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02 Dec 2019, 09:58
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X (%): 125
Y (%): 80
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
75%
(hard)
Question Stats:
58% (02:05) correct
42%
(02:34)
wrong
based on 1027
sessions
History
Date
Time
Result
Not Attempted Yet
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.
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.
| X (%) | Y (%) | Values |
| 25 | ||
| 50 | ||
| 80 | ||
| 125 | ||
| 160 | ||
| 250 |
ShowHide Answer
Official Answer
X (%): 125
Y (%): 80
09 Jan 2021, 05:46
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Official Explanation
The wording in this question is tricky. The store raised the price of each widget to X%. This is different than saying that the store increased the price by X%. In other words, X% was not added to the original price; rather, the new price is equal to X% of the original price. In order for the new price to be an increase, as the question stem states (raised the price), the value of X must be larger than 100. As a result, the only possible values for X are choices (D), (E), and (F).
The question also states that the store sold only Y% as many widgets as last month. Again, this is not saying that they sold Y% fewer units; rather, the number of units will be equal to Y% of the original.
Since revenues were the same in both months, and the price increased in the second month, the number of units sold must have fallen (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 you are asked about a joint relationship between X and Y. Consider using Smart Numbers. Since you’re working with percents, set the starting price to $100 and the starting quantity sold to 10 units. The starting revenue was therefore (100)(10) = $1,000.
Test the possible answer choices for X using $100 as the original price and 10 as the original number of units.
1.jpg [ 52.23 KiB | Viewed 19807 times ]
The only pair that appears in the answers is X = 125 and Y = 80. Note: You can stop as soon as you find a pair of answers that works, so if you try 125 first, you don’t have to try the other two.
Alternatively, if you feel very comfortable with this kind of math, you may be able to save time via a conceptual algebraic approach. If the total price is the same for both scenarios, then this equation must be true:
(Original price per widget)(Original number of widgets) = (New price per widget)(New number of widgets)
Since the new price went up, the new number sold must go down. In order to make both sides of the equation equal, the fraction by which the new price goes up must be the reciprocal of the fraction by which the new number of widgets goes down. For example, if the price increased to 150%, or 3/2, of the original price, then the new number sold must go down by 2/3, in order for the two fractions to “cancel out” to 1:
(Original price)(Original number) = (3/2 × New price) ((2/3 × New number)
Convert the possible values for X into fraction form, then take the reciprocal to find the corresponding value for Y:
X = 125% = 5/4. The reciprocal of 5/4 is 4/5 or 80%. (You can stop here; 80% appears in the answer choices.)
X = 160% = 8/5. The reciprocal of 8/5 is 5/8 or 60%. This value (60%) is not in the answers.
X = 250% = 5/2. The reciprocal of 5/2 is 2/5 or 40%. This value (40%) is not in the answers.
Column 1: The correct answer is (D).
Column 2: The correct answer is (C).
The wording in this question is tricky. The store raised the price of each widget to X%. This is different than saying that the store increased the price by X%. In other words, X% was not added to the original price; rather, the new price is equal to X% of the original price. In order for the new price to be an increase, as the question stem states (raised the price), the value of X must be larger than 100. As a result, the only possible values for X are choices (D), (E), and (F).
The question also states that the store sold only Y% as many widgets as last month. Again, this is not saying that they sold Y% fewer units; rather, the number of units will be equal to Y% of the original.
Since revenues were the same in both months, and the price increased in the second month, the number of units sold must have fallen (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 you are asked about a joint relationship between X and Y. Consider using Smart Numbers. Since you’re working with percents, set the starting price to $100 and the starting quantity sold to 10 units. The starting revenue was therefore (100)(10) = $1,000.
Test the possible answer choices for X using $100 as the original price and 10 as the original number of units.
Attachment:
1.jpg [ 52.23 KiB | Viewed 19807 times ]
Alternatively, if you feel very comfortable with this kind of math, you may be able to save time via a conceptual algebraic approach. If the total price is the same for both scenarios, then this equation must be true:
(Original price per widget)(Original number of widgets) = (New price per widget)(New number of widgets)
Since the new price went up, the new number sold must go down. In order to make both sides of the equation equal, the fraction by which the new price goes up must be the reciprocal of the fraction by which the new number of widgets goes down. For example, if the price increased to 150%, or 3/2, of the original price, then the new number sold must go down by 2/3, in order for the two fractions to “cancel out” to 1:
(Original price)(Original number) = (3/2 × New price) ((2/3 × New number)
Convert the possible values for X into fraction form, then take the reciprocal to find the corresponding value for Y:
X = 125% = 5/4. The reciprocal of 5/4 is 4/5 or 80%. (You can stop here; 80% appears in the answer choices.)
X = 160% = 8/5. The reciprocal of 8/5 is 5/8 or 60%. This value (60%) is not in the answers.
X = 250% = 5/2. The reciprocal of 5/2 is 2/5 or 40%. This value (40%) is not in the answers.
Column 1: The correct answer is (D).
Column 2: The correct answer is (C).
