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The sale price of a certain jacket was \(15\) percent less than its original price, and the sale price of a certain shir

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by Vincen » Wed Nov 18, 2020 10:28 am

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Difficulty—

The sale price of a certain jacket was \(15\) percent less than its original price, and the sale price of a certain shirt was \(10\) percent less than its original price. How much greater was the original price of the jacket than the original price of the shirt?

(1) The sale price of the jacket was \(\$83\) greater than the sale price of the shirt.
(2) The original price of the jacket was \(\$140.\)

Answer: C

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Source: — Data Sufficiency |
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Re: The sale price of a certain jacket was \(15\) percent less than its original price, and the sale price of a certain

by deloitte247 » Fri Nov 20, 2020 4:48 pm
Let the original price of jacket = j
Let the original price of shirt = s
Sale price of jacket = 100% j - 15% of j = 85% j
Sale price of shirt = 100% s - 10% of s = 90% s
Target question: How much greater was the original price of the jacket than the original price of the shirt?

Statement 1: The sale price of the jacket was $8 greater than the sale price of the shirt.
i.e what is j-s?
85% j - 90% s = $83
0.85j - 0.9s = 83
The value of j and s is unknown; so, statement 1 is NOT SUFFICIENT.

Statement 2: The original price of the jacket was $140
j=140 and j-s = 140 - s
The value of s is unknown, so, statement 2 is NOT SUFFICIENT.

Combining both statements:
From statement 1: 0.85j - 0.9s = 83
From statement 2: j = 140
0.85 (140) - 0.9s = 83
119 - 0.9s = 83
0.9s = 36
s = 40
So, j - s = 140 - 40 = 100
Therefore, both statements combined are SUFFICIENT.
Answer = option C
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