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banona: Senior | Next Rank: 100 Posts; Posts: 38; Joined: Sat Dec 30, 2006 7:46 pm; Thanked: 1 times

question from Gmatprep test1

by banona » Sat Mar 03, 2007 11:22 am

Can somebody tell me what the most efficient way to solve this kind of DS GMAT questions ;

the question says , if the remainder of the division of (n-1)*(n+1) by 24 is r, what's the value of r ?
1- n is not divisible by 2
2- n is not divisible by3

I appologize if the question rose somewhere else here in this forum while,butI didn't see it.

Thanks

Quote

Source: Beat The GMAT — Data Sufficiency | Sat Mar 03, 2007 11:22 am

jayhawk2001: Community Manager; Posts: 789; Joined: Sun Jan 28, 2007 3:51 pm; Location: Silicon valley, California; Thanked: 30 times; Followed by:1 members

by jayhawk2001 » Sun Mar 04, 2007 6:36 pm

Not sure if this is the most efficient way but here goes...

1 - insufficient. Take n = 1 and n = 3 for example.
They yield remainders of 0 and 8 resp. No unique value. So rule out 1.

2 - insufficient. Take n = 1 and n = 2.
They yield remainders of 0 and 3 resp. No unique value. So, rule out 2

A number that is not divisible by 2 AND not divisible by 3 can be
written as n = 6x + 1 or n = 6x - 1

For n = 6x+1
(n-1)*(n+1) / 24
= 6x * (6x+2) / 24
= 12x * (x+1) / 24

We know that x*(x+1) will be even or 0, so the above equation will
always yield a remainder of 0.

Similarly for n=6x-1
(n-1)*(n+1) / 24
= (6x - 2)*6x
= 12x*(x-1) / 24

Again, x*x(-1) will be even or 0 and hence remainder r will be 0.

So, C looks like the correct answer.

On the actual GMAT, in the interest of time, it might be worthwhile
trying n = 1, 3, 5, 7, 9 etc. We can see that the remainder is 8 when n
is not divisible by 3 and remainder is 0 when n is divisible by 3 (for
all values n > 0). Using this pattern, I guess we can settle on C.