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# if y is a positive integer, is radical y an integer?

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Manager
Joined: 06 Jan 2008
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if y is a positive integer, is radical y an integer? [#permalink]  07 Apr 2008, 16:47
if y is a positive integer, is radical y an integer?
2)Radical 3y is not an integer

I chose e here, because if y=1/4, radical (4*(1/4))= radical 1 = 1, therefore, y may or may not be an integer.

VP
Joined: 10 Jun 2007
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Re: if y is a positive integer, is radical y an integer? [#permalink]  07 Apr 2008, 17:03
Manbehindthecurtain wrote:
if y is a positive integer, is radical y an integer?
2)Radical 3y is not an integer

I chose e here, because if y=1/4, radical (4*(1/4))= radical 1 = 1, therefore, y may or may not be an integer.

y cannot be 1/4 because it is a positive integer

I got A

The question is asking if sqrt(y) = integer?
(1) sqrt(4y) = 2sqrt(y) = integer
This means either sqrt(y) = 1/2 or sqrt(y) = integer
We know that sqrt(y) != 1/2 because y is an integer. So sqrt(y) = integer
SUFFICIENT
(2) sqrt(3y) != integer
if y=2, then sqrt(2) != integer
if y=4, then sqrt(4) = integer
INSUFFICIENT
Manager
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Re: if y is a positive integer, is radical y an integer? [#permalink]  07 Apr 2008, 17:05
bkk145 wrote:
y cannot be 1/4 because it is a positive integer

DOH!

Thanks. Yup A.
Manager
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Re: if y is a positive integer, is radical y an integer? [#permalink]  08 Apr 2008, 10:28
what is the radical mean ?
Director
Joined: 20 Feb 2008
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Re: if y is a positive integer, is radical y an integer? [#permalink]  08 Apr 2008, 18:50
Also, you know in 1) y must equal 4 (16), 9 (36), 16 (64)...etc. which are all perfect roots which makes y an integer

If you look at two, the first number that makes y an integer is 3, so y can not equal 3, but could equal 1, 2, 4,...etc. which makes it not an integer.

Re: if y is a positive integer, is radical y an integer?   [#permalink] 08 Apr 2008, 18:50
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