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# If y = x^2, is the equation (2^5y)(4^120) = 16^20x true?

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Director
Joined: 11 Feb 2015
Posts: 614
If y = x^2, is the equation (2^5y)(4^120) = 16^20x true?  [#permalink]

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23 Jul 2018, 05:48
00:00

Difficulty:

55% (hard)

Question Stats:

63% (02:43) correct 37% (02:52) wrong based on 46 sessions

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If $$y = x^2$$, is the equation $$(2^{5y})(4^{120}) = 16^{20x}$$ true?

(1) $$(4 − x)(12 − x) = 0$$

(2) $$(x − 4)(x − 8)(x − 24) = 0$$

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Manish

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Re: If y = x^2, is the equation (2^5y)(4^120) = 16^20x true?  [#permalink]

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23 Jul 2018, 06:02
CAMANISHPARMAR wrote:
If $$y = x^2$$, is the equation $$(2^{5y})(4^{120}) = 16^{20x}$$ true?
1. $$(4 − x)(12 − x) = 0$$
2. $$(x − 4)(x − 8)(x − 24) = 0$$

$$(2^{5y})(4^{120}) = 16^{20x}........2^{5y}2^{2*120}=2^{4*20x}...........2^{5y+240}=2^{80x}$$....
Equating powers of 2 on both sides..
5y+240=80x........y+48=16x........y-16x+48=0
Replace X=y^2.....
$$x^2-16x+48=0.......(x-12)(x-4)=0$$..
So question is x equal to 12 or 4...

1. $$(4 − x)(12 − x) = 0$$
This is what we are looking for
Sufficient
2. $$(x − 4)(x − 8)(x − 24) = 0$$
x can be 4 or 8 or 24 or two of them or all three..
If x is 4, Ans is YES..
But if $$x\neq{0}$$, Ans is NO
Insufficient

A
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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 y = x^2, is the equation (2^5y)(4^120) = 16^20x true? &nbs [#permalink] 23 Jul 2018, 06:02
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