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# M06-33

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Math Expert
Joined: 02 Sep 2009
Posts: 56303

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16 Sep 2014, 02:51
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Difficulty:

15% (low)

Question Stats:

90% (01:18) correct 10% (01:54) wrong based on 29 sessions

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A music store has 90 different CD's. If an average price is $12 per CD and 20 of the most expensive ones are$20 each, what is the average price of the remaining CD's?

A. 8.33
B. 8.75
C. 9.23
D. 9.71
E. 10.07

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Math Expert
Joined: 02 Sep 2009
Posts: 56303

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16 Sep 2014, 02:51
Official Solution:

A music store has 90 different CD's. If an average price is $12 per CD and 20 of the most expensive ones are$20 each, what is the average price of the remaining CD's?

A. 8.33
B. 8.75
C. 9.23
D. 9.71
E. 10.07

The sum of the prices of all CD's is $$90 * 12 = 1,080$$.

The sum of the prices of the most expensive CD's is \$400. So, $$1,080 - 400 = 680$$ is left for 70 remaining CD's. Thus the average price is $$\frac{680}{70} = 9.71$$

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IIMA, IIMC School Moderator
Joined: 04 Sep 2016
Posts: 1362
Location: India
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10 Jul 2018, 07:41
Hi chetan2u niks18 pushpitkc pikolo2510 Abhishek009

Is below approach (presumably of weighted average) valid:

[(20*20) + (x*70)] / 90 =12

Simplifying gives same result
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Joined: 31 Jul 2017
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10 Jul 2018, 07:45
first we need to find total sum then subtract the most expensive ones and divide the rest
12*90=1080-400(20*20)=680/70=9.7 (D)
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10 Jul 2018, 08:25
Hi chetan2u niks18 pushpitkc pikolo2510 Abhishek009

Is below approach (presumably of weighted average) valid:

[(20*20) + (x*70)] / 90 =12

Simplifying gives same result

If you look closely, It is actually the same method as bunuel solved it.

Multiple by 90 on RHS and subtract 20*20 i.e.

x*70 = 90*12 - 20*20
x*70 = 1080 - 400
x*70 = 680
x = 680/70

x = 9.71
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Re: M06-33   [#permalink] 10 Jul 2018, 08:25
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# M06-33

Moderators: chetan2u, Bunuel