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If x > 0, what is the value of x^5 ?

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Bunuel
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If x > 0, what is the value of x^5 ? [#permalink] New post  06 Oct 2016, 05:01
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If x > 0, what is the value of x^5?


(1) \(\sqrt{x} =32\)

(2) \(x^2 = 2^{20}\)



(DS05172)
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Bunuel
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If x > 0, what is the value of x^5 ? [#permalink] New post  02 Aug 2018, 05:27
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If x > 0, what is the value of x^5?

(1) \(\sqrt{x} =32\). Square: \(x = 32^2\). So, \(x^5 = (32^2)^5=32^{10}\). Sufficient.


(2) \(x^2 = 2^{20}\). Take the square root: \(|x| = \sqrt{2^{20}}\). Since given that x > 0, then |x| = x and thus we get: \(x = \sqrt{2^{20}}=2^{10}\). So, \(x^5 = (2^{10})^5=2^{50}\). Sufficient.

Answer: D.

Hope it helps.
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ScottTargetTestPrep
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Re: If x > 0, what is the value of x^5 ? [#permalink] New post  08 Oct 2016, 13:10
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Bunuel wrote:
If x > 0, what is the value of x^5 ?

(1) \(\sqrt{x}=32\)
(2) x^2 = 2^20


We are given that x is greater than zero and need to determine the value of x^5.

Statement One Alone:

√x = 32

Using the equation in statement one, we can determine a value of x.

√x = 32

(√x)^2 = 32^2

x = 32^2 = (2^5)^2 = 2^10

Since x = 2^10, x^5 = (2^10)^5 = 2^50

Statement one alone is sufficient to answer the question. We can eliminate answer choices B, C, and E.

Statement Two Alone:

x^2 = 2^20

Using the equation in statement two, we can determine a value of x.

√(x^2) = +/-√(2^20)

x = +/-2^10

Since x is positive, x = 2^10.

Since x = 2^10, x^5 = (2^10)^5 = 2^50.

Answer: D
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Re: If x > 0, what is the value of x^5 ? [#permalink] New post  06 Oct 2016, 08:04
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x is positive; x^5 = ?

St1: sqrt(x) = 2^5
x = 2^10
x^5 = (2^10)^5 = 2^50
Sufficient

St2: x^2 = 2^20
x = 2^10
x^5 = 2^50
Sufficient

Answer: D
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Re: If x > 0, what is the value of x^5? (1) x^(1/2) = 32 (2) x^2 = 2^20 [#permalink] New post  Updated on: 02 Aug 2018, 05:38
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Bunuel wrote:
If x > 0, what is the value of x^5?


(1) \(\sqrt{x} =32\)

(2) \(x^2 = 2^{20}\)


NEW question from GMAT® Quantitative Review 2019


(DS05172)



Note : x is positive.

Statement 1:

\(\sqrt{x} =32\)

\(x = 32^2\)

\(x^5 = (32^2)^5\)

Sufficient.

Statement 2:

\(x^2 = 2^{20}\)

x^2 = 2^10^2

\(x = 2^{10}\)

x^5 = 2^10^5

Sufficient .

The best answer is D.

Originally posted by KSBGC on 02 Aug 2018, 05:34.
Last edited by KSBGC on 02 Aug 2018, 05:38, edited 2 times in total.
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Re: If x > 0, what is the value of x^5? (1) x^(1/2) = 32 (2) x^2 = 2^20 [#permalink] New post  Updated on: 02 Aug 2018, 05:42
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x^5 = ?

(1) \(\sqrt{x} =32\)
\(\sqrt{x} =2^5\)
Squaring we get
x = 2^10
Since x is Positive, x^5 gives unique value
Sufficient

(2) \(x^2 = 2^{20}\)
x = 2^10
Since x positive, x^5 gives unique value
Sufficient

Hence, D.
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Originally posted by sudarshan22 on 02 Aug 2018, 05:36.
Last edited by sudarshan22 on 02 Aug 2018, 05:42, edited 1 time in total.
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Re: If x > 0, what is the value of x^5 ? [#permalink] New post  06 Oct 2016, 10:01
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IMO D must be the answer.
1. √x=32 -->x=32^2 (since √x=|x| and hence always positive) . Therefore x^5=32^10. Sufficient
2. x^2 = 2^20 --> x=+2^10 or -2^10. Since x>0--> x^5 will be positive. Sufficient.
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Re: If x > 0, what is the value of x^5 ? [#permalink] New post  07 Oct 2016, 08:13
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In my opinion the correct answer is D.
(1) would be sufficient even if we didn't know that x is positive.
(2) is sufficient because we have x positive.
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Re: If x > 0, what is the value of x^5? (1) x^(1/2) = 32 (2) x^2 = 2^20 [#permalink] New post  02 Aug 2018, 05:38
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sudarshan22 wrote:
x^5 = ?

