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In 1986 the book value of a certain car was 2/3 original

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In 1986 the book value of a certain car was 2/3 original  [#permalink]

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New post Updated on: 12 Aug 2012, 08:48
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In 1986 the book value of a certain car was 2/3 original price, and in 1988 its book value was 1/2 the original purchase price. By what percent did the book value for this car decrease from 1986 to 1988?

(A) 16 2/3%
(B) 25%
(C) 33 1/3
(D) 50%
(E) 75%

Originally posted by JustinDragna on 12 Aug 2012, 08:39.
Last edited by Bunuel on 12 Aug 2012, 08:48, edited 1 time in total.
Edited the question.
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Re: In 1986 the book value of a certain car...  [#permalink]

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New post 12 Aug 2012, 08:41
i can see it if i draw it, but i cannot for some reason solve it arithmetically. i feel like it should be easy, but I can't see it.
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Re: In 1986 the book value of a certain car was 2/3 original  [#permalink]

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New post 12 Aug 2012, 08:55
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JustinDragna wrote:
In 1986 the book value of a certain car was 2/3 original price, and in 1988 its book value was 1/2 the original purchase price. By what percent did the book value for this car decrease from 1986 to 1988?

(A) 16 2/3%
(B) 25%
(C) 33 1/3
(D) 50%
(E) 75%


General formula for percent increase or decrease, (percent change): \(percent=\frac{Change}{Original}*100\).

Say the original price was $6, then:
In 1986 the book value of the car was 2/3*6=$4;
In 1988 the book value of the car was 1/2*6=$3;

Hence from 1986 to 1988 the book value for this car decreased by \(percent=\frac{Change}{Original}*100=\frac{4-3}{4}*100=25%\).

Answer: B.
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Re: In 1986 the book value of a certain car was 2/3 original  [#permalink]

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New post 12 Aug 2012, 09:27
Ok, that makes sense. If you have 4 and then go to 3, that's going to be a 25$ decrease from the original value of 4.

I thought the question was asking the percent it decreased from the original price between 1986 and 1988, which would just be the difference between the two fractions *100, or 1/6(100).

Now, that I look back at my original drawing, it doesn't even make sense the way i was thinking about it.

Anyway, thanks for the help.
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Re: In 1986 the book value of a certain car was 2/3 original  [#permalink]

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New post 16 Aug 2012, 22:56
Let say the original price of a car is 30 000 $, in 1986 its price is 20 000 $ (2/3 of 30000), in 1988 its value is 15 000$ (1/2 of 30000). The change in price between 86 and 88 is 5000, 5000 is 25% of 20000 (we need to take 20000 because we calculate the change from this year).
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Re: In 1986 the book value of a certain car was 2/3 original  [#permalink]

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New post 05 Jul 2014, 08:01
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Best numbers: 300- Original

In 1986- 200
In 1988- 150

Decrease of 50 over 200 between 86 and 88
So 25%
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Re: In 1986 the book value of a certain car was 2/3 original  [#permalink]

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New post 18 Feb 2015, 16:13
Bunuel wrote:
JustinDragna wrote:
In 1986 the book value of a certain car was 2/3 original price, and in 1988 its book value was 1/2 the original purchase price. By what percent did the book value for this car decrease from 1986 to 1988?

(A) 16 2/3%
(B) 25%
(C) 33 1/3
(D) 50%
(E) 75%


General formula for percent increase or decrease, (percent change): \(percent=\frac{Change}{Original}*100\).

Say the original price was $6, then:
In 1986 the book value of the car was 2/3*6=$4;
In 1988 the book value of the car was 1/2*6=$3;

Hence from 1986 to 1988 the book value for this car decreased by \(percent=\frac{Change}{Original}*100=\frac{4-3}{4}*100=25%\).

Answer: B.



Thanks this is very helpful - quick question though, i see the percentage change formula is change/originalx100.. shouldn't the original be $6 dollars instead of 4 dollars?
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Re: In 1986 the book value of a certain car was 2/3 original  [#permalink]

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New post 19 Feb 2015, 00:08
pinkcupcake wrote:
Bunuel wrote:
JustinDragna wrote:
In 1986 the book value of a certain car was 2/3 original price, and in 1988 its book value was 1/2 the original purchase price. By what percent did the book value for this car decrease from 1986 to 1988?

(A) 16 2/3%
(B) 25%
(C) 33 1/3
(D) 50%
(E) 75%


General formula for percent increase or decrease, (percent change): \(percent=\frac{Change}{Original}*100\).

Say the original price was $6, then:
In 1986 the book value of the car was 2/3*6=$4;
In 1988 the book value of the car was 1/2*6=$3;

Hence from 1986 to 1988 the book value for this car decreased by \(percent=\frac{Change}{Original}*100=\frac{4-3}{4}*100=25%\).

Answer: B.



Thanks this is very helpful - quick question though, i see the percentage change formula is change/originalx100.. shouldn't the original be $6 dollars instead of 4 dollars?


Original means "base value" or the "reference value"

"By what percent did the book value for this car decrease from 1986 to 1988"
means that as compared with the value in 1986, by what percent did the value decrease in 1988?

So the base value is the 1986 value which is 4.
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Re: In 1986 the book value of a certain car was 2/3 original  [#permalink]

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New post 19 Feb 2015, 02:25
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Let the original value = 1

Change \(= \frac{1}{2} * 100 * \frac{3}{2} = 75\)

Percent change = 100-75 = 25%
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Re: In 1986 the book value of a certain car was 2/3 original  [#permalink]

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New post 24 Oct 2017, 08:43
Suppose, the price was $300

in 1986 book value = 2/3 of $300 = $200
in 1988 book value = 1/2 of $300 = $150

Change in book value = $50
percentage change of book value= (50/200) * 100 = 25%

Ans: B.
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Re: In 1986 the book value of a certain car was 2/3 original  [#permalink]

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New post 24 Oct 2017, 10:31
JustinDragna wrote:
In 1986 the book value of a certain car was 2/3 original price, and in 1988 its book value was 1/2 the original purchase price. By what percent did the book value for this car decrease from 1986 to 1988?

(A) 16 2/3%
(B) 25%
(C) 33 1/3
(D) 50%
(E) 75%


Lets say original value be x
in 1986 book value = 2/3x
In 1988 book value = 1/2x
Change from 1986 to 1988 = 2/3x - 1/2 x = 1/6 x
Percentage change from 1986 to 1988 = [(1/6x)/(2/3x)]*100 = 25%

Answer B
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Re: In 1986 the book value of a certain car was 2/3 original  [#permalink]

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New post 24 Oct 2017, 10:35
JustinDragna wrote:
In 1986 the book value of a certain car was 2/3 original price, and in 1988 its book value was 1/2 the original purchase price. By what percent did the book value for this car decrease from 1986 to 1988?

(A) 16 2/3%
(B) 25%
(C) 33 1/3
(D) 50%
(E) 75%


Alternatively since the LCM of 3 and 2 is 6 . So lets take original price as some multiple of 6, say 60
Original price = 60
In 1986, book value = 2/3*60 = 40
In 1988 book value = 1/2*60 = 30
Percentage change from 1986 to 1988 = (40-30)/40 * 100 = 25%

Answer B

We can solve by either method.. Taking a value will help us to solve this question in a faster manner.
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Re: In 1986 the book value of a certain car was 2/3 original &nbs [#permalink] 24 Oct 2017, 10:35
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