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A coat’s original price of $112 was reduced by 20 percent for a sale.

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A coat’s original price of $112 was reduced by 20 percent for a sale.  [#permalink]

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New post 28 Jun 2017, 01:05
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A
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Question Stats:

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A coat’s original price of $112 was reduced by 20 percent for a sale. If the sale price was then increased by 20 percent, which of the following, expresses the single percent change, which when applied to the original price of the coat, would result in the same final price of the coat now?

(A) 100(1 − 0.2)^2
(B) 100 (1 − 0.4)
(C) 100(1 − 0.4)^2
(D) 100 (1 − 0.8)
(E) 100 (1 − 0.96)

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A coat’s original price of $112 was reduced by 20 percent for a sale.  [#permalink]

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New post Updated on: 29 Jun 2017, 10:53
Bunuel wrote:
A coat’s original price of $112 was reduced by 20 percent for a sale. If the sale price was then increased by 20 percent, which of the following, expresses the single percent change, which when applied to the original price of the coat, would result in the same final price of the coat now?

(A) 100(1 − 0.2)^2
(B) 100 (1 − 0.4)
(C) 100(1 − 0.4)^2
(D) 100 (1 − 0.8)
(E) 100 (1 − 0.96)


\(P\) = Original amount \(= $112\).

Let the first discount be \(r_1\) and second discount be \(r_2\).

Price after \(2\) successive discounts \(= (\frac{100 - r_2}{100} ) * (\frac{100 + r_1}{100} ) * P\)

Required Price \(= (\frac{100 - 20}{100}) * (\frac{100 + 20}{100}) * 112\)

Required Price \(= \frac{80}{100} * \frac{120}{100} * 112 = $107.52\)

Difference between original and final price \(= 112 - 107.52 = $4.48\)

Required percent \(= \frac{4.48}{112} * 100 = 4\)%.

Lets check options to find \(4\)%.

(E) \(100(1 − 0.96) = 100 (0.04) = 4\)%. Answer (E)...

Originally posted by sashiim20 on 28 Jun 2017, 01:45.
Last edited by sashiim20 on 29 Jun 2017, 10:53, edited 2 times in total.
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A coat’s original price of $112 was reduced by 20 percent for a sale.  [#permalink]

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New post 28 Jun 2017, 01:59
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Bunuel wrote:
A coat’s original price of $112 was reduced by 20 percent for a sale. If the sale price was then increased by 20 percent, which of the following, expresses the single percent change, which when applied to the original price of the coat, would result in the same final price of the coat now?

(A) 100(1 − 0.2)^2
(B) 100 (1 − 0.4)
(C) 100(1 − 0.4)^2
(D) 100 (1 − 0.8)
(E) 100 (1 − 0.96)


Price is first reduced by 20%, so price of coat = 0.80 x Coat Price
Price is then increased by 20%, so price of coat = 1.2 x 0.80 x Coat Price
= 0.96 x Coat Price
= 96% of Coat Price

Hence Answer E
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A coat’s original price of $112 was reduced by 20 percent for a sale.  [#permalink]

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New post 29 Jun 2017, 10:38
Bunuel wrote:
A coat’s original price of $112 was reduced by 20 percent for a sale. If the sale price was then increased by 20 percent, which of the following, expresses the single percent change, which when applied to the original price of the coat, would result in the same final price of the coat now?

(A) 100(1 − 0.2)^2
(B) 100 (1 − 0.4)
(C) 100(1 − 0.4)^2
(D) 100 (1 − 0.8)
(E) 100 (1 − 0.96)

Hmm. I got B. I think I might be confused.

Discount = .8
Subsequent price increase = 1.2

(.8) * (1.2) = (.96)

(.96) * (112) = $107.52

That matches other answers. But if 100 equals the original, and the original is multiplied by (.96), shouldn't it be Answer B?

100 (1 − 0.4) = (100)(.96), or 96% of original price. In bold above, I multiplied price by .96 and got the correct end figure.

What am I missing?
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Re: A coat’s original price of $112 was reduced by 20 percent for a sale.  [#permalink]

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New post 29 Jun 2017, 10:49
1
genxer123 wrote:
Bunuel wrote:
A coat’s original price of $112 was reduced by 20 percent for a sale. If the sale price was then increased by 20 percent, which of the following, expresses the single percent change, which when applied to the original price of the coat, would result in the same final price of the coat now?

