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# If x and y are positive integers and 2^x + 2^x + 2^x + 2^x = y, what

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Math Expert
Joined: 02 Sep 2009
Posts: 49251
If x and y are positive integers and 2^x + 2^x + 2^x + 2^x = y, what  [#permalink]

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02 Oct 2017, 00:42
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Difficulty:

35% (medium)

Question Stats:

57% (01:26) correct 43% (00:49) wrong based on 68 sessions

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If x and y are positive integers and 2^x + 2^x + 2^x + 2^x = y, what is the value of y?

(1) 122 < y < 250
(2) 3 < x < 6

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Joined: 25 Jul 2017
Posts: 38
Re: If x and y are positive integers and 2^x + 2^x + 2^x + 2^x = y, what  [#permalink]

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02 Oct 2017, 03:30
2^x+2^x+2^x+2^x = 4.2^x = 2^ (2+x) = y

1/ 122<y<250 => only y=128 is available => suff

2/ 3<x<6 => if X=4,5 => we have different value of Y => Insuff

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Re: If x and y are positive integers and 2^x + 2^x + 2^x + 2^x = y, what  [#permalink]

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02 Oct 2017, 03:36
Bunuel wrote:
If x and y are positive integers and 2^x + 2^x + 2^x + 2^x = y, what is the value of y?

(1) 122 < y < 250
(2) 3 < x < 6

Question stem can be written as $$4*2^x=y$$ or $$2^{x+2}=y$$
As x and y are positive integers so y must be some power of 2.

Statement 1: this implies $$122<2^{x+2}<250$$, in this range only $$128$$ or $$2^7$$ is possible because $$2^8=256$$ which is outside the range. Hence Sufficient

Statement 2: x can have multiple values, hence y will have multiple values. Insufficient

Option A
Re: If x and y are positive integers and 2^x + 2^x + 2^x + 2^x = y, what &nbs [#permalink] 02 Oct 2017, 03:36
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