CAT 2022 Question Paper | Quant Slot 2

CAT Previous Year Paper | CAT Quant Questions | Question 16

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 16 : Five students, including Amit, appear for an examination in which possible marks are integers between 0 and 50, both inclusive. The average marks for all the students is 38 and exactly three students got more than 32. If no two students got the same marks and Amit got the least marks among the five students, then the difference between the highest and lowest possible marks of Amit is

  1. 21
  2. 24
  3. 20
  4. 22

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Explanatory Answer

The case where Amit gets the least amount of marks looks like…
Marks of 5 students
The maximum mark that Amit can get is 31, He can get it if he can grab 20 marks from the people who score 48, 49 and 50.
In fact, it is possible for Amit to do that…
Marks of 5 students
The difference between the highest and lowest marks if Amit = 31 - 11 = 20.

The answer is '20'

Choice C is the correct answer.

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