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If x = 4, then −2^{2 x^1/2} + 2 =?

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Senior RC Moderator
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V
Joined: 02 Nov 2016
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If x = 4, then −2^{2 x^1/2} + 2 =?  [#permalink]

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New post 07 Jul 2019, 05:06
3
00:00
A
B
C
D
E

Difficulty:

  45% (medium)

Question Stats:

44% (00:37) correct 56% (00:42) wrong based on 61 sessions

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If \(x = 4\), then \(−2^{2 \sqrt{x}} + 2 =\)?

(A) –14
(B) –8
(C) –2
(D) 0
(E) 18

Source: Nova GMAT
Difficulty Level: 650

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Re: If x = 4, then −2^{2 x^1/2} + 2 =?  [#permalink]

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New post 07 Jul 2019, 05:38
If x=4, then √4=2.
-2^4+2= -16+2=-14.
Answer choice is A.

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Re: If x = 4, then −2^{2 x^1/2} + 2 =?  [#permalink]

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New post 19 Jul 2019, 05:32
If x=4 then √x=2
=> 2√x=4
=> (-2)^4= 16
=> 16+2=18
Answer has to be E

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Re: If x = 4, then −2^{2 x^1/2} + 2 =?  [#permalink]

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New post 19 Jul 2019, 05:45
-2^4 is not equal to (-2)^4
Let’s see why
-2^4 =(-1)(2)^4=-16
(-2)^4 =-2•-2•-2•-2=16
Hope it helps
Amarjoth wrote:
If x=4 then √x=2
=> 2√x=4
=> (-2)^4= 16
=> 16+2=18
Answer has to be E

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Re: If x = 4, then −2^{2 x^1/2} + 2 =?  [#permalink]

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New post 19 Jul 2019, 05:57
In that case it must be explicitly mentioned as
-(2)^2√x which will clear out ambiguity by writing it as -2^2√x it can be interpreted in 2 manners

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Re: If x = 4, then −2^{2 x^1/2} + 2 =?  [#permalink]

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New post 19 Jul 2019, 06:00
3
Amarjoth wrote:
In that case it must be explicitly mentioned as
-(2)^2√x which will clear out ambiguity by writing it as -2^2√x it can be interpreted in 2 manners

Posted from my mobile device


Nope. Everything is correct there.

\(−2^{2 \sqrt{x}}\) can only mean \(−(2^{2 \sqrt{x}})\) and not \((−2)^{2 \sqrt{x}}\). If it were \((−2)^{2 \sqrt{x}}\) it would have been written that way.
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Re: If x = 4, then −2^{2 x^1/2} + 2 =?  [#permalink]

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New post 19 Jul 2019, 06:06
Bunuel
(my Maths genius) has explained it above
Amarjoth wrote:
In that case it must be explicitly mentioned as
-(2)^2√x which will clear out ambiguity by writing it as -2^2√x it can be interpreted in 2 manners

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GMAT Club Bot
Re: If x = 4, then −2^{2 x^1/2} + 2 =?   [#permalink] 19 Jul 2019, 06:06
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If x = 4, then −2^{2 x^1/2} + 2 =?

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