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At the beginning of each year, the price of item X is 10 percent highe

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Bunuel
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At the beginning of each year, the price of item X is 10 percent highe [#permalink] New post   22 May 2020, 04:34
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At the beginning of each year, the price of item X is 10 percent higher than its price at the beginning of the previous year. During three consecutive years, if the price of item X is $8 at the beginning of the first year, what is its price at the beginning of the third year?

A. $8.80
B. $9.60
C. $9.68
D. $10.00
E. $16.00


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At the beginning of each year, the price of item X is 10 percent highe [#permalink] New post   Updated on: 22 May 2020, 11:09
1 year = \( 8\)
2 year = \(8+0.8= 8.8\)
3 year = \(8.8+0.88=9.68\)

Answer C

Originally posted by Ravixxx on 22 May 2020, 05:50.
Last edited by Ravixxx on 22 May 2020, 11:09, edited 1 time in total.
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Re: At the beginning of each year, the price of item X is 10 percent highe [#permalink] New post   22 May 2020, 06:26
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Bunuel wrote:
At the beginning of each year, the price of item X is 10 percent higher than its price at the beginning of the previous year. During three consecutive years, if the price of item X is $8 at the beginning of the first year, what is its price at the beginning of the third year?

A. $8.80
B. $9.60
C. $9.68
D. $10.00
E. $16.00


PS21150


Solution


    The price of item X is increasing 10% each year then the previous year.
      • At the beginning of the first year, the price of item X \(= $8\)
      • At the beginning of the second year, the price of item X \(= 8*(1+\frac{10}{100}) =$(8*1.1)\)
      • At the beginning of the third year, the price of X \(= 8*1.1*1.1 =8*1.21 = $9.68\)
Thus, the correct answer is Option C.
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BrentGMATPrepNow
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Re: At the beginning of each year, the price of item X is 10 percent highe [#permalink] New post   22 May 2020, 06:32
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Bunuel wrote:
At the beginning of each year, the price of item X is 10 percent higher than its price at the beginning of the previous year. During three consecutive years, if the price of item X is $8 at the beginning of the first year, what is its price at the beginning of the third year?

A. $8.80
B. $9.60
C. $9.68
D. $10.00
E. $16.00

PS21150


APPROACH #1
Time : Price
Beginning of first year : $8
Beginning of second year : $8 + (10% of $8) = $8 + ($0.80) = $8.80
Beginning of 3rd year: $8.80 + (10% of $8.80) = $8.80 + $0.88 = 9.68
Answer: C

APPROACH #2
Key concept: Increasing a value by 10% is the same as multiplying that value by 1.10
We get:
Beginning of first year : $8
Beginning of second year : ($8)(1.10)
Beginning of 3rd year: ($8)(1.10)(1.10) = ($8)(1.21) = $9.68
Answer: C

Cheers,
Brent
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Re: At the beginning of each year, the price of item X is 10 percent highe [#permalink] New post   22 May 2020, 08:40
Bunuel wrote:
At the beginning of each year, the price of item X is 10 percent higher than its price at the beginning of the previous year. During three consecutive years, if the price of item X is $8 at the beginning of the first year, what is its price at the beginning of the third year?

A. $8.80
B. $9.60
C. $9.68
D. $10.00
E. $16.00


PS21150

Net Increase is \(10 + 10 + \frac{10*10}{100} = 21\)

Hence, Value of the item after 3rd year is \(8*\frac{121}{100} = 9.68\), Answer must be (C)
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Re: At the beginning of each year, the price of item X is 10 percent highe [#permalink] New post   21 Feb 2022, 11:29
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Re: At the beginning of each year, the price of item X is 10 percent highe [#permalink]
21 Feb 2022, 11:29
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