CAT 2020 Slot 1 QA Q1 Number Systems

Question 1 of the Quantitative Ability (QA) section, CAT 2020 Slot 1, with CAT's official answer and a worked solution.

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

TITA: type in the answer. There are no options and no negative marking.

Answer: 21 Number Systems TITA

Solution

The product must be 3, 4, 5 or 6, so no digit is 0 and digits come from 1 to 6.
Product 3: {1,1,3}, 3 numbers. Product 4: {1,1,4} and {1,2,2}, 3 + 3 = 6. Product 5: {1,1,5}, 3.
Product 6: {1,1,6} gives 3 and {1,2,3} gives \(3! = 6\), total 9.
Total \(= 3+6+3+9 = 21\).