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sasyaharry
Joined: 22 Nov 2016
Last visit: 11 Mar 2023
Posts: 199
Given Kudos: 49
Concentration: Leadership, Strategy
Schools: Wharton Exec '22 (A) Haas EWMBA '23 (A)
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Updated on: 11 Nov 2024, 02:40
Originally posted by sasyaharry on 26 Jul 2017, 14:54.
Last edited by Bunuel on 11 Nov 2024, 02:40, edited 5 times in total.
Last edited by Bunuel on 11 Nov 2024, 02:40, edited 5 times in total.
Updated - Complete topic (62).
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X: 160
Y: 62.5
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:
66% (02:52) correct
34%
(03:13)
wrong
based on 1245
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A factory produces one type of widget. This month, the factory raised the price of each widget to X% of the original price. However, the factory only sold Y% as many widgets as last month, and the total revenue from the sale of widgets was equal for last month and this month.
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 | |
| 50 | ||
| 62.5 | ||
| 75 | ||
| 150 | ||
| 160 | ||
| 180 |
ShowHide Answer
Official Answer
X: 160
Y: 62.5
14 Oct 2017, 21:46
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This is pretty simple. Lets say original price is 1 and he sold 1 unit.
Price is raised to x% of original price, new price = x/100
Qty decreased to y%, new quantity = y/100
Also, x > 100 (since price is increased) and y <100 (since qty is decreased)
new price * new qty = old revenue
\(xy/10000 = 1\)
\(xy =10000\)
Try x = 150, you would get y = 66.66
Now try x = 160, you would get y = 62.5
Here is your answer.
Price is raised to x% of original price, new price = x/100
Qty decreased to y%, new quantity = y/100
Also, x > 100 (since price is increased) and y <100 (since qty is decreased)
new price * new qty = old revenue
\(xy/10000 = 1\)
\(xy =10000\)
Try x = 150, you would get y = 66.66
Now try x = 160, you would get y = 62.5
Here is your answer.
15 Feb 2024, 02:33
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Revenue = Price x Quantity.
Before I get into my solution, let me take an example:
Let's say the factory doubles the price.
And after doubling the price, the revenue remains the same.
What would have happened to the Quantity?
If the price doubles, but the revenue remains the same, the quantity must be halved.
Since the overall revenue was the same, the increase in the price will correspond to a proportional decrease in the quantity. In maths terms, if the price became 2x, the quantity would have become 1/2x.
--
We can answer the question using this underlying understanding.
1. "the factory raised the price of each widget to X% of the original price"
a. The price has been raised.
b. The price is not raised by X%. It is raised to X% of the original price. e.g. Say last month's price was $100, and this month's price is $110. Is X = 110 or 10? The price has been raised by 10%. It has been raised to 110% of the previous price. So, X = 110.
Since the price has been raised, X > 100.
2. "the factory only sold Y% as many widgets as last month, and the total revenue from the sale of widgets was equal for last month and this month."
a. The factory sold Y% as many widgets, not Y% less than last month, but Y%.
e.g. Let's say the quantity sold went down from 100 to 80. Would Y be 20 or 80? The factory sold 80% as many widgets as last month. Or, the factory sold 20% less widgets than last month. In this example, Y would be 80.
b. The total revenue was equal. The price per widget had increased. So, the quantity of widgets must have reduced.
Y < 100.
X can only be 150, 160, or 180.
Y can only be 50, 62.5, or 75.
Now, how to deal with the remaining values.
I will start with the potential answers for X: 150, 160, 180 and check if the corresponding value of Y is there in the table. (We could start with Y as well and then check if the corresponding value of X exists in the table. I chose X because I want to avoid dealing with 62.5/100.)
i.
If the price became 150%, = 150/100 = 3/2 times, the quantity would have to be 2/3 times last month's quantity to keep the revenue the same.
2/3 times last month's quantity means 66.7% of the old quantity. (Knowing 1/3 = 33.3% helped me here.)
66.7% is not an option. I'll reject 150 for X.
ii.
If the price became 160% = 160/100 = 8/5 times, the quantity would have to be 5/8 times last month's quantity to keep the revenue the same.
5/8 times last month's quantity means 62.5% of the old quantity. (I used a calculator to calculate 5/8).
62.5 is present in the table.
We could very well mark
X: 160
Y: 62.5
at this point and move on. We can't have two sets of values that would be consistent with the information provided. We've found one set of values that's consistent. This will be the only consistent pair.
iii.
Nevertheless, for practice, let me try X = 180.
If the price became 180% = 180/100 = 9/5 times, the quantity would have to be 5/9 times last month's quantity to keep the revenue the same.
5/9 times last month's quantity means 55.5% of the old quantity. (I knew that 1/9 = 11.11%. So, 5/9 must be 55.55%).
55.5 is not present in the table. Reject 180 for X.
Before I get into my solution, let me take an example:
Let's say the factory doubles the price.
And after doubling the price, the revenue remains the same.
What would have happened to the Quantity?
If the price doubles, but the revenue remains the same, the quantity must be halved.
Since the overall revenue was the same, the increase in the price will correspond to a proportional decrease in the quantity. In maths terms, if the price became 2x, the quantity would have become 1/2x.
--
We can answer the question using this underlying understanding.
1. "the factory raised the price of each widget to X% of the original price"
a. The price has been raised.
b. The price is not raised by X%. It is raised to X% of the original price. e.g. Say last month's price was $100, and this month's price is $110. Is X = 110 or 10? The price has been raised by 10%. It has been raised to 110% of the previous price. So, X = 110.
Since the price has been raised, X > 100.
2. "the factory only sold Y% as many widgets as last month, and the total revenue from the sale of widgets was equal for last month and this month."
a. The factory sold Y% as many widgets, not Y% less than last month, but Y%.
e.g. Let's say the quantity sold went down from 100 to 80. Would Y be 20 or 80? The factory sold 80% as many widgets as last month. Or, the factory sold 20% less widgets than last month. In this example, Y would be 80.
b. The total revenue was equal. The price per widget had increased. So, the quantity of widgets must have reduced.
Y < 100.
X can only be 150, 160, or 180.
Y can only be 50, 62.5, or 75.
Now, how to deal with the remaining values.
I will start with the potential answers for X: 150, 160, 180 and check if the corresponding value of Y is there in the table. (We could start with Y as well and then check if the corresponding value of X exists in the table. I chose X because I want to avoid dealing with 62.5/100.)
i.
If the price became 150%, = 150/100 = 3/2 times, the quantity would have to be 2/3 times last month's quantity to keep the revenue the same.
2/3 times last month's quantity means 66.7% of the old quantity. (Knowing 1/3 = 33.3% helped me here.)
66.7% is not an option. I'll reject 150 for X.
ii.
If the price became 160% = 160/100 = 8/5 times, the quantity would have to be 5/8 times last month's quantity to keep the revenue the same.
5/8 times last month's quantity means 62.5% of the old quantity. (I used a calculator to calculate 5/8).
62.5 is present in the table.
We could very well mark
X: 160
Y: 62.5
at this point and move on. We can't have two sets of values that would be consistent with the information provided. We've found one set of values that's consistent. This will be the only consistent pair.
iii.
Nevertheless, for practice, let me try X = 180.
If the price became 180% = 180/100 = 9/5 times, the quantity would have to be 5/9 times last month's quantity to keep the revenue the same.
5/9 times last month's quantity means 55.5% of the old quantity. (I knew that 1/9 = 11.11%. So, 5/9 must be 55.55%).
55.5 is not present in the table. Reject 180 for X.
