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# Is X to the power 3 an odd integer? (1) 3 square root X is

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Is X to the power 3 an odd integer? (1) 3 square root X is [#permalink]

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06 Feb 2005, 13:19
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Is X to the power 3 an odd integer?

(1) 3 square root X is an odd integer.
(2) X is an odd integer.
Director
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06 Feb 2005, 16:07
(1) 3 square root X is an odd integer.

3*SQRT(x) is odd
this does not mean that x is an integer

For example x can be 1/9, yet x^3 is not even an integer
or x can be 9 and x^3 is an odd integer

Can't say

(2) X is an odd integer.

Yes this means X^3 has to be an Odd integer
odd*odd*odd = odd

B
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06 Feb 2005, 16:52
MA wrote:
Is X to the power 3 an odd integer?

(1) 3 square root X is an odd integer.
(2) X is an odd integer.

It has to be D.

1) odd*odd=odd
even * even = even
Thus root of an odd integer will always be odd and root of even integer will always be even.

Product of 3 and root of x is odd. This means root x is odd. this means x is odd. Therefore x^3 is odd

2) If x is odd, x^3 is also odd.

Thus D.
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06 Feb 2005, 18:52
x^3 will be odd only if x is not even. (since any even number in multiplication will make the product even)

1) 3(x^1/2)= odd. This means x^1/2=odd (since only odd*odd=odd)
x= odd*odd= odd. So A is sufficient.

2) X is odd. B is sufficient.

Ans:D
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06 Feb 2005, 21:10
nocilis wrote:
(1) 3 square root X is an odd integer.

3*SQRT(x) is odd
this does not mean that x is an integer

For example x can be 1/9, yet x^3 is not even an integer
or x can be 9 and x^3 is an odd integer

Can't say

(2) X is an odd integer.

Yes this means X^3 has to be an Odd integer
odd*odd*odd = odd. B

you have the same explanation as i had. it should be B however OA is D, which is wrong. this is what i was trying to prove.
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06 Feb 2005, 21:36
It should be (D), both are sufficient.

If 3 square root of x to be an integer, x must be an integer.

For example if x=1/27, 3 square root would be 1/3, not an integer.
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06 Feb 2005, 21:40
HongHu wrote:
It should be (D), both are sufficient.

If 3 square root of x to be an integer, x must be an integer.

For example if x=1/27, 3 square root would be 1/3, not an integer.

suppose x = 1/9
3 sqrt(1/9)=3X1/3=1, which an odd integer. it does not satisfy that x^3 is an odd integer.
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06 Feb 2005, 21:45
Oh I thought 3 sqrt x means x^(1/3). Hmmm.. Yes if it means 3*x^(1/2) then you are right.
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06 Feb 2005, 22:27
you missed my last part. I did give my OA as D. Just as a sidenote, we do not need to consider fractions as we are just considering integers. Integers are whole numbers.
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06 Feb 2005, 22:53
ywilfred wrote:
you missed my last part. I did give my OA as D. Just as a sidenote, we do not need to consider fractions as we are just considering integers. Integers are whole numbers.

the statement has not mentioned that x is an integer. therefore, we do not know x is an integer. if the question were like this, your reasoning would be correct:

Is X, an integer, to the power 3 an odd integer?

(1) 3 square root X is an odd integer.
(2) X is an odd integer.
06 Feb 2005, 22:53
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