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

Question

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

(1)  \sqrt{x} =32

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

(DS05172)

Kurtosis · Answer

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 · Answer

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@ · Answer

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 · Answer

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.

ScottTargetTestPrep · Answer

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

aditya4444 · Answer

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 · Answer

Check the highlighted part above.

Bunuel · Answer

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.

KSBGC · Answer

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.

sudarshan22 · Answer

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  .

KSBGC · Answer

x>0. given in the question bro.

sudarshan22 · Answer

Holy crap! You are right

I hope that does not happen on D-Day. Thanks for rectifying the blunder selim

Rhl5084 · Answer

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

Bunuel · Answer

\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 {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 .

Rhl5084 · Answer

Bunuel , thanks ! that helps

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

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