CAT 2020 Slot 1 QA Question 4: How many 3-digit numbers are there, for which the product of their digits is more than 2 but less than 7?

Question

How many 3-digit numbers are there, for which the product of their digits is more than 2 but less than 7?

Accepted Answer

The product of the digits must be 3, 4, 5 or 6. Since the product is greater than 2, no digit can be 0.

Product 3: digits 1, 1, 3 can be arranged in 3 ways.
Product 4: digits 1, 1, 4 in 3 ways and 1, 2, 2 in 3 ways.
Product 5: digits 1, 1, 5 can be arranged in 3 ways.
Product 6: digits 1, 1, 6 in