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If n is the square of a positive integer, which of the

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Intern
Joined: 05 Apr 2008
Posts: 23

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If n is the square of a positive integer, which of the [#permalink]

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10 Sep 2008, 11:16
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If n is the square of a positive integer, which of the following must be equal to the square of the next positive integer?

a) n^(1/2)+1
b) n+1
c) n^2+1
d) n+2n^(1/2)+1
e) n^2+2n+1

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SVP
Joined: 17 Jun 2008
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10 Sep 2008, 11:21
D.

Say, n = x^2. then, x = sqrt(n).

now ,(x+1)^2 = x^2 + 2x + 1 = n + 2(sqrt(n)) + 1.

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Director
Joined: 26 Jul 2007
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Schools: Stern, McCombs, Marshall, Wharton

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10 Sep 2008, 11:34
This is one of those problems where I just pick numbers.

Positive integer = 3
N = 9

3+1 = 4 and 4^2 = 16

Look for the answer that equals 16 when you plug in 9 for N.

You can see it's not A, B, or C in a matter of seconds.

D gives 16 so it correct.

Double check E and in a couple of seconds you can see it too high.

So D it is.

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Manager
Joined: 07 Jan 2008
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10 Sep 2008, 15:04
D

let p be the positive integer
so p^(2) = n
need to find (p+1)^(2)

p^(2) = n => p = n^(1/2)

p+1 ==> n^(1/2) + 1
(p+1)^(2) = (n^(1/2) + 1)^(2)
= n + 1 + 2(n)^(1/2)

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Re: Math Question   [#permalink] 10 Sep 2008, 15:04
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