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(cube root x) = root x
cube root of x
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- hemant_rajput
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Last edited by hemant_rajput on Wed Jul 24, 2013 7:03 am, edited 1 time in total.
I'm no expert, just trying to work on my skills. If I've made any mistakes please bear with me.
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Possible values of x are 4, 9, 16, 25, 36, 49, 64, and 81
Statement 1: Only possible value of x is 64.
So, statement 1 is sufficient.
Statement 2: I guess this statement originally meant to say 2*(cube root of x) = square root of x
Now, as square root of x is an integer, i.e. left hand side of the equation is an integer, the right-hand side must be an integer too.
So, cube root of x is an integer.
So, statement 2 is same as statement 1.
So, statement 2 is sufficient.
Answer : D
Statement 1: Only possible value of x is 64.
So, statement 1 is sufficient.
Statement 2: I guess this statement originally meant to say 2*(cube root of x) = square root of x
Now, as square root of x is an integer, i.e. left hand side of the equation is an integer, the right-hand side must be an integer too.
So, cube root of x is an integer.
So, statement 2 is same as statement 1.
So, statement 2 is sufficient.
Answer : D
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Hi hemant_rajput,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
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
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I'm sorry for creating confusion. I've edited my original post.
I'm no expert, just trying to work on my skills. If I've made any mistakes please bear with me.
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Target question: What is the value of x?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
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
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Statement 2: 2 * x^(1/3) = x^(1/2)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(cube root x) = root x
2 = x^(1/2) / x^(1/3)
2 = x^(1/6)
2� = x.
SUFFICIENT.
Statement 1: x^(1/3) = integer
For both x^(1/2) and x^(1/3) to be integers, x must be an integer raised to a power divisible by both 2 and 3.
The only value between 2 and 100 that satisfies this constraint is the same value yielded by statement 1: 2�.
SUFFICIENT.
The correct answer is D.
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Followed here and elsewhere by over 1900 test-takers.
I have worked with students based in the US, Australia, Taiwan, China, Tajikistan, Kuwait, Saudi Arabia -- a long list of countries.
My students have been admitted to HBS, CBS, Tuck, Yale, Stern, Fuqua -- a long list of top programs.
As a tutor, I don't simply teach you how I would approach problems.
I unlock the best way for YOU to solve problems.
For more information, please email me (Mitch Hunt) at [email protected].
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