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The original price of a jacket was $80. This price was discounted x pe

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Russ19
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The original price of a jacket was $80. This price was discounted x pe [#permalink] New post   21 Jan 2021, 07:33
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60% (02:03) correct 40% (02:16) wrong based on 98 sessions
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The original price of a jacket was $80. This price was discounted \(x \) percent during a sale. Mary used a coupon to buy a jacket for \(y\) percent off the sale price. How much did Mary pay for the jacket?

(1) \(x + y - \frac{xy}{100} = 32\)

(2) \(x + y = 35\)
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The original price of a jacket was $80. This price was discounted x pe [#permalink] New post   Updated on: 23 Jan 2021, 09:45
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It is a successive percent change question
The price got decreased by x% and further decreased by y%
Final price = 80(1 - x/100) ( 1 - y/100)
= 80 (1 - x/100 - y/100 + xy/10000)
= 80/100 ( 100 - x - y + xy/100)
= 80/100 [100 - (x + y - xy/100)]

1) Final price can be calculated
Sufficient

2) Only value of x + y is known
Not sufficient

A is correct

Originally posted by QuantMadeEasy on 21 Jan 2021, 23:20.
Last edited by QuantMadeEasy on 23 Jan 2021, 09:45, edited 1 time in total.
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Re: The original price of a jacket was $80. This price was discounted x pe [#permalink] New post   22 Jan 2021, 14:36
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If you decrease something by x%, you multiply it by 1 - (x/100). In this question, we're decreasing an $80 price by x%, then by y%, so the final price will be:

80(1 - (x/100))(1 - (y/100)) = 80(1 - x/100 - y/100 + xy/10,000)
= 80 - (80/100)(x + y - (xy/100))

so if we can find the value of x + y - xy/100, we can answer the question. So Statement 1 is sufficient. Statement 2 is not, as you can see by taking any two different numerical examples at all.
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Re: The original price of a jacket was $80. This price was discounted x pe [#permalink] New post   22 Jan 2021, 22:07
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When we provide successive discounts, it can be calculated one by one on final price.
or you can directly use the formula :

If the first discount is x% and 2nd discount is y% then Successive Discount Formula –

Total discount = ( x + y – xy /100)%

sjuniv32 wrote:
IanStewart, BrentGMATPrepNow, avigutman, EMPOWERgmatRichC, GMATBusters
Dear mentors, could you please resolve the DS posted above? Thanks in advance!
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Re: The original price of a jacket was $80. This price was discounted x pe [#permalink] New post   22 Jan 2021, 12:38
IanStewart, BrentGMATPrepNow, avigutman, EMPOWERgmatRichC, GMATBusters
Dear mentors, could you please resolve the DS posted above? Thanks in advance!
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Re: The original price of a jacket was $80. This price was discounted x pe [#permalink] New post   20 Feb 2024, 08:09
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Re: The original price of a jacket was $80. This price was discounted x pe [#permalink]
20 Feb 2024, 08:09
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