CAT Quantitative Ability Questions | CAT Number System questions
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CAT/2021.1
Question . 4
How many three-digit numbers are greater than 100 and increase by 198 when the three digits are arranged in the reverse order?
Explanatory Answer
Method of solving this CAT Quantitative Ability Question from Number System question
We are considering a three-digit number in the form 'abc', where 'a', 'b', and 'c' represent the hundreds, tens, and units digits, respectively. The given condition states that the number increases by 198 when the digits are arranged in reverse order.
We can express the number as 100a + 10b + c. When we reverse the digits, we get 100c + 10b + a. According to the condition, the difference between these two numbers is 198:
(100c + 10b + a) - (100a + 10b + c) = 198
Simplifying the equation, we have:
99c - 99a = 198
Dividing both sides by 99:
c - a = 2
This equation tells us that the difference between the units digit (c) and the hundreds digit (a) is 2.
The possible combinations of 'a' and 'c' that satisfy this equation are as follows:
a c 1 3 2 4 3 5 4 6 5 7 6 8 7 9
For each combination, there are 10 possible values for 'b' (0 to 9), resulting in 10 three-digit numbers for each combination. Therefore, the total number of three-digit numbers that satisfy the given conditions is:
7 combinations * 10 numbers per combination = 70
Hence, there are a total of 70 three-digit numbers that are greater than 100 and increase by 198 when their digits are arranged in reverse order.
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