price of each widget to X%. This basically implies that X% was not added to the original price; rather, the new price is equal to X% of the original price. Accordingly, in order to ensure that the price of each widget increases, the value of X must be larger than 100. As a result, the only possible values for X are choices (D), (E), and (F).
However, the question also states that the store sold only Y% as many widgets as last month. Although this does not imply that they sold Y% fewer units; rather, the number of units will be equal to Y% of the original.
Revenues incurred by the store were the same in both months, and the price increased in the second month. This typically implies that the number of units sold must have fallen. This can be equated as Price per Unit ´ Units Sold = Revenue. The only possible values for Y are choices (A), (B), and (C).
Finally, there are no real values provided in the question stem, and the question asks about a joint relationship between X and Y. for this it is important to make use of smart numbers. Accordingly, since the main set of problems revolves around percent, set the starting price to $100 and the starting quantity sold to 10 units. The starting revenue can be calculated as therefore (100)(10) = $1,000.
The following table represents the values of X considering the starting price of each widget as $100 and the number of quantities sold is 10 units.
| X% | New Price (X% of $100) | New Quantity ($1000/New Price) | % of Original Units (New Quantity/10) |
|---|---|---|---|
| 125 | $125 | $1000/$125 = 8 Units | 8/10 = 80% |
| 160 | $160 | $1000/$160 = 6.3 Units | 6.3/10 = 63% |
| 250 | $250 | $1000/$250 = 4 Units | 4/10 = 40% |
The only pair that appears in the above evaluations, is X with a value of 125 and the value of Y is 80.
Therefore, the value of X and Y for the above table can be determined as-
X = 125
Y = 80
Thus, the correct answer for the value of X is option D and that for Y is option C.
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