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Manager  Joined: 30 Sep 2010
Posts: 51
In the interior of a forest, a certain number of apes equal to the squ  [#permalink]

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5 00:00

Difficulty:   65% (hard)

Question Stats: 70% (03:13) correct 30% (02:38) wrong based on 209 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
Intern  B
Joined: 15 Aug 2017
Posts: 13
In the interior of a forest, a certain number of apes equal to the squ  [#permalink]

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3
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
Kudos Retired Moderator Joined: 02 Sep 2010
Posts: 755
Location: London
Re: In the interior of a forest, a certain number of apes equal to the squ  [#permalink]

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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 Posted from GMAT ToolKit
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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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2
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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1
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) Re: In the interior of a forest, a certain number of apes equal to the squ   [#permalink] 24 Dec 2017, 07:11
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# In the interior of a forest, a certain number of apes equal to the squ

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