CAT 2022 Question Paper | Quant Slot 3

CAT Previous Year Paper | CAT Quant Questions | Question 8

CAT 2022 Quant was dominated by Arithmetic followed by Algebra. In Arithmetic, the questions were dominated by topics like Speed-time-distance, Mixture and Alligations. This year, there was a surprise. The questions from Geometry were relatively on the lower side as compared to the previous years. There were 8 TITA Qs this year. Overall this section was at a medium level of difficulty.

Question 8 : The arithmetic mean of all the distinct numbers that can be obtained by rearranging the digits in 1421, including itself, is

  1. 2442
  2. 2222
  3. 3333
  4. 2592

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Explanatory Answer

The total number of possible rearrangements of the number 1421 = \( \frac { 4 ! } { 2 ! } = 4 * 3 = 12 \)
Now consider only the units place.In these 12 rearrangements,
How many times does 1 occur in the unit's place?
How many times does 2 occur in the unit's place?
How many times does 4 occur in the unit's place?
1 occurs 6 times in the unit's place.
2 occurs 3 times in the unit's place.
4 occurs 3 times in the unit's place.
The total sum of digits of the units place in all the 12 arrangements combined = 1(6) + 2(3) + 4(3) = 24.
Similarly, the sum of digits in ten’s, hundred’s or thousand’s place will also be 24.
So the sum of all the 12 rearrangements = 24(1111)
The average of all these rearrangements = \( \frac { 24 ( 1111 ) } { 12 } \) = 2222.


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

Hence, the answer is '2222'

Choice B is the correct answer.

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