DS 22 set 15

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radhika1306: Master | Next Rank: 500 Posts; Posts: 144; Joined: Fri Apr 13, 2007 2:25 am

by radhika1306 » Thu Aug 30, 2007 11:52 am

If n is a positive integer and r is the remainder when (n – 1)(n + 1) is divided by 24, what
is the value of r?
(1) 2 is not a factor of n.
(2) 3 is not a factor of n.

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Source: Beat The GMAT — Data Sufficiency | Thu Aug 30, 2007 11:52 am

ratindasgupta: Senior | Next Rank: 100 Posts; Posts: 98; Joined: Mon Jun 11, 2007 10:32 pm; Location: Mumbai

Re: DS 22 set 15

by ratindasgupta » Thu Aug 30, 2007 12:26 pm

radhika1306 wrote:If n is a positive integer and r is the remainder when (n – 1)(n + 1) is divided by 24, what
is the value of r?
(1) 2 is not a factor of n.
(2) 3 is not a factor of n.

1) If 2 is not factor of n, then n is an odd number. So if n is is a factor of 3, the remainder is always 8 and if otherwise, the remainder is 0. So INSUFF

2) If 3 is not a factor, then we get all kinds of values of r since n could be an even number as well as an odd number. So INSUFF

Combining, we know that n is an odd number and not divisible by 3. So r will always be 0. So answer is C.

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