Comprehension
GadRev is a rm that reviews different latest gadgets through a team of four reviewers (R1, R2, R3, and R4). Recently the reviewers reviewed four different tech gadgets (A, B, C, and D) on a scale of 1 to 5 (all integer values) where 1 denotes poor and 5 denotes excellent. These review ratings were then tabulated. However, due to a technical glitch, some of these ratings got deleted. The average rating given by each reviewer, and the average rating given to each gadget were earlier communicated to the team management in a separate email and hence can be useful to retrieve the deleted ratings. The available ratings along with the average ratings are represented in the following table:
Question: 1
What rating provided by Reviewer R1 to Gadget A can help determining the remaining ratings uniquely?
What rating provided by Reviewer R1 to Gadget A can help determining the remaining ratings uniquely?
Show Hint
When dealing with average and missing data, try different possibilities and check if each assumption leads to a unique solution.
Updated On: Dec 9, 2025
- 1
- 5
- 2
- 3
- 4
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The Correct Option is B
Solution and Explanation
Step 1: Analyze the table.
We are given the ratings of four reviewers for four gadgets, with some ratings missing. The average rating for each reviewer and gadget is provided.
Step 2: Determine the impact of each possible rating for Gadget A.
By trying each possible rating for Gadget A from Reviewer R1, we can determine which rating allows the remaining missing ratings to be filled in uniquely. After testing each rating, we find that if Reviewer R1 gives Gadget A a rating of 5, the remaining ratings can be uniquely determined.
Final Answer: \[ \boxed{\text{(B) 5}} \]
We are given the ratings of four reviewers for four gadgets, with some ratings missing. The average rating for each reviewer and gadget is provided.
Step 2: Determine the impact of each possible rating for Gadget A.
By trying each possible rating for Gadget A from Reviewer R1, we can determine which rating allows the remaining missing ratings to be filled in uniquely. After testing each rating, we find that if Reviewer R1 gives Gadget A a rating of 5, the remaining ratings can be uniquely determined.
Final Answer: \[ \boxed{\text{(B) 5}} \]
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Question: 2
In how many different ways could Reviewer R2 have rated Gadget B so that the ratings lead to the same averages for the gadgets and the reviewers as shown in the table?
In how many different ways could Reviewer R2 have rated Gadget B so that the ratings lead to the same averages for the gadgets and the reviewers as shown in the table?
Show Hint
When dealing with averages, use the given information to backtrack and calculate all possible values for the missing data that satisfy the conditions.
Updated On: Dec 9, 2025
- 2
- 3
- 4
- 1
- 5
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The Correct Option is C
Solution and Explanation
Step 1: Understand the question.
We are asked to find how many different ratings Reviewer R2 could have given to Gadget B while maintaining the same average ratings for the gadgets and the reviewers.
Step 2: Analyze the possibilities.
The possible ratings for Gadget B given by Reviewer R2 can be calculated based on the average ratings for that gadget and the consistency in the overall averages. We find that there are 4 possible valid ratings that R2 could have given.
Final Answer: \[ \boxed{\text{(C) 4}} \]
We are asked to find how many different ratings Reviewer R2 could have given to Gadget B while maintaining the same average ratings for the gadgets and the reviewers.
Step 2: Analyze the possibilities.
The possible ratings for Gadget B given by Reviewer R2 can be calculated based on the average ratings for that gadget and the consistency in the overall averages. We find that there are 4 possible valid ratings that R2 could have given.
Final Answer: \[ \boxed{\text{(C) 4}} \]
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Question: 3
How many different valid combinations of the missing ratings are possible?
How many different valid combinations of the missing ratings are possible?
Show Hint
When multiple variables are missing, systematically check each possible combination and validate it against the known averages.
Updated On: Dec 9, 2025
- 5
- 4
- 1
- 3
- 2
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Verified By Collegedunia
The Correct Option is B
Solution and Explanation
Step 1: Analyze the combinations.
We need to determine how many different ways the missing ratings can be filled in such that the averages for each reviewer and gadget match the given values.
Step 2: Identify the valid combinations.
After testing the different possibilities, we find that there are 4 different valid combinations of missing ratings that satisfy all the given conditions.
Final Answer: \[ \boxed{\text{(B) 4}} \]
We need to determine how many different ways the missing ratings can be filled in such that the averages for each reviewer and gadget match the given values.
Step 2: Identify the valid combinations.
After testing the different possibilities, we find that there are 4 different valid combinations of missing ratings that satisfy all the given conditions.
Final Answer: \[ \boxed{\text{(B) 4}} \]
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