yikes000 wrote:
A shirt and a jacket are each for sale at a price that is discounted from the item's original price. Which has the lower discounted price?
(1) The jacket's original price was twice the shirt's original price.
(2) The percent of discount on the jacket's original price is three times the percent of discount on the shirt's original price.
Assume:
- Original Price of the shirt = \(s\)
- Original Price of the jacket = \(j\)
- Discounted Price of the shirt = \(s_d\)
- Discounted Price of the jacket = \(j_d\)
Statement 1(1) The jacket's original price was twice the shirt's original price.\(j = 2s\)
We do not have any information on the percentage of discount offered. Hence, we cannot comment on anything about the final discounted price. Depending on the original price and the percentage of discount offered the discounted price of the jacket and shirt is calculated. Hence, this statement is not sufficient to answer the question between the discounted price of the shirt, \(s_d\), and the discounted price of the jacket, \(j_d\), which is lower.
Statement 2(2) The percent of discount on the jacket's original price is three times the percent of discount on the shirt's original price.- Percentage of discount offered on the shirt = \(x\)
- Percentage of discount offered on the jacket = \(3x\)
We do not have any information on the original price of the merchandise. Hence, we cannot comment on anything about the final discounted price of the shirt or the jacket. Depending on the original price and the percentage of discount offered the discounted price of the jacket and shirt is calculated. Hence, this statement is not sufficient to answer the question between the discounted price of the shirt, \(s_d\), and the discounted price of the jacket, \(j_d\), which is lower.
Combined- Original Price of the shirt = \(s\)
- Original Price of the jacket = \(j = 2s\)
- Percentage of discount offered on the shirt = \(x\)
- Percentage of discount offered on the jacket = \(3x\)
- Discounted Price of the shirt = \(s_d = s[1-\frac{x}{100}]\)
- Original Price of the jacket = \(j_d = 2s[1-\frac{3x}{100}]\)
This information is also not sufficient to determine whether \(j_d\) is lower than \(s_d\) or vice versa as we do not have the absolute value of the discount percentage. Depending on the discount percentage one of the values can be lower or the values can be equal.
For example for \(s_d\) to be equal to \(j_d\)
\(s_d = j_d\)
\(s[1-\frac{x}{100}] = 2s[1-\frac{3x}{100}]\)
Dividing by \(s\) on both sides
\([1-\frac{x}{100}] = 2[1-\frac{3x}{100}]\)
\(\frac{5x}{100} = 1\)
\(x = 20\)
Hence, if the discount percentage is 20%, the value of the discounted price of the shirt and the value of the discounted price of the jacket is equal.
If the discount percentage is more than 20%, the value of the discounted price of the shirt is greater than the value of the discounted price of the jacket.
If the discount percentage is less than 20%, the value of the discounted price of the shirt is less than the value of the discounted price of the jacket.
Hence, without knowing the actual discount percentage, we cannot comment on the discounted price of the merchandise.
Option E