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# The price of an item is discounted 10 percent on day 1 of a sale. On d

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Math Expert
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Posts: 61385
The price of an item is discounted 10 percent on day 1 of a sale. On d  [#permalink]

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16 Jun 2019, 23:07
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Difficulty:

75% (hard)

Question Stats:

50% (01:39) correct 50% (01:18) wrong based on 113 sessions

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The price of an item is discounted 10 percent on day 1 of a sale. On day 2, the item is discounted another 10 percent, and on day 3, it is discounted an additional 20 percent. The price of the item on day 3 is what percentage of the sale price on day 1?

A. 28%
B. 40%
C. 64.8%
D. 70%
E. 72%

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Re: The price of an item is discounted 10 percent on day 1 of a sale. On d  [#permalink]

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16 Jun 2019, 23:13
D1= 90%
D2= 90%*.9=81%
D3=81%*.8= 64.8%

D3/D1= 64.8/90=72% IMO E

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Re: The price of an item is discounted 10 percent on day 1 of a sale. On d  [#permalink]

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16 Jun 2019, 23:17
Bunuel wrote:
The price of an item is discounted 10 percent on day 1 of a sale. On day 2, the item is discounted another 10 percent, and on day 3, it is discounted an additional 20 percent. The price of the item on day 3 is what percentage of the sale price on day 1?

A. 28%
B. 40%
C. 64.8%
D. 70%
E. 72%

Let the initial price be 100

Day 1 : 100 * 0.9 = 90

Day 2 : 90 * 0.9 = 81

Day 3 : 81 * 0.8 = 64.8.

Required % : (price of day 3 / price of day 1)*100 = (64.8 / 90) * 100 = 72 .

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Re: The price of an item is discounted 10 percent on day 1 of a sale. On d  [#permalink]

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17 Jun 2019, 07:44
Bunuel wrote:
The price of an item is discounted 10 percent on day 1 of a sale. On day 2, the item is discounted another 10 percent, and on day 3, it is discounted an additional 20 percent. The price of the item on day 3 is what percentage of the sale price on day 1?

A. 28%
B. 40%
C. 64.8%
D. 70%
E. 72%

intial 100$day 1= 90$
day 2= 81 $day 3 = 64.8$
so % of day 3 of day 1= 64.8/90 ; 72%
IMO E
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Re: The price of an item is discounted 10 percent on day 1 of a sale. On d  [#permalink]

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05 Oct 2019, 16:00
Bunuel wrote:
The price of an item is discounted 10 percent on day 1 of a sale. On day 2, the item is discounted another 10 percent, and on day 3, it is discounted an additional 20 percent. The price of the item on day 3 is what percentage of the sale price on day 1?

A. 28%
B. 40%
C. 64.8%
D. 70%
E. 72%

If n = original price, then with all the discounts, the price of the item is:

n(0.9)(0.9)(0.8) = 0.648n

Thus, the answer is 0.648/0,.9 = 0.72 = 72%

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Re: The price of an item is discounted 10 percent on day 1 of a sale. On d  [#permalink]

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17 Jan 2020, 06:52
The question asks for the percentage of the price in day 3 to the price in day 1.
Therefore, if P1 and P3 are the prices of the item in day 1 and 3 respectively, we need to answer P3/P1. We can see that we actually dont care about the price reduction in the first day since the answer will not depend on that. We can just see that between the first and the second day the price was lowered by 10% and then by 20%. Therefore the answer will be 0.9*0.8=72%.

Therefore the option E is the answer. I dont see the reason to do the intermediate steps that other solutions propose. Its just adding math without needing it.
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Re: The price of an item is discounted 10 percent on day 1 of a sale. On d  [#permalink]

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17 Jan 2020, 07:53
Bunuel wrote:
The price of an item is discounted 10 percent on day 1 of a sale. On day 2, the item is discounted another 10 percent, and on day 3, it is discounted an additional 20 percent. The price of the item on day 3 is what percentage of the sale price on day 1?

A. 28%
B. 40%
C. 64.8%
D. 70%
E. 72%

$$100*\frac{90}{100}*\frac{90}{100}*\frac{80}{100}=64.8$$

Quote:
The price of the item on day 3 is what percentage of the sale price on day 1?

$$= \frac{64.80}{90}*100$$

$$= 72$$, Answer must be (E)
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Re: The price of an item is discounted 10 percent on day 1 of a sale. On d   [#permalink] 17 Jan 2020, 07:53
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