# CAT 2021 Exam Question Papers Slot 1 | CAT Quants

### CAT Quantitative Aptitude | CAT 2021 Question Papers

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All CAT 2021 Quantitative aptitude questions have detailed answer keys and solutions provided by our experts. Watch the videos below to learn the fastest ways to answer the questions:

10).

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

1. 80

2. 60

3. 50

4. 70

### Explanation

Let the three digit number be pqr.

Arranging the digits in reverse order, the number becomes rqp

As per the question,

rqp – pqr = (100 r + 10 q + p) – (100 p + 10 q + r)

= 99 (r – p) = 198

=>   r – p = 2

The minimum vaue that p can have is 1 (when r = 3), and the maximum value that p can have is 7 (when r = 9). r cannot be chosen independently since r – p = 2 has to be satisfied. Thus, p and r can be chosen in 7 ways.

q can be chosen in 10 ways (0 to 9) for each value of p/r.

There are 7 x 10 = 70 three-digit numbers satisfying given conditions

Ans(4)