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CAT 2018 Slot 2 — QA Question 25

Number TheoryEasy

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?

Answer & solution

  • 6

  • B

    8

  • C

    7

  • D

    5

Solution

Let the original number be 'xy' = 10x + y and
the number formed by reversing the digits = 'yx' = 10y + x. 

We have the following:

10x + y > 3(10y + x)

∴ x > 297y

When y = 1, x = 5, 6, 7, 8 or 9 (Total 5 values)

When y = 2, x = 9 (Total 1 value)

If y > 3, x has to be a 2 digit number which is not possible.

∴ The required answer is 5 + 1 = 6.

Hence, option (a).

CAT 2018 Slot 2 QA Q25: How many two-digit numbers, with a non-zero digit in the units place, are there which are more than thrice the — Solution | TheCATExam