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Question Stats:
68% (02:30) correct
32%
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At a certain store, the retail price of a coat was \(p\) percent less than its list price. If the sale price of the coat was \(r\) percent less than its retail price, then the sale price of the coat was what percent of its list price?
(1) \(p - r + \frac{pr}{100} = 10\)
(2) \(p + r - \frac{pr}{100} = 40\)
Coat.png [ 36.36 KiB | Viewed 14298 times ]
(1) \(p - r + \frac{pr}{100} = 10\)
(2) \(p + r - \frac{pr}{100} = 40\)
Attachment:
Coat.png [ 36.36 KiB | Viewed 14298 times ]
18 Nov 2024, 03:31
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edwin.que
This is a 30 second question.
We are told that to the list price, a p% discount is applied (to get retail price) and then an r% discount is applied to get sale price. So 2 successive discounts are applied.
This means the overall discount is p + r - pr/100 (successive percentage changes that you must know for GMAT. It does appear in questions)
Statement 2 directly gives this value as 40% which means overall discount is 40% so sale price was 60% of list price.
Sufficient alone.
Statement 1 gives the relation between p and r but we cannot get p + r - pr/100 (overall discount percentage) from it. There is one equation with two variables. This is like saying that we need the value of x + y and we are given (x - y) = 10. Can we get (x+y)? No.
Answer (B)
Here is a post in which I have discussed this in successive percentage changes:
https://anaprep.com/arithmetic-successi ... e-changes/
MBAToronto2024
anirchat
28 Oct 2023, 22:51
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edwin.que
Assume that -
- the retail price of the coat = \(R\)
- the list price of the coat = \(L\)
- the sale price of the coat = \(S\)
"...At a certain store, the retail price of a coat was \(p\) percent less than its list price..."
\(R = L(1-\frac{p}{100})\)
"...If the sale price of the coat was \(r\) percent less than its retail price..."
\(S = R(1-\frac{r}{100}) = L(1-\frac{p}{100})(1-\frac{r}{100})\)
Question: ...then the sale price of the coat was what percent of its list price...
\(\frac{S}{L} * 100\) = ?
Let's simplify this my multiplying \(\frac{100}{L}\) on both sides of the equation-
\(S = L(1-\frac{p}{100})(1-\frac{r}{100})\)
\(\frac{S}{L} * 100 = 100(1-\frac{p}{100})(1-\frac{r}{100})\)
\(\frac{S}{L} * 100 = 100(1-\frac{p}{100})(1-\frac{r}{100})\)
\(\frac{S}{L} * 100 = 100(1 - \frac{r}{100} - \frac{p}{100} + \frac{pr}{100^2})\)
\(\frac{S}{L} * 100 = 100 - r - p + \frac{pr}{100}\)
\(\frac{S}{L} * 100 = 100 - (r + p - \frac{pr}{100})\)
Let's start with Statement 2
Statement 2
(2) \(p + r - \frac{pr}{100} = 40\)
We are given the value of \(r + p - \frac{pr}{100}\), hence that's sufficient to answer the question.
Eliminate A, C, and E.
Statement 1
(1) \(p - r + \frac{pr}{100} = 10\)
Not sufficient, as we can multiple possible values of \(p\) and \(r\) satisfying the equation.
Option B
