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

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Director
Status: Learning stage
Joined: 01 Oct 2017
Posts: 930
WE: Supply Chain Management (Energy and Utilities)
If a and b are positive and 5ab=24-a^2b^2, then b^2=  [#permalink]

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14 Jul 2018, 06:47
1
00:00

Difficulty:

35% (medium)

Question Stats:

56% (01:45) correct 44% (01:43) wrong based on 16 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) $$\frac{9}{a^2}$$
Manager
Joined: 09 Jun 2014
Posts: 188
Location: India
Concentration: General Management, Operations
Schools: Tuck '19
Re: If a and b are positive and 5ab=24-a^2b^2, then b^2=  [#permalink]

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14 Jul 2018, 07:47
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

Press Kudos if it helps !!

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Math Expert
Joined: 02 Aug 2009
Posts: 7025
Re: If a and b are positive and 5ab=24-a^2b^2, then b^2=  [#permalink]

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14 Jul 2018, 08:29
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
_________________

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, 08:29
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