CAT 2022 Question Paper | Quant Slot 3

CAT Previous Year Paper | CAT Quant Questions | Question 13

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 13 : Consider six distinct natural numbers such that the average of the two smallest numbers is 14, and the average of the two largest numbers is 28. Then, the maximum possible value of the average of these six numbers is

  1. 22.5
  2. 23.5
  3. 24
  4. 23

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Explanatory Answer

We know the sum of the first pair of numbers is 14 * 2 = 28
Sum of the last pair of numbers is 28 * 2 = 56
To maximize the average of all the 6 numbers, we must try to maximize the two numbers in between. This is possible when the last pair of numbers are 27 and 29.
The maximum average case is
a, b, 25, 26, 27, 29
Where a + b = 28
The average of these 6 numbers is 22.5

The answer is '22.5'

Choice A is the correct answer.

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