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CAT 1998 Question-1

Q.) How many five-digit numbers can be formed using the digits 2,3,8,7,5 exactly once such that the number is divisible by 125?
A)0
B)1
C)4
D)3

Solution :

For a number to be divisible by 125 , the last three digits should be divisible by 125.

Let us take multiples of 125 : 125,250,375,500,625,750,875,1000,…….

Out of these multiples, the possible last three digits with given digits = 375,875

Now last three digits are fixed which can be filled in 2 ways. First 2 digits can be filled in 2! = 2 ways.

Hence , total number of numbers which are divisible by 125 = 2X2 = 4.

Hence , OPTION(C)


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