1308: Number System - Remainder - CAT 2000

The integers 34041 and 32506, when divided by a three-digit integer n, leave the same remainder.
What is the value of n?

a. 289          b. 367         c. 453     d. 307
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Let r be the remainder. Then 34041 – r and 32506 – r are perfectly divisible by n.
Hence, their difference should also be divisible by the same.
(34041 – r) – (32506 – r) = 1535, which is divisible by only 307.
Answer : D 

1307 : Permutation Combination CAT 2000

One red flag, three white flags and two blue flags are arranged in a line such that:

I. No two adjacent flags are of the same colour
II. The flags at the two ends of the line are of different colours

In how many different ways can the flags be arranged?
   a. 6    b. 4    c. 10   d. 2


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Soln : 63. a The possibilities are W@W@W@ (or) @W@W@W,
where 2 blue and 1 red flag occupy the space marked
as @. Hence, the total permutation is 2(3!/2!) = 6