(1) \(\sqrt{x} =32\)
\(\sqrt{x} =2^5\)
Squaring we get
x = 2^10
Since x is Positive, x^5 gives unique value
Sufficient

(2) \(x^2 = 2^{20}\)
x could be negative or positive, and that gives two values of x^5
Insufficient

Hence, A.



x>0. given in the question bro.
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Bunuel
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Re: If x > 0, what is the value of x^5 ? [#permalink] New post  25 Sep 2020, 09:27
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Rhl5084 wrote:
Hey Bunuel, one silly doubt: what root4 will yield, only +2 or +/- 2 :roll:


\(\sqrt{4}=2\) only, not +2/-2.

When the GMAT provides the square root sign for an even root, such as a square root, fourth root, etc. then the only accepted answer is the non-negative root. That is:

\(\sqrt{9} = 3\), NOT +3 or -3;
\(\sqrt[4]{16} = 2\), NOT +2 or -2;

Notice that in contrast, the equation \(x^2 = 9\) has TWO solutions, +3 and -3. Because \(x^2 = 9\) means that \(x =-\sqrt{9}=-3\) or \(x=\sqrt{9}=3\).
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Re: If x > 0, what is the value of x^5 ? [#permalink] New post  06 Oct 2016, 08:20
Bunuel wrote:
If x > 0, what is the value of x^5 ?

(1) \(\sqrt{x}=32\)
(2) x^2 = 2^20



IMO D
Given x>0

From statement 1
Squaring x=2^10
x^5=2^50 Sufficient

From statement 2
x^2=2^20 implies x=2^10
x^5=2^50 Sufficient
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aditya4444
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Re: If x > 0, what is the value of x^5 ? [#permalink] New post  25 Jul 2018, 07:38
Bunuel wrote:
If x > 0, what is the value of x^5 ?

(1) \(\sqrt{x}=32\)
(2) x^2 = 2^20

Hey Bunuel,

Just wanted to understand that in Statement 2 when we are taking the square root, why can't the right side of the equation take 2 values of +/- underoot 2^20?
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Bunuel
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Re: If x > 0, what is the value of x^5 ? [#permalink] New post  25 Jul 2018, 08:22
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aditya4444 wrote:
Bunuel wrote:
If x > 0, what is the value of x^5 ?

(1) \(\sqrt{x}=32\)
(2) x^2 = 2^20

Hey Bunuel,

Just wanted to understand that in Statement 2 when we are taking the square root, why can't the right side of the equation take 2 values of +/- underoot 2^20?


Check the highlighted part above.
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Re: If x > 0, what is the value of x^5? (1) x^(1/2) = 32 (2) x^2 = 2^20 [#permalink] New post  Updated on: 02 Aug 2018, 05:53
selim wrote:
sudarshan22 wrote:
x^5 = ?

(1) \(\sqrt{x} =32\)
\(\sqrt{x} =2^5\)
Squaring we get
x = 2^10
Since x is Positive, x^5 gives unique value
Sufficient

(2) \(x^2 = 2^{20}\)
x could be negative or positive, and that gives two values of x^5
Insufficient

Hence, A.


x>0. given in the question bro.

Holy crap! You are right :(
I hope that does not happen on D-Day.
Thanks for rectifying the blunder selim
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Originally posted by sudarshan22 on 02 Aug 2018, 05:44.
Last edited by sudarshan22 on 02 Aug 2018, 05:53, edited 1 time in total.
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Re: If x > 0, what is the value of x^5 ? [#permalink] New post  25 Sep 2020, 09:21
Hey Bunuel, one silly doubt: what root4 will yield, only +2 or +/- 2 :roll:
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Re: If x > 0, what is the value of x^5 ? [#permalink] New post  25 Sep 2020, 09:33
Bunuel, thanks !

that helps :)
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