Discount

vinay1983 wrote:A soccer store typically sells replica jerseys at a discount of 30 percent to 50 percent off list price. During the annual summer sale, everything in the store is an additional 20 percent off the original list price. If a replica jersey's list price is $80, approximately what percent of the list price is the lowest possible sale price?

A. 20
B. 25
C. 30
D. 40
E. 50

The jersey's original list price is irrelevant here, since the question asks us to find what percent of the list price is the lowest possible sale price?

Notice that the LOWEST possible sale price occurs when the first discount is MAXIMIZED. That is, when the first discount is 50 percent off the list price. This is followed by a 20% discount.

At this point, we can calculate the answer faster if we use an original list price of $100.
A 50% discount results in a sale price of $50
From here, a further 20% discount results in a summer sale price of $40
$40 is [spoiler]40%[/spoiler] of $100

Answer: D

Aside: Notice that we get the same answer if we use an original list price of $80.
A 50% discount results in a sale price of $40
From here, a further 20% discount results in a summer sale price of $32
$32 is [spoiler]40%[/spoiler] of $80

Cheers,
Brent

vipulgoyal wrote:I guess i found the flaw

additional 20% should be diducted first then 50 % on new list price

100(original list price) - 20 = 80(becomes list price), 80 - 40 = 40%

I have a feeling that the word "additional" threw you off at first. It sounds like we should add 20% to the price.


Your interpretation above isn't quite right. As the question is worded, the 50% reduction is first, and the 20% reduction comes second. Having said that, the order in which the deductions are performed doesn't matter. To reduce a price by 20%, we multiply by 0.8, and to reduce a price by 50%, we multiply by 0.5
So, final price = (list price)(0.5)(0.8)
This is the same as" final price = (list price)(0.8)(0.5)

Cheers,
Brent