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# The average price of an antique car increases over the years. If from

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Joined: 02 Sep 2009
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The average price of an antique car increases over the years. If from  [#permalink]

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21 Jun 2016, 03:09
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15% (low)

Question Stats:

89% (02:02) correct 11% (02:18) wrong based on 82 sessions

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The average price of an antique car increases over the years. If from 1990 to 1996, the price of the car increased by 13% and from 1996 to 2001 it increased by 20%, what is the price of the car in 2001 if the price in 1990 was \$11,500?

A. \$15,594.
B. \$15,322.
C. \$14,786.
D. \$14,543.
E. \$12,988.

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Re: The average price of an antique car increases over the years. If from  [#permalink]

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21 Jun 2016, 07:27
5
Bunuel wrote:
The average price of an antique car increases over the years. If from 1990 to 1996, the price of the car increased by 13% and from 1996 to 2001 it increased by 20%, what is the price of the car in 2001 if the price in 1990 was \$11,500?

A. \$15,594.
B. \$15,322.
C. \$14,786.
D. \$14,543.
E. \$12,988.

Ofcourse EXACt method is already given above, just another way due to the choices available...

ans is 11500*1.13*1.2 , so a multiple of 3...
Only A is multiple of 3..
A
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Re: The average price of an antique car increases over the years. If from  [#permalink]

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21 Jun 2016, 04:56
price of the car in 1990 = \$11500
from 1990 to 1996
increase = 13%
which is (13*115)
price of the car in 1996= \$12995

from 1996 to 2001
increase = 20 %
which is (12995)/5 =2599

price of the car in 2001 = 15594
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Re: The average price of an antique car increases over the years. If from  [#permalink]

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21 Jun 2016, 07:14
11500 *1.13 *1.2 = 15594
option A
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Re: The average price of an antique car increases over the years. If from  [#permalink]

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Updated on: 21 Jun 2016, 07:38
Whenever you have a question in which a value is increased by x% and then increased by y% then the overall effective increase = (x + y + xy/100 ) %

Let's apply the formula in the question.

The effective increase = 13 + 20 + (13×20/100) = 35.6%

This is a little more 33% or 1/3 the original value.

THE QUICKEST WAY TO SOLVE THIS QUESTION IS TO USE APPROXIMATION.

11500 + 1/ 3 (12000) = 15500

Therefore option A is the answer.

I selected 12000 because it's value is a little more 11500 and it's easier to divide by 3 ( ie to calculate 1/3 or 33%).
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Originally posted by LightYagami on 21 Jun 2016, 07:25.
Last edited by LightYagami on 21 Jun 2016, 07:38, edited 1 time in total.
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Re: The average price of an antique car increases over the years. If from  [#permalink]

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21 Jun 2016, 08:35
1
Bunuel wrote:
The average price of an antique car increases over the years. If from 1990 to 1996, the price of the car increased by 13% and from 1996 to 2001 it increased by 20%, what is the price of the car in 2001 if the price in 1990 was \$11,500?

A. \$15,594.
B. \$15,322.
C. \$14,786.
D. \$14,543.
E. \$12,988.

11,500 *1.13*1.20= Units digit of this expression would be 4.

Only option A has units digit of 4. And hence is the answer
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Re: The average price of an antique car increases over the years. If from  [#permalink]

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14 Jul 2017, 17:56
Bunuel wrote:
The average price of an antique car increases over the years. If from 1990 to 1996, the price of the car increased by 13% and from 1996 to 2001 it increased by 20%, what is the price of the car in 2001 if the price in 1990 was \$11,500?

A. \$15,594.
B. \$15,322.
C. \$14,786.
D. \$14,543.
E. \$12,988.

11,500 *1.13*1.20= Units digit of this expression would be 4.

Only option A has units digit of 4. And hence is the answer

That's a really elegant solution! Quick question, how were you able to tell the units digit from 11,500*1.13*1.2. I'm only familiar with doing that for whole numbers.

I got as far as:
11,500*1.13*1.2 --> 115*113*1.2 and then I wasn't quite sure how to see the unit's digit coming to 4.

Re: The average price of an antique car increases over the years. If from   [#permalink] 14 Jul 2017, 17:56
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