CAT 2018 Question Paper (Slot 2) Question 72

Question 72

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?

Correct Answer: 6

Solution

Let 'ab' be the two digit number. Where b $$\neq$$ 0.

We will get number 'ba' after interchanging its digit.

It is given that 10a+b > 3*(10b + a)

7a > 29b

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

If b = 2, then a = {9}

If b = 3, then no value of 'a' is possible. Hence, we can say that there are a total of 6 such numbers.

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