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A motorcycle costs $2,500 when it is brand new. At the end of each yea

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A motorcycle costs $2,500 when it is brand new. At the end of each yea [#permalink]

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New post 05 Nov 2017, 01:54
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A motorcycle costs $2,500 when it is brand new. At the end of each year it is worth 80 percent of what it was worth at the beginning of the year. What is the motorcycle worth when it is 3 years old?

(A) $1,000
(B) $1,200
(C) $1,280
(D) $1,340
(E) $1,430
[Reveal] Spoiler: OA

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Re: A motorcycle costs $2,500 when it is brand new. At the end of each yea [#permalink]

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New post 05 Nov 2017, 02:05
Bunuel wrote:
A motorcycle costs $2,500 when it is brand new. At the end of each year it is worth 80 percent of what it was worth at the beginning of the year. What is the motorcycle worth when it is 3 years old?

(A) $1,000
(B) $1,200
(C) $1,280
(D) $1,340
(E) $1,430


After three years the motor cycle is worth \((0.8)^3*x\), if the present price of the motor cycle is x

Since the current price of the motor cycle is 2500$, the price after 3 years is \(0.512*2500 = 1280\)$(Option C)
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A motorcycle costs $2,500 when it is brand new. At the end of each yea [#permalink]

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New post 05 Nov 2017, 13:39
Bunuel wrote:
A motorcycle costs $2,500 when it is brand new. At the end of each year it is worth 80 percent of what it was worth at the beginning of the year. What is the motorcycle worth when it is 3 years old?

(A) $1,000
(B) $1,200
(C) $1,280
(D) $1,340
(E) $1,430

A brand new motorcycle is worth $2,500.

At the end of each year, it is worth 80% of its value from the beginning of that year -- in other words, it loses 20% of its value from the beginning of the year.

Calculating the multiplier (.8)\(^3\), then multiplying that by $2,500 seemed more labor-intensive than just subtracting 20 percent from each year's value. Your mileage may vary.

Year 1: loses 20 percent of $2,500
10% = $250, so 20% = $500
End of year 1: ($2,500 - 500) = $2000

Year 2: loses 20 percent of $2,000
10% = $200, so 20% = $400
End of year 2: ($2,000 - 400) = $1,600

Year 3: loses 20 percent of $1,600
10% = $160, so 20% = $320
End of year 3: ($1,600 - 320) = $1,280

Answer C

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Re: A motorcycle costs $2,500 when it is brand new. At the end of each yea [#permalink]

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New post 06 Nov 2017, 20:07
easy calculation

2500 x 4^3/5^3

= $1280

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Re: A motorcycle costs $2,500 when it is brand new. At the end of each yea [#permalink]

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New post 08 Nov 2017, 17:33
Bunuel wrote:
A motorcycle costs $2,500 when it is brand new. At the end of each year it is worth 80 percent of what it was worth at the beginning of the year. What is the motorcycle worth when it is 3 years old?

(A) $1,000
(B) $1,200
(C) $1,280
(D) $1,340
(E) $1,430



Noting that 80% = 0.80 = ⅘, we see that after 3 years, the motorcycle is worth:

2,500 x 4/5 x 4/5 x 4/5 = 2,500 x 64/125 = 20 x 64 = $1,280

Answer: C
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Re: A motorcycle costs $2,500 when it is brand new. At the end of each yea   [#permalink] 08 Nov 2017, 17:33
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