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At the start of his 3 years graduation program Mr. John bought a car

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Bunuel
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At the start of his 3 years graduation program Mr. John bought a car [#permalink] New post   05 Nov 2021, 04:45
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58% (02:32) correct 42% (02:26) wrong based on 38 sessions
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At the start of his 3 years graduation program Mr. John bought a car at the market price of $x and sold it to Mr. Max at the end of 3rd year at the market price of $y. If the market price of car depreciated by 20%, 50/3% and 25% respectively in 3 consecutive years, which of the following is true?


A. \(3x-2y=0\)

B. \(2x=y\)

C. \(x+y=3y\)

D. \(4x-3y=3x\)

E. None of these
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C
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IanStewart
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At the start of his 3 years graduation program Mr. John bought a car [#permalink] New post   Updated on: 05 Nov 2021, 08:40
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If something depreciates, or decreases, by x%, then it becomes (100 - x)% of what it used to be. So if something depreciates by 20%, it becomes 80%, or 0.8 = 4/5, of what it used to be. So the value of this car is multiplied, over the three year period, by 4/5, by 100 - 50/3 = 250/300 = 5/6, and by 3/4, so

y = (4/5)(5/6)(3/4)x
y = (2/3)(3/4)x
y = x/2
x = 2y

and if we rewrite answer C, that's what C says.

Originally posted by IanStewart on 05 Nov 2021, 04:54.
Last edited by IanStewart on 05 Nov 2021, 08:40, edited 1 time in total.
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Re: At the start of his 3 years graduation program Mr. John bought a car [#permalink] New post   05 Nov 2021, 08:39
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IanStewart wrote:
If something depreciates, or decreases, by x%, then it becomes (100 - x)% of what it used to be. So if something depreciates by 20%, it becomes 80%, or 0.8 = 4/5, of what it used to be. So the value of this car is multiplied, over the three year period, by 4/5, by 100 - 50/3 = 250/300 = 5/6, and by 3/4, so

y = (4/5)(5/6)(3/4)x
y = (2/3)(3/4)x
y = x/2
x = 2y

and if we rewrite answer D, that's what D says.
Sir, I believe you mean option (C).
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At the start of his 3 years graduation program Mr. John bought a car [#permalink] New post   05 Nov 2021, 08:42
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PyjamaScientist wrote:
IanStewart wrote:
I
and if we rewrite answer D, that's what D says.
Sir, I believe you mean option (C).


Yes, you're right, thank you! I forgot which answer was which. :)

Actually looking back, I think I just saw that the right answer was second from the bottom, not counting the 'none of the above', and thought it was D. The real GMAT would never have a 'none of the above' answer choice to a question like this.

Edited my post.
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Re: At the start of his 3 years graduation program Mr. John bought a car [#permalink] New post   05 Nov 2021, 09:19
Bunuel wrote:
At the start of his 3 years graduation program Mr. John bought a car at the market price of $x and sold it to Mr. Max at the end of 3rd year at the market price of $y. If the market price of car depreciated by 20%, 50/3% and 25% respectively in 3 consecutive years, which of the following is true?


A. \(3x-2y=0\)

B. \(2x=y\)

C. \(x+y=3y\)

D. \(4x-3y=3x\)

E. None of these


Breaking Down the Info:

A good habit is to always write the percent increase/decrease as the percent factor we are multiplying by to achieve the result.

x is multiplied by \(1 - 20\% = 80\% = \frac{4}{5}\), then \(1 - \frac{50}{3}\% = 1 - \frac{0.5}{3} = \frac{5}{6}\), and finally \(1 - 25\% = 75\% = \frac{3}{4}\) respectively to land on y.

Therefore \(x*\frac{4}{5}*\frac{5}{6}*\frac{3}{4} = x*\frac{1}{2} = y\), which is \(x = 2y\).

Answer: C
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Re: At the start of his 3 years graduation program Mr. John bought a car [#permalink]
05 Nov 2021, 09:19
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