**Question:**

How many numbers with distinct digits are possible product of whose digits is 28?

A. 6

B. 4

C. 8

D. 12

**Correct Answer: (C)**

**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.

**Answer Choice (****C****)**

**Difficulty Level 2**

### Related posts

- October 31, 2014 CAT Preparation Online – Permutation and Combination
Question
Product of the distinct digits of a natural number is 60. How many such numbers are possible?
Explanation
60 = 2^2 * 3 * 5
60 cannot be written as a product of […] Posted in Combinatorics
- July 15, 2013 Number Theory
Question
What is the remainder when (13100 +17100) is divided by 25?
A. 2
B. 0
C. 15
D. 8
Correct Answer: Choice (A)
Explanation:
What is the remainder when (13100 […] Posted in Number Theory
- November 8, 2010 Number Theory Remainders – 2 more questions
Have given below two more questions on remainders.
Question 1:
A prime number p greater than 100 leaves a remainder q on division by 28. How many values can q take?.
Question […] Posted in Number Theory
- November 2, 2010 Number theory questions – Factors II
Two more questions in Number Theory. These are also focused on finding the number of factors of a given number.
Question 1
How many factors of the number 2^8 * 3^6 * 5^4 * 10^5 […] Posted in Number Theory