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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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Joined: 02 Sep 2009
Posts: 42249

Kudos [?]: 132595 [0], given: 12326

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

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New post 02 Oct 2017, 00:42
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Question Stats:

57% (01:17) correct 43% (00:46) wrong based on 43 sessions

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Kudos [?]: 132595 [0], given: 12326

Intern
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Joined: 25 Jul 2017
Posts: 14

Kudos [?]: 18 [0], given: 20

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

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New post 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

=> Answer A

Kudos [?]: 18 [0], given: 20

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Joined: 25 Feb 2013
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Kudos [?]: 246 [0], given: 33

Location: India
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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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New post 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

Kudos [?]: 246 [0], given: 33

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