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# Jaime has n comic books. He sells one half of them and then gives one

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VP
Status: Preparing for the GMAT
Joined: 02 Nov 2016
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Jaime has n comic books. He sells one half of them and then gives one [#permalink]

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14 May 2017, 11:02
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Question Stats:

78% (00:48) correct 22% (00:58) wrong based on 59 sessions

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Jaime has n comic books. He sells one half of them and then gives one third of the ones he has left to a friend. If he has 10 comic books left, how many did he have originally?

A. 30
B. 40
C. 60
D. 80
E. 90
[Reveal] Spoiler: OA

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Kudos [?]: 1099 [2], given: 543

Senior Manager
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Re: Jaime has n comic books. He sells one half of them and then gives one [#permalink]

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14 May 2017, 13:33
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Jaime has n comic books.

He sells one half of them -- Jaime now has n/2 comic books left

Then gives one third of the ones he has left to a friend -- Jaime now has 2/3 of the n/2 comic books left = n/3 comic books left

If he has 10 comic books left => n/3 = 10 => n=30

Kudos [?]: 188 [1], given: 48

Manager
Joined: 07 Jul 2012
Posts: 219

Kudos [?]: 66 [0], given: 65

Location: India
Concentration: Finance
Re: Jaime has n comic books. He sells one half of them and then gives one [#permalink]

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15 May 2017, 01:07
Let Jamie has n comic books
As per question, we can simplify as follows:

n-$$\frac{n}{2}$$-$$\frac{n}{2}$$*$$\frac{1}{3}$$= 10

n-$$\frac{n}{2}$$-$$\frac{n}{6}$$= 10

$$\frac{6n-3n-n}{6}$$= 10

$$\frac{2n}{6}$$=10=> n=30

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Kudos [?]: 66 [0], given: 65

Manager
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Kudos [?]: 10 [1], given: 80

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Jaime has n comic books. He sells one half of them and then gives one [#permalink]

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15 May 2017, 10:21
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Total number of comic books = n.

$$\frac{n}{2}$$ sold. Remaining = $$\frac{n}{2}$$.

$$\frac{1}{3}$$$$(\frac{n}{2})$$ given to friend. Remaining = $$\frac{2}{3}(\frac{n}{2})$$.

Now,$$\frac{2}{3}(\frac{n}{2}$$) = 10

=> $$\frac{n}{3}$$ = 10

=> 30

Ans: A

Last edited by singhabhijeet on 16 Oct 2017, 06:36, edited 1 time in total.

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Re: Jaime has n comic books. He sells one half of them and then gives one [#permalink]

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14 Oct 2017, 09:43
Jaime has n comic books.

He sells one half of them -- Jaime now has n/2 comic books left

Then gives one third of the ones he has left to a friend -- Jaime now has 2/3 of the n/2 comic books left = n/3 comic books left

If he has 10 comic books left => n/3 = 10 => n=30

Kudos [?]: 7 [0], given: 182

Re: Jaime has n comic books. He sells one half of them and then gives one   [#permalink] 14 Oct 2017, 09:43
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