If X is a perfect square, is X also a perfect cube?
(1) X = K^6, where K is a positive integer.
(2) X^(1/6) =N , where N is a positive integer.
Question on Perfect Square 4
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- richachampion
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OA: D
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I think both statement 1 and statement 2 are same thing.
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- fiza gupta
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Yes, both the statements should be same
both represents positive integers
1) X = K^6, where K is a positive integer.
X^(1/3) = K^2 (k is integer)
X^(1/3) will always result in an integer
SUFFICIENT
(2) X^(1/6) =N , where N is a positive integer.
X^(1/3) = N^2 (N is integer)
SUFFICIENT
both represents positive integers
1) X = K^6, where K is a positive integer.
X^(1/3) = K^2 (k is integer)
X^(1/3) will always result in an integer
SUFFICIENT
(2) X^(1/6) =N , where N is a positive integer.
X^(1/3) = N^2 (N is integer)
SUFFICIENT
Fiza Gupta
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- Jay@ManhattanReview
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Let us take another perspective of the question.
For a number X to be a perfect square as well as a perfect cube, it should be in the form of K^(6n), where K and n are positive integers. We took 6 as it is the LCM of 2 and 3.
Both the statements are in fact one and the same.
Hope this helps!
--Jay
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For a number X to be a perfect square as well as a perfect cube, it should be in the form of K^(6n), where K and n are positive integers. We took 6 as it is the LCM of 2 and 3.
Both the statements are in fact one and the same.
Hope this helps!
--Jay
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Easier way:
S1:
x = k� = (k²)³
So x is a cube.
S2:
Raise both sides to the sixth power:
x = n� = (n²)³
So x is a cube.
S1:
x = k� = (k²)³
So x is a cube.
S2:
Raise both sides to the sixth power:
x = n� = (n²)³
So x is a cube.
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More or less!richachampion wrote:I think both statement 1 and statement 2 are same thing.
A good follow up question for you, though: taken together, does this mean that k = n?