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How many two-digit numbers | Quantitative Aptitude - Modern Maths - P and C

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The question below is from previous year CAT question from CAT 2018 exam comes from CAT 2018 exam comes from CAT Modern Maths – P and C – How many two-digit numbers … . Find out by answering this question which tests an aspirant’s Quantitative Ability Skills:

CAT 2018 – Slot 2 - P and C - Question 2 - How many two-digit numbers

Q. 2: How many two-digit numbers, with a non-zero digit in the units place, are there which are more than thrice the number formed by interchanging the positions of its digits?
1. 5
2. 6
3. 8
4. 7

Let ‘ab’ be the two digit number. Where b  0.

On interchanging the digits, the new number will be ‘ba’ As per the condition 10a+b > 3×(10b + a)

7a > 29b

For b = 1, a = {5, 6, 7, 8, 9}

For b = 2, a = {9}

For b = 3, no value of ‘a’ is possible. Hence, there are a total of 6 such numbers

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