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CAT Previous Year Paper | CAT Number Theory Questions | Question 26

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The CAT Exam is one of those exams where you are tested on your sense of numbers and your ability to comprehend concepts much more than your ability to remember gazillion formulae. CAT 2018 Question Paper is a perfect example of that!. Here's a delightful question from Number Theory taken from CAT previous year paper 2018. See if you can get to the answer without looking at the solution provided.
To practice more questions from CAT Previous Year Paper, visit 2IIM's CAT Question Bank.

Question 26 : 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?

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Explanatory Answer

Method of solving this CAT Question from Number Theory

Let the two-digit number be xy, which can be expressed as 10x + y
Given that the two-digit number is more than thrice the number obtained by interchanging the digits
So, 10x + y > 3 × (10y + x)
=> 10x + y > 30y + 3x
=> 7x > 29y
=> x > \\frac{29}{7}) × y
Approximately, x > 4y
Let us fix values for y and check for conditions,
For y = 1, x can take the values of 5 , 6 , 7 , 8 , 9 (As, 51 > (3 × 15), 61 > (3 ×16), 71> (3 × 17), 81 > (3 × 18), 91 > (3 × 19))
Similarly, for y = 2, the condition satisfies only for x = 9 (As, 92 > (3 × 29))
The remaining values of y does not satisfy the given conditions.
So, Total = 5 + 1 = 6 numbers

The question is "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?"