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