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Re: If 0 < x < 100, what is the value of x? [#permalink]
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Hi GMATinsight
x may be 1 in statement 2



GMATinsight wrote:
Bunuel wrote:
If 0 < x < 100, what is the value of x?


(1) \(\sqrt{x}\) is a multiple of 8.

(2) \(\sqrt{x}\) and \(\sqrt[3]{x}\) are integers.


Project DS Butler Data Sufficiency (DS3)


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Statement 1: \(\sqrt{x}\) is a multiple of 8.

i.e. √x = 8, 16, 24, 32...
ie.. x = 64, 256..

ie.. x = 64 in teh given range

SUFFICINT

Statement 2: \(\sqrt{x}\) and \(\sqrt[3]{x}\) are integers.

i.e. x is a perfect square as well as a oerfect cube

ie.. x = 2^6 or 3^6 or...

But less than 100 x can only be 2^6 = 64

SUFFICINT

Answer: Option D
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Re: If 0 < x < 100, what is the value of x? [#permalink]
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Solution



0<x<100 (given) ----- (A)

We need to find the value(definite) of x.

Statements:

(1) (x)^1/2 is a multiple of 8.

Solving. (x)^1/2 = 8k ( k is an integer )
=> x = (64)k^2

Therefore, x can be 64, 64(4), 64(9) ...

But because of (A), only acceptable value is 64.

Sufficient

(2) (x)^1/2 and (x)^1/3 are integers

Since both the square root and the cube root of x are integers, x must be in the power of 6 (2*3).

Therefore, x can be (1^6), (2^6), (3^6) .....

Acceptable values are 1^6 and 2^6.

Not Sufficient


Hence. Option (A).

Edit: Initially marked option (D). Forget to take into consideration case of x=1 in Statement (2).
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Re: If 0 < x < 100, what is the value of x? [#permalink]
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Re: If 0 < x < 100, what is the value of x? [#permalink]
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