OG11 DS# 146

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Source: — Data Sufficiency |

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Re: OG11 DS# 146

by Ian Stewart » Sun Nov 15, 2009 3:10 pm
anaitalt wrote:(pg 290)

Is n an integer?

(1) n^2 is an integer
(2) n^(1/2) is an integer

Can anyone please give better reasoning than the OG?

Thanx
Statement 1: n^2 = z, where z is an integer. So n = ±sqrt(z). Well, if z=2 then n is not an integer, while if z=1, n is an integer. Not sufficient.

Statement 2: sqrt(n) = z, where z is an integer. So n = z^2, and n is the square of an integer, so must be an integer. Sufficient.
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