CAT 2024 Question Paper | DILR Slot 2

CAT Questions

CAT 2024 DILR did not have a change in pattern. Atleast two sets were doable in each slot and one of the four sets was extremely tough. Choice of Sets became a crucial factor. Overall this section was at a medium to high level of difficulty.

An online e-commerce firm receives daily integer product ratings from 1 through 5 given by buyers. The daily average is the average of the ratings given on that day. The cumulative average is the average of all ratings given on or before that day.
The rating system began on Day 1, and the cumulative averages were 3 and 3.1 at the end of Day 1 and Day 2, respectively. The distribution of ratings on Day 2 is given in the figure below.


The following information is known about ratings on Day 3.
1. 100 buyers gave product ratings on Day 3.
2. The modes of the product ratings were 4 and 5.
3. The numbers of buyers giving each product rating are non-zero multiples of 10.
4. The same number of buyers gave product ratings of 1 and 2, and that number is half the number of buyers who gave a rating of 3.

Question 17 : What is the median of all ratings given on Day 3?

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Video Explanation

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Explanatory Answer

Day 2

Ratings	Number of Buyers
1	5
2	10
3	5
4	20
5	10

Total number of Buyers in Day 2 = 50.

Daily Average on Day 2 =
(1×5 + 2×10 + 3×5 + 4×20 + 5×10) / 50 = 170 / 50 = 3.4

DAY 1:

Cumulative averages on Day 1 and Day 2 were 3 and 3.1 respectively.

Let the number of Buyers in Day 1 = x.

(3x + 170) / (x + 50) = 3.1

Solving, 3x + 170 = 3.1(x + 50);
3x + 170 = 3.1x + 155;
0.1x = 15;
x = 150.

Therefore, the number of Buyers in Day 1 = 150.

DAY 3:

Total number of Buyers in Day 3 = 100.

The numbers of buyers giving each product rating are non-zero multiples of 10.
Number of buyers giving rating 1 = Number of buyers giving rating 2 = Half of number of buyers giving rating 3.
The modes of the product ratings were 4 and 5.

DAY 3

Ratings	Number of Buyers
1	A
2	A
3	2A
4	B (Mode)
5	B (Mode)

Sum of the number of buyers = 4A + 2B = 100.

The only possible solution for the equation and B value being the mode is A = 10 and B = 30.

DAY 3

Ratings	Number of Buyers
1	10
2	10
3	20
4	30
5	30

Product rating on Day 3 = (1×10 + 2×10 + 3×20 + 4×30 + 5×30) / 100 = 360 / 100 = 3.6

Cumulative rating on Day 3 = (3×150 + 3.4×50 + 3.6×100) / (150 + 50 + 100) = 980 / 300 = 3.266

DAY	NUMBER OF PASSENGERS	DAILY AVERAGE	CUMULATIVE AVERAGE
1	150	3	3
2	50	3.4	3.1
3	100	3.6	3.266

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The question is "What is the median of all ratings given on Day 3?"

Answer: No of 1s’= 10; No of 2’s= 10; No of 3’s= 20; No of 4’s= 30; No of 5’s= 30.
Therefore, the median will be average of 50th and 51st term which is (4+4)/2 = 4.

Hence, the answer is '4'

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