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If a and b are positive and 5ab=24-a^2b^2, then b^2=

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Director
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If a and b are positive and 5ab=24-a^2b^2, then b^2=  [#permalink]

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New post 14 Jul 2018, 07:47
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A
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D
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  35% (medium)

Question Stats:

53% (01:52) correct 47% (01:43) wrong based on 15 sessions

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If 'a' and 'b' are positive and \(5ab=24-a^2b^2\), then \(b^2=\)


(A) \(\frac{81}{a^2}\)

(B) \(\frac{64}{a^2}\)

(C) \(\frac{35}{a^2}\)

(D) \(\frac{15}{a^2}\)

(E) \(\frac{9}{a^2}\)
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Concentration: General Management, Operations
Schools: Tuck '19
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Re: If a and b are positive and 5ab=24-a^2b^2, then b^2=  [#permalink]

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New post 14 Jul 2018, 08:47
5ab=24-a^2b^2
Let ab=x
5x=24-x^2
x^2+5x-24=0
Gives x=3,-8
Since a,b is positive . So X is 3

Therefor ab=3
b=-3/a
So b^2=9/(a^2)

Option E

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Re: If a and b are positive and 5ab=24-a^2b^2, then b^2=  [#permalink]

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New post 14 Jul 2018, 09:29
PKN wrote:
If 'a' and 'b' are positive and \(5ab=24-a^2b^2\), then \(b^2=\)

(A) \(\frac{81}{a^2}\)
(B) \(\frac{64}{a^2}\)
(C) \(\frac{35}{a^2}\)
(D) \(\frac{15}{a^2}\)
(E) \(\frac{9}{a^2}\)



\(5ab=24-a^2b^2\)..
let ab = x
\(5x=24-x^2........x^2+5x-24=0........x^2+8x-3x-24=0...........(x+8)(x-3)=0\)

but a and b are positive and x = ab, so x has to be positive thus x=3

\(ab=3.....a^2b^2=9.............b^2=\frac{9}{a^2}\)

E
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1) Absolute modulus : http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html
3) effects of arithmetic operations : https://gmatclub.com/forum/effects-of-arithmetic-operations-on-fractions-269413.html


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Re: If a and b are positive and 5ab=24-a^2b^2, then b^2= &nbs [#permalink] 14 Jul 2018, 09:29
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