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 5 : In an examination, the average marks of students in sections A and B are 32 and 60, respectively. The number of students in section A is 10 less than that in section B. If the average marks of all the students across both the sections combined is an integer, then the difference between the maximum and minimum possible number of students in section A is

Video Explanation

Explanatory Answer

Let the possible average marks of all the students combined be a.
We know that 32 < a < 60.
If the overall average is ‘a’, the ratio of the number of students in class A to the number of students in class B is (60 - a) : (a - 32).
Also when there are equal numbers of students in class A and class B, the value of a is simply $\frac { 60 + 32 } { 2 } = 46$. If there are more students in class B than class A, the value of a is greater than 46 and if there are fewer students in class B than class A, the value of a is less than 46.
Since there are 10 more students in class B than class A, 46 < a < 60.
The extreme values of the number of students depend on the extreme values of a.
When a = 47, the ratio of students in class A to class B is 13 : 15
15x - 13x = 10
2x = 10
x = 5
Total number of students in class A = 13x = 65.
When a = 56, the ratio of students in class A to class B is 1 : 6
6x - x = 10
5x = 10
x = 2
Total number of students in class A = x = 2.
The difference between the maximum and minimum possible number of students in section A is 65 - 2 = 63

The answer is '63'

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