CAT 1998 — QA Question 22
Direction: Answer the question based on the following information.
A, B, C and D collected one-rupee coins following the given pattern.
- Together they collected 100 coins.
- Each one of them collected even number of coins.
- Each one of them collected at least 10 coins.
- No two of them collected the same number of coins.
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?
Answer & solution
- A
0
- B
1
4
- D
3
Let us find some of the smaller multiples of 125. They are 125, 250, 375, 500, 625, 750, 875, 1000 ... A five-digit number is divisible by 125, if the last three digits are divisible by 125.
So the possibilities are 375 and 875, 5 should come in unit’s place, and 7 should come in ten’s place. Thousand’s place should contain 3 or 8. We can do it in 2! ways. Remaining first two digits, we can arrange in 2! ways. So we can have 2! × 2! = 4 such numbers.
There are: 23875, 32875, 28375, 82375.
Hence, option (c).