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dv2020: Master | Next Rank: 500 Posts; Posts: 112; Joined: Sun Nov 08, 2009 9:39 pm; Location: Delhi; Thanked: 2 times

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by dv2020 » Fri Jun 03, 2011 10:35 am

If n is a positive integer & r is the remainder when (n-1)(n+1) is divided by 24, what is the value of r

I) n is not divisible by 2
II) n is not divisible by 3

Last edited by dv2020 on Fri Jun 03, 2011 10:49 am, edited 1 time in total.

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Source: Beat The GMAT — Data Sufficiency | Fri Jun 03, 2011 10:35 am

cans: Legendary Member; Posts: 1309; Joined: Mon Apr 04, 2011 5:34 am; Location: India; Thanked: 310 times; Followed by:123 members; GMAT Score:750

by cans » Fri Jun 03, 2011 10:42 am

IMO C
a) n is not divisible by 2. thus (n-1) and (n+1) are divisible by 2.
Also as they are consecutive even numbers, atleast one of them is divisible by 4.
Thus (n-1)(n+1) is divisible by 8
Insufficient. if n=1,r=0 ; if n=3;r=8 insufficient
b)n is not divisible by 3. thus one of (n-1) or (n+1) is divisible by 3.

Thus (n-1)(n+1) is divisible by 3
Insufficient. if n=1,r=0 ; if n=5;r=8 insufficient

a&b together) (n-1)(n+1) is divisible by 24. Thus r= 0 always
Sufficient

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