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27 Oct 2025, 17:34
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E
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
55%
(hard)
Question Stats:
68% (02:00) correct
32%
(02:08)
wrong
based on 158
sessions
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A vendor sold an item after reducing the price of the item by p percent from its original level. If the cost of the item to the vendor was $80, did the vendor make a profit on the sale of the item?
(1) The original price of the item was greater than $105.
(2) p < 25
(1) The original price of the item was greater than $105.
(2) p < 25
27 Oct 2025, 18:21
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A vendor sold an item after reducing the price of the item by p percent from its original price. If the cost of the item to the vendor was $80, did the vendor make a profit on the sale of the item?
To make a profit, the vendor would have had to sell the item for more than the vendor's cost of $80. So, we can simplify the question to "Did the vendor sell the item for more than $80?'
(1) The original price of the item was greater than $105.
This statement limits the price before the reduction to values greater than $105 but does not limit how much the price was reduced by.
Given what this statement says, p could be any percentage.
So, the information provided by this statement does not at all restrict the price at which the item was sold.
Insufficient.
(2) p < 25
This statement tells us the percentage by which the price was reduced from the original price.
However, it does not indicate what the original price was. So, given what this statement says, the vendor could have sold the item for any price.
Insufficient.
Statements (1) and (2) combined
The statements combined are a little tricky to handle because we could see that statement (1) says that the original price was greater than $105 and that statement (2) says that p < 25 and decide that $105 - (something less than 25) must be greater than $80 since 105 - 25 = 80.
So, what's key to notice is that 25 percent of 105 isn't 25. It's (0.25 × 100) + (0.25 × 5) = 26.25.
Accordingly, 105 - (0.25 × 105) = 78.75.
Thus, even if the original price was slightly over $105 and p was slightly less than 25, the item could have been sold for less than $80.
Example:
Original price: 105.01
p: 24.99
Final selling price: 105.01 × 0.7501 ≈ 78.77
We don't need to calculate the above example to see that we can increase the original price by a small amount from $105 and decrease p from 25 by a small amount and still get a selling price below $80. After all, there's room for a small increase between 78.75 and 80.
At the same time, we can also see that, if we sufficiently increase the original price or decrease p, we can get a final selling price above $80.
So, given the information provided by the statements combined, the final selling price could be below or above $80.
Insufficient.
Correct answer E
To make a profit, the vendor would have had to sell the item for more than the vendor's cost of $80. So, we can simplify the question to "Did the vendor sell the item for more than $80?'
(1) The original price of the item was greater than $105.
This statement limits the price before the reduction to values greater than $105 but does not limit how much the price was reduced by.
Given what this statement says, p could be any percentage.
So, the information provided by this statement does not at all restrict the price at which the item was sold.
Insufficient.
(2) p < 25
This statement tells us the percentage by which the price was reduced from the original price.
However, it does not indicate what the original price was. So, given what this statement says, the vendor could have sold the item for any price.
Insufficient.
Statements (1) and (2) combined
The statements combined are a little tricky to handle because we could see that statement (1) says that the original price was greater than $105 and that statement (2) says that p < 25 and decide that $105 - (something less than 25) must be greater than $80 since 105 - 25 = 80.
So, what's key to notice is that 25 percent of 105 isn't 25. It's (0.25 × 100) + (0.25 × 5) = 26.25.
Accordingly, 105 - (0.25 × 105) = 78.75.
Thus, even if the original price was slightly over $105 and p was slightly less than 25, the item could have been sold for less than $80.
Example:
Original price: 105.01
p: 24.99
Final selling price: 105.01 × 0.7501 ≈ 78.77
We don't need to calculate the above example to see that we can increase the original price by a small amount from $105 and decrease p from 25 by a small amount and still get a selling price below $80. After all, there's room for a small increase between 78.75 and 80.
At the same time, we can also see that, if we sufficiently increase the original price or decrease p, we can get a final selling price above $80.
So, given the information provided by the statements combined, the final selling price could be below or above $80.
Insufficient.
Correct answer E
09 Nov 2025, 02:49
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MartyMurray
Let's assume that the orginal price of the item = x
Discounted price = \(x(1- \frac{p}{100})\)
Question :
\(x(1- \frac{p}{100}) > 80\)
Statement 1
(1) The original price of the item was greater than $105.
x = 105
Is \(105(1- \frac{p}{100}) > 80\)
As we don't know the value of \(1- \frac{p}{100}\) we cannot comment on the final value of \(105(1- \frac{p}{100})\)
Hence, we can eliminate A and D
Statement 2
(2) p < 25
We don't have any information on the value of x, and the value of p. Hence, we can't find the value of \(x(1- \frac{p}{100})\)
Eliminate B.
Combined
Let's assume that p = 25
\(105(1- \frac{25}{100}) \approx 78\)
Therefore the minimum possible value of \(105(1- \frac{p}{100}) \), however the value can be also greater depending on the value of p. Let's assume that the value of p is very close to 0, then the value of dicounted price is almost equal to 105.
As we can have both possibilities on in which \(x(1- \frac{p}{100}) \) > 80 and in other not, the statements combined is not sufficient.
Option E
