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CAT 2025 Lesson : DILR: Jan '25 to Feb '25 - DILR - Live Solving - 24 Jan 2025
Read the following and answer the Questions that follow
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.
1) How many buyers gave ratings on Day 1?
Answer:
2) What is the daily average rating of Day 3?
(1) 3.5
(2) 3.0
(3) 3.2
(4) 3.6
3) What is the median of all ratings given on Day 3?
Answer:
4) Which of the following is true about the cumulative average ratings of Day 2 and Day 3?
(1) The cumulative average of Day 3 increased by more than 8% from Day 2.
(2) The cumulative average of Day 3 increased by less than 5% from Day 2.
(3) The cumulative average of Day 3 decreased from Day 2.
(4) The cumulative average of Day 3 increased by a percentage between 5% and 8% from Day 2.
Read the following and answer the Questions that follow
Eight gymnastics players numbered 1 through 8 underwent a training camp where they were coached by three coaches - Xena, Yuki, and Zara. Each coach trained at least two players. Yuki trained only even numbered players, while Zara trained only odd numbered players. After the camp, the coaches evaluated the players and gave integer ratings to the respective players trained by them on a scale of 1 to 7, with 1 being the lowest rating and 7 the highest.
The following additional information is known.
1. Xena trained more players than Yuki.
2. Player-1 and Player-4 were trained by the same coach, while the coaches who trained Player-2, Player-3 and Player-5 were all different.
3. Player-5 and Player-7 were trained by the same coach and got the same rating. All other players got a unique rating.
4. The average of the ratings of all the players was 4.
5. Player-2 got the highest rating.
6. The average of the ratings of the players trained by Yuki was twice that of the players trained by Xena and two more than that of the players trained by Zara.
7. Player-4's rating was double of Player-8's and less than Player-5's.
5) What best can be concluded about the number of players coached by Zara?
(1) Either 2 or 3
(2) Either 2 or 3 or 4
(3) Exactly 3
(4) Exactly 2
6) What was the rating of Player-7?
Answer:
7) What was the rating of Player-6?
Answer:
8) For how many players the ratings can be determined with certainty?
Answer:
9) Who all were the players trained by Xena?
(1) Player-1, Player-4, Player-6, Player-8
(2) Player-1, Player-3, Player-4, Player-8
(3) Player-1, Player-3, Player-4
(4) Player-1, Player-3, Player-4, Player-6
Read the following and answer the Questions that follow
The numbers 1, 2, 3, 4, 5, 6, 7, 8, 9, and 10 are placed in ten slots of the following grid based on the conditions below.
1. Numbers in any row appear in an increasing order from left to right.
2. Numbers in any column appear in a decreasing order from top to bottom.
3. 1 is placed either in the same row or in the same column as 10.
4. Neither 2 nor 3 is placed in the same row or in the same column as 10.
5. Neither 7 nor 8 is placed in the same row or in the same column as 9.
6. 4 and 6 are placed in the same row.
10) What is the row number which has the least sum of numbers placed in that row?
Answer:
11) Which of the following statements MUST be true?
I. 10 is placed in a slot in Row 1.
II. 1 is placed in a slot in Row 4.
(1) Only I
(2) Both I and II
(3) Only II
(4) Neither I nor II
12) Which of the following statements MUST be true?
I. 2 is placed in a slot in Column 2.
II. 3 is placed in a slot in Column 3.
(1) Only I
(2) Both I and II
(3) Only II
(4) Neither I nor II
13) For how many slots in the grid, placement of numbers CANNOT be determined with certainty?
Answer:
14) What is the sum of the numbers placed in Column 4?
Answer:
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.
1) How many buyers gave ratings on Day 1?
Answer:
2) What is the daily average rating of Day 3?
(1) 3.5
(2) 3.0
(3) 3.2
(4) 3.6
3) What is the median of all ratings given on Day 3?
Answer:
4) Which of the following is true about the cumulative average ratings of Day 2 and Day 3?
(1) The cumulative average of Day 3 increased by more than 8% from Day 2.
(2) The cumulative average of Day 3 increased by less than 5% from Day 2.
(3) The cumulative average of Day 3 decreased from Day 2.
(4) The cumulative average of Day 3 increased by a percentage between 5% and 8% from Day 2.
Read the following and answer the Questions that follow
Eight gymnastics players numbered 1 through 8 underwent a training camp where they were coached by three coaches - Xena, Yuki, and Zara. Each coach trained at least two players. Yuki trained only even numbered players, while Zara trained only odd numbered players. After the camp, the coaches evaluated the players and gave integer ratings to the respective players trained by them on a scale of 1 to 7, with 1 being the lowest rating and 7 the highest.
The following additional information is known.
1. Xena trained more players than Yuki.
2. Player-1 and Player-4 were trained by the same coach, while the coaches who trained Player-2, Player-3 and Player-5 were all different.
3. Player-5 and Player-7 were trained by the same coach and got the same rating. All other players got a unique rating.
4. The average of the ratings of all the players was 4.
5. Player-2 got the highest rating.
6. The average of the ratings of the players trained by Yuki was twice that of the players trained by Xena and two more than that of the players trained by Zara.
7. Player-4's rating was double of Player-8's and less than Player-5's.
5) What best can be concluded about the number of players coached by Zara?
(1) Either 2 or 3
(2) Either 2 or 3 or 4
(3) Exactly 3
(4) Exactly 2
6) What was the rating of Player-7?
Answer:
7) What was the rating of Player-6?
Answer:
8) For how many players the ratings can be determined with certainty?
Answer:
9) Who all were the players trained by Xena?
(1) Player-1, Player-4, Player-6, Player-8
(2) Player-1, Player-3, Player-4, Player-8
(3) Player-1, Player-3, Player-4
(4) Player-1, Player-3, Player-4, Player-6
Read the following and answer the Questions that follow
The numbers 1, 2, 3, 4, 5, 6, 7, 8, 9, and 10 are placed in ten slots of the following grid based on the conditions below.
1. Numbers in any row appear in an increasing order from left to right.
2. Numbers in any column appear in a decreasing order from top to bottom.
3. 1 is placed either in the same row or in the same column as 10.
4. Neither 2 nor 3 is placed in the same row or in the same column as 10.
5. Neither 7 nor 8 is placed in the same row or in the same column as 9.
6. 4 and 6 are placed in the same row.
10) What is the row number which has the least sum of numbers placed in that row?
Answer:
11) Which of the following statements MUST be true?
I. 10 is placed in a slot in Row 1.
II. 1 is placed in a slot in Row 4.
(1) Only I
(2) Both I and II
(3) Only II
(4) Neither I nor II
12) Which of the following statements MUST be true?
I. 2 is placed in a slot in Column 2.
II. 3 is placed in a slot in Column 3.
(1) Only I
(2) Both I and II
(3) Only II
(4) Neither I nor II
13) For how many slots in the grid, placement of numbers CANNOT be determined with certainty?
Answer:
14) What is the sum of the numbers placed in Column 4?
Answer:
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