Data Sufficiency

hemant_rajput wrote:64. If x is an integer between 2 and 100 and if root x is also an integer,
what is the value of x?
(1) cube root x or (x)^(1/3) is an integer.
(2) 2(root 33 x) = root x

Hi hemant_rajput,

Can you tell us what statement 2 is supposed to say? It's not clear what you mean by 2(root 33 x) = root x

Cheers,
Brent

hemant_rajput wrote:64. If x is an integer between 2 and 100 and if sqrt x is also an integer,
what is the value of x?
(1) cuberoot x is an integer.
(2) 2(cuberoot x) = sqrt x

Target question: What is the value of x?

Given: x is an integer between 2 and 100 and sqrt x is an integer.
In other words, x is the square of an integer, which means x must equal 4, 9, 16, 25, 36, 49, 64 or 81

Statement 1: cuberoot(x) is an integer.
In other words, x is the cube of an integer
Among the possible values of x (4, 9, 16, 25, 36, 49, 64, 81), only 64 is the cube of an integer.
So, x must equal 64
Since we can answer the target question with certainty, statement 1 is SUFFICIENT

Statement 2: 2(cuberoot x) = sqrt x
Since the right-hand side, sqrt x, must be an integer, it must be the case that the left-hand side, 2(cuberoot x), is also an integer
So, it must be the case that EITHER cuberoot x is an integer OR cuberoot x equals some decimal ending in .5 (e.g., 3.5) so that we get an integer after multiplying by 2.
Well, among the possible values of x, none will yield decimal ending in .5, so we're looking for a value of x such that cuberoot x is an integer.
In other words, x is the cube of an integer
Among the possible values of x (4, 9, 16, 25, 36, 49, 64, 81), only 64 is the cube of an integer.
So, x must equal 64
Since we can answer the target question with certainty, statement 2 is SUFFICIENT

Answer = D

Cheers,
Brent