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]

02 Aug 2018, 04:27

Kudos

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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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Re: If x > 0, what is the value of x^5 ? [#permalink]

08 Oct 2016, 12:10

Kudos

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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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General Discussion

Kurtosis

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Re: If x > 0, what is the value of x^5 ? [#permalink]

06 Oct 2016, 07:04

Kudos

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

Vinayak Shenoy

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Re: If x > 0, what is the value of x^5 ? [#permalink]

06 Oct 2016, 07:20

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

@p00rv@

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Re: If x > 0, what is the value of x^5 ? [#permalink]

06 Oct 2016, 09:01

Kudos

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.

albo94

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Re: If x > 0, what is the value of x^5 ? [#permalink]

07 Oct 2016, 07:13

Kudos

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.

aditya4444

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Re: If x > 0, what is the value of x^5 ? [#permalink]

25 Jul 2018, 06:38

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?

Bunuel

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Joined: 02 Sep 2009

Posts: 90060

Re: If x > 0, what is the value of x^5 ? [#permalink]

25 Jul 2018, 07:22

Expert Reply

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]

Updated on: 02 Aug 2018, 04:38

Kudos

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, 04:34.
Last edited by KSBGC on 02 Aug 2018, 04:38, edited 2 times in total.

sudarshan22

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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]

Updated on: 02 Aug 2018, 04:42

Kudos

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, 04:36.
Last edited by sudarshan22 on 02 Aug 2018, 04:42, edited 1 time in total.

KSBGC

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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]

02 Aug 2018, 04:38

Kudos

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.

sudarshan22

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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]

Updated on: 02 Aug 2018, 04:53

selim wrote:

sudarshan22 wrote:

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, 04:44.
Last edited by sudarshan22 on 02 Aug 2018, 04:53, edited 1 time in total.

Rhl5084

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Re: If x > 0, what is the value of x^5 ? [#permalink]

25 Sep 2020, 08:21

Hey Bunuel, one silly doubt: what root4 will yield, only +2 or +/- 2

Bunuel

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Posts: 90060

Re: If x > 0, what is the value of x^5 ? [#permalink]

25 Sep 2020, 08:27

Kudos

Expert Reply

Rhl5084 wrote:

Hey Bunuel, one silly doubt: what root4 will yield, only +2 or +/- 2

$\sqrt{4}=2$ 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]

25 Sep 2020, 08:33

Bunuel, thanks !

that helps

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Re: If x > 0, what is the value of x^5 ? [#permalink]

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