Solution:
Consider (1) alone.
Let n = 5.
So (n-1)(n+1) = 4 * 6 = 24.
24 on being divided by 24 gives a remainder of 0.
Next let n = 9.
So (n-1)(n+1) = 8*10 = 80.
80 gives a remainder of 8 on being divided by 24.
Since nothing definite can be said, (1) alone is not sufficient.
Next consider (2) alone.
Take the examples of n = 5 and n = 4.
When n = 5, remainder is 0 on dividing (n-1)(n+1) by 24.
When n = 4, (n-1)(n+1) = 3*5 = 15 and remainder is 15.
Again nothing definite said be said from (2) alone.
Next combine both the statements together and check.
Since both 2 and 3 do not divide n, n is of the form 6k+1 or 6k+5, k being an integer.
Let n = 6k+1.
So (n-1)(n+1) = (6K+1-1)(6k+1+1) = 6k(6k+2) = 12k(3k+1).
If k is even, then 12k is a multiple of 24 and hence 12k(3k+1) is divisible by 24. Or remainder r is 0.
If k is odd 3k+1 is even . Or 12(3k+1) is divisible by 24 and so 12k(3k+1) is also divisible by 24. So remainder r is 0.
Next let n = 6k+5.
Or (n-1)(n+1) = (6k+5-1)(6k+5+1) = (6k+4)(6k+6) = 12(k+1)(3k+2).
If k is even (3k+2) is even or 12(3k+2) is divisible by 24 and so 12(k+1)(3k+2) is also divisible by 24.
If k is odd, (k+1) is even and 12(k+1) is divisible by 24. Or 12(k+1)(3k+2) is also divisible by 24
In any case remainder r is zero.
Or both statements together are sufficient and answer is (C).
Remainder
This topic has expert replies
Source: Beat The GMAT — Data Sufficiency |
GMAT/MBA Expert
-
Rahul@gurome
- GMAT Instructor
- Posts: 1179
- Joined: Sun Apr 11, 2010 9:07 pm
- Location: Milpitas, CA
- Thanked: 447 times
- Followed by:88 members
Rahul Lakhani
Quant Expert
Gurome, Inc.
https://www.GuroMe.com
On MBA sabbatical (at ISB) for 2011-12 - will stay active as time permits
1-800-566-4043 (USA)
+91-99201 32411 (India)
Quant Expert
Gurome, Inc.
https://www.GuroMe.com
On MBA sabbatical (at ISB) for 2011-12 - will stay active as time permits
1-800-566-4043 (USA)
+91-99201 32411 (India)
