CAT 2022 Question Paper | Quant Slot 3

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

Video Explanation

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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