NinetynineCAT 2022 Slot 3 QA Q8 Ratio, Mixtures & Averages
Question 8 of the Quantitative Ability (QA) section, CAT 2022 Slot 3, with CAT's official answer and a worked solution.
The arithmetic mean of all the distinct numbers that can be obtained by rearranging the digits in 1421, including itself, is
- A2442
- B2222
- C3333
- D2592
Answer: (B) 2222 Ratio, Mixtures & Averages MCQ
Solution
- Digits 1,1,2,4 give \(\frac{4!}{2!}=12\) distinct numbers.
- In each place, 1 appears 6 times, 2 appears 3 times and 4 appears 3 times; average digit \(=\frac{6+6+12}{12}=2\).
- So the mean is \(2222\).
Shortcut. The average digit is the average of the digits, \(\frac{1+1+2+4}4=2\), so the mean is 2222.