Saturday, 29 October 2011

Algebra-15 (CAT-2002)

For all integers n>0, 76n-66n is divisible by:
(1)13  (2)128  (3)549  (4) None of these
For Answer Click on "Read more" below:
Solution:
76n-66n = (73n+63n) (73n-63n)
= (7n+6n) (72n+62n-7n6n) (7n-6n) (72n+62n+7n6n)
= (7n+6n) (7n-6n) (72n+62n-7n6n) (72n+62n+7n6n)
For odd n, (7n+6n) is divisible by 7+6 ie., 13
For even n, (7n-6n) is divisible by 7+6 ie., 13
Hence the given number is divisible by 13 for all n
Answer(1)

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