# CAT 2021 Question Paper | Quant Slot 1

###### CAT Previous Year Paper | CAT Quant Questions | Question 20

CAT 2021 Quant was dominated by Arithmetic followed by Algebra. In Arithmetic, the questions were dominated by topics like Speed-time-distance, Mixture and Alligations. This year, there was a surprise. The questions from Geometry were relatively on the lower side as compared to the previous years. There were 8 TITA Qs this year. Overall this section was at a medium level of difficulty.

Question 20 : How many three-digit numbers are greater than 100 and increase by 198 when the three digits are arranged in the reverse order?

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Let's consider a three-digit number to be ‘abc’.
Given that, three-digit numbers increase by 198 when the three digits are arranged in the reverse order.
100c + 10b + a - 100a - 10b - c = 198
99c - 99a = 198
c - a = 2
So, the difference between the hundreds place digit and the units place digit is 2.
The possible combinations are:
1 _ 3, 2 _ 4, 3 _ 5, 4 _ 6, 5 _ 7, 6 _ 8, 7 _ 9.
We have 10 numbers for each combination.
Hence, the total numbers are 70.

The question is " How many three-digit numbers are greater than 100 and increase by 198 when the three digits are arranged in the reverse order? "

##### Hence, the answer is '70'

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