CAT 2024 Slot 2 · DILR · Question 10

CAT 2024 Slot 2 previous year question on Reasoning Based DI, with the answer and a step-by-step solution.

Reasoning Based DIDATA INTERPRETATION -High LevelType in the answer (TITA)Medium

Set 3: Daily Product Ratings of an E-commerce Firm — this question belongs to a set. Read the full set with all 4 questions →

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.

Distribution of Ratings on Day 2

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.

How many buyers gave ratings on Day 1?

Answer & solution

Answer: 150

Solving the set

Step 1 – Day 2 data from the chart.

Rating	Buyers on Day 2	Rating × Buyers
1	5	5
2	10	20
3	5	15
4	20	80
5	10	50
Total	50	170

Step 2 – Day 1. Let n buyers rate on Day 1. Their average is 3, so their total is 3n. The cumulative average after Day 2 is 3.1: (3n + 170)/(n + 50) = 3.1 ⇒ 3n + 170 = 3.1n + 155 ⇒ 0.1n = 15 ⇒ n = 150. Day 1 total = 450.

Step 3 – Day 3. Let ratings 1 and 2 each have x buyers; rating 3 then has 2x (fact 4). Ratings 4 and 5 are both modes, so they have the same number y, and y must be more than 2x. Total: x + x + 2x + y + y = 100 ⇒ 4x + 2y = 100. All counts are non-zero multiples of 10.

Buyers giving 1 (= giving 2)	Buyers giving 3	Buyers giving 4 (= giving 5)	Are 4 and 5 the modes?
10	20	(100 − 40)/2 = 30	Yes (30 > 20 > 10)
20	40	(100 − 80)/2 = 10	No (3 has 40 buyers)

Only x = 10, y = 30 works.

Rating	Buyers on Day 3	Rating × Buyers	Cumulative buyers
1	10	10	1–10
2	10	20	11–20
3	20	60	21–40
4	30	120	41–70
5	30	150	71–100
Total	100	360

Step 4 – Cumulative averages.

Day	Buyers	Sum of ratings	Cumulative buyers	Cumulative sum	Cumulative average
1	150	450	150	450	3.00
2	50	170	200	620	3.10
3	100	360	300	980	3.27

This question

From Step 2, n = 150. Check: (450 + 170)/(150 + 50) = 620/200 = 3.1 ✓.

Hence, the answer is 150.

CAT 2024 Slot 2 · DILR · Question 10

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