(A) 100(1 − 0.2)^2
(B) 100 (1 − 0.4)
(C) 100(1 − 0.4)^2
(D) 100 (1 − 0.8)
(E) 100 (1 − 0.96)

Hmm. I got B. I think I might be confused.

Discount = .8
Subsequent price increase = 1.2

(.8) * (1.2) = (.96)

(.96) * (112) = $107.52

That matches other answers. But if 100 equals the original, and the original is multiplied by (.96), shouldn't it be Answer B?

100 (1 − 0.4) = (100)(.96), or 96% of original price. In bold above, I multiplied price by .96 and got the correct end figure.

What am I missing?


They asked for percent change, not percent of original price.

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Re: A coat’s original price of $112 was reduced by 20 percent for a sale.  [#permalink]

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New post 29 Jun 2017, 11:00
MarkusKarl wrote:
genxer123 wrote:

[107.52] matches other answers. But if 100 equals the original, and the original is multiplied by (.96), shouldn't it be Answer B?

100 (1 − 0.4) = (100)(.96), or 96% of original price. In bold above, I multiplied price by .96 and got the correct end figure.

What am I missing?


They asked for percent change, not percent of original price.

MarkusKarl whose screen name makes me grin, thank you! What a dumb mistake! :( Lesson learned.
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Re: A coat’s original price of $112 was reduced by 20 percent for a sale.  [#permalink]

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New post 29 Jun 2017, 11:30
Imo 112*.8*1.2=.96*112
Required percentage will be 4 percent reduction thus E

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Re: A coat’s original price of $112 was reduced by 20 percent for a sale.  [#permalink]

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New post 29 Jun 2017, 11:34
drop in the price of coat by 20 % results in a price of 0.8*112 (1-0.2=0.8)
subsequent 20% increase results in a price of 1.2 * 0.8 * 112 (1+0.2=1.2)

the final price is thus 0.96 *112 = 107.48 (i.e 96% of the original price implying a 4% decrease)

Answer to the question would be 100(1-0.96) i.e (E)
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Re: A coat’s original price of $112 was reduced by 20 percent for a sale.  [#permalink]

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New post 29 Jun 2017, 12:19
genxer123 wrote:
MarkusKarl wrote:
genxer123 wrote:

[107.52] matches other answers. But if 100 equals the original, and the original is multiplied by (.96), shouldn't it be Answer B?

100 (1 − 0.4) = (100)(.96), or 96% of original price. In bold above, I multiplied price by .96 and got the correct end figure.

What am I missing?


They asked for percent change, not percent of original price.

MarkusKarl whose screen name makes me grin, thank you! What a dumb mistake! :( Lesson learned.



Dumb indeed. I did the same thing :)

Is it the name or the picture? :-|

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Re: A coat’s original price of $112 was reduced by 20 percent for a sale.  [#permalink]

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New post 29 Jun 2017, 13:14
112*0.80=89.6
89.6*1.20=107.5
difference is of 4.5 so
{4.5/112}=0.04
ans=e
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Re: A coat’s original price of $112 was reduced by 20 percent for a sale.  [#permalink]

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New post 29 Jun 2017, 15:44
MarkusKarl wrote:
genxer123 wrote:
MarkusKarl whose screen name makes me grin, thank you! What a dumb mistake! :( Lesson learned.

Dumb indeed. I did the same thing :)
Is it the name or the picture? :-|

MarkusKarl It's both. In a good way! One of my degrees in in political economy, so the name made me grin fondly. Then I saw the picture -- I so want a cool picture -- and the picture is both not what I was expecting, which made me grin, and cool/adorable, which made me grin. Both name and pic are keepers! 8-)
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Re: A coat’s original price of $112 was reduced by 20 percent for a sale.  [#permalink]

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New post 16 Sep 2018, 21:08
take x = 100
so 100*4/5*6/5 = 96
so there is 4% change
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Re: A coat’s original price of $112 was reduced by 20 percent for a sale. &nbs [#permalink] 16 Sep 2018, 21:08
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