# Number Theory Questions and Solutions

Question:
How many numbers with distinct digits are possible product of whose digits is 28?
A.  6
B.  4
C.  8
D.  12

Explanation:

Two digit numbers; The two digits can be 4 and 7: Two possibilities 47 and 74
Three-digit numbers: The three digits can be 1, 4 and 7: 3! Or 6 possibilities.

We cannot have three digits as (2, 2, 7) as the digits have to be distinct.

We cannot have numbers with 4 digits or more without repeating the digits.

So, there are totally 8 numbers.

Difficulty Level 2
IIM CAT Preparation Tips: Number Theory Questions and Solutions

## Aug 16, 2013

### Number Theory Questions and Solutions

Question:
How many numbers with distinct digits are possible product of whose digits is 28?
A.  6
B.  4
C.  8
D.  12

Explanation:

Two digit numbers; The two digits can be 4 and 7: Two possibilities 47 and 74
Three-digit numbers: The three digits can be 1, 4 and 7: 3! Or 6 possibilities.

We cannot have three digits as (2, 2, 7) as the digits have to be distinct.

We cannot have numbers with 4 digits or more without repeating the digits.

So, there are totally 8 numbers.