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# CAT 2018 [SLOT 2] Quant Question with Solution 02

Question:
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 $\ne$ 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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