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CAT 2022 Question Paper (Slot 3) Question 55
Question 55

The arithmetic mean of all the distinct numbers that can be obtained by rearranging the digits in 1421, including itself, is

Solution

The number of 4-digit numbers possible using 1,1,2, and 4 is $$\frac{4!}{2!}=12$$

Number of 1's, 2's and 4's in units digits will be in the ratio 2:1:1, i.e. 6 1's, 3 2's and 3 4's.

Sum = 6(1) + 3(2) + 3(4) = 24

Similarly, in tens digit, hundreds digit and thousands digit as well.

Therefore, sum = 24 + 24(10) + 24(100) + 24(1000) = 24(1111)

Mean = $$\frac{24\left(1111\right)}{12}=2222$$

The answer is option A.


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