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JEE Advanced 2018 · Paper 1, Mathematics question 8

The number of 5 digit numbers which are divisible by 4, with digits from the set {1,2,3,4,5}\{1, 2, 3, 4, 5\} and the repetition of digits is allowed, is _____ .

Answer and worked solution

Official answer: 625

A number is divisible by 4 when its last two digits are. Using the digits 1-5, the possible endings are
12, 24, 32, 44, 52,12,\ 24,\ 32,\ 44,\ 52,
which is 5 choices.

The first three digits are free: 53=1255^3=125 ways.

Total: 125×5=625125\times5=625.

Answer: 625