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In the interior of a forest, a certain number of apes equal to the squ

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In the interior of a forest, a certain number of apes equal to the squ [#permalink]

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New post 15 Nov 2010, 20:39
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Question Stats:

69% (02:43) correct 31% (02:08) wrong based on 192 sessions

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In the interior of a forest, a certain number of apes equal to the square of one-eighth of the total number are playing and having great fun. The remaining twelve apes are on a hill and the echo of their shrieks by the adjoining hills frightens them. They came and join the apes in the forest and play with enthusiasm. What is the total number of apes?

A. 48
B. 16
C. 64
D. 80
E. 16 or 48
[Reveal] Spoiler: OA

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Re: In the interior of a forest, a certain number of apes equal to the squ [#permalink]

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New post 15 Nov 2010, 20:47
Let total number be x
No in the interior = (x/8)^2
No outside = 12
So : x - (x/8)^2=12
x^2-64x+12*64=0
x^2-16x-48x+16*48=0
(x-16)(x-48)=0

So either x=16 or x=48

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Re: In the interior of a forest, a certain number of apes equal to the squ [#permalink]

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New post 08 Sep 2014, 23:02
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Let total no of apes = x

Square of \(\frac{1}{8} th\) are playing \(= (\frac{x}{8})^2 = \frac{x^2}{64}\)

Remaining = 12

Setting up quadratic equation

\(x = \frac{x^2}{64} + 12\)

\(x^2 - 64x + 12*64 = 0\)

This equation will not have -ve value of x as middle term is -ve & last term is +ve; This will have two answers

In the OA, only option E has two answers

Answer = E
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Re: In the interior of a forest, a certain number of apes equal to the squ [#permalink]

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New post 24 Dec 2017, 06:11
Let total number of apes = 8x
number of playing = \(x^2\)
remaining = 12

given: \(x^2 + 12 = 8x\) => \(x^2 - 8x + 12 = 0\)=> x = 2 or 6
so total number of apes = 16 or 48 (E)

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In the interior of a forest, a certain number of apes equal to the squ [#permalink]

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New post 24 Dec 2017, 08:21
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Verifying answer options with the given condintion,
Take 1 st option If total apes 48
apes interior= total-exterior= 48-12=36
apes interior= square of {(1/8)th of total(48)}= 6^2 =36.
So 48 is a possible solution.
So either A or E.
When checking with 16 we can find that it satisfies too.
So E
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In the interior of a forest, a certain number of apes equal to the squ   [#permalink] 24 Dec 2017, 08:21
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