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CAT 2001 — QA Question 47

Permutation & CombinationEasy
Passage / Data

Answer the following question based on the information given below.

The batting average (BA) of a test batsman is computed from runs scored and innings played-completed innings and incomplete innings (not out) in the following manner:

r1 = number of runs scored in completed innings; n1 = number of completed innings

r2 = number of runs scored in incomplete innings; n2 = number of incomplete innings

BA = r1+r2n1

To better assess batsman's accomplishments, the ICC is considering two other measures MBA1 and MBA2 defined as follows:

MBA1 = r1n1+n2n1× max[0, (r2n2-r1n1])

MBA2 = r1+r2n1+n2

Let n be the number of different 5 digit numbers, divisible by 4 with the digits 1, 2, 3, 4, 5 and 6, no digit being repeated in the numbers. What is the value of n?

Answer & solution

  • A

    144

  • B

    168

  • 192

  • D

    None of these

Solution

For a number to be divisible by 4, the last two digits should be divisible by 4.

There are eight such two digit combinations that can be formed from the given digits so that no digits are repeated.

The last two digit combinations are 12, 16, 24, 32, 36, 52, 56 and 64.

∴ There are 8 ways to fill the last two places.

∴ Number of ways in which the first three places can be filled = 4 × 3 × 2 = 24

∴ Total number of ways = 24 × 8 = 192

Hence, option (c).

CAT 2001 QA Q47: Let n be the number of different 5 digit numbers, divisible by 4 with the digits 1, 2, 3, 4, 5 and 6, no digit — Solution | TheCATExam