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# For each positive integer n, the integer n* is defined by n* = n^2 + 1

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Math Expert
Joined: 02 Sep 2009
Posts: 51188
For each positive integer n, the integer n* is defined by n* = n^2 + 1  [#permalink]

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07 Nov 2017, 22:38
00:00

Difficulty:

45% (medium)

Question Stats:

63% (01:35) correct 37% (01:34) wrong based on 43 sessions

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For each positive integer n, the integer n* is defined by n* = n^2 + 1. What is the value of the positive integer k ?

(1) When k is divided by 4, the remainder is 1.
(2) 18 ≤ k* ≤ 36

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Intern
Joined: 28 Dec 2010
Posts: 49
Re: For each positive integer n, the integer n* is defined by n* = n^2 + 1  [#permalink]

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07 Nov 2017, 23:08
1. k could be any number of 4n+1. For eg 5, 9, 13 etc
Insufficient.

2. $$18 ≤ k^2 + 1 ≤ 36$$
If k = 4, k* = 17
If k = 5, k* = 26
If k = 6, k* = 37
So k=5.
Sufficient.

B.
_________________

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Re: For each positive integer n, the integer n* is defined by n* = n^2 + 1 &nbs [#permalink] 07 Nov 2017, 23:08
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