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:
What rating provided by Reviewer R1 to Gadget A can help determining the remaining ratings uniquely?
Show Hint
- 1
- 5
- 2
- 3
- 4
The Correct Option is B
Solution and Explanation
Ratings for four reviewers and four gadgets are provided, with some entries missing. Averages for each reviewer and gadget are also given.
Step 2: Determine the impact of each possible rating for Gadget A.
Each potential rating for Gadget A by Reviewer R1 is tested to ascertain which rating enables a unique completion of the remaining missing ratings. Upon evaluation, a rating of 5 from Reviewer R1 for Gadget A permits the unique determination of all other missing ratings.
Final Answer: \[\boxed{\text{(B) 5}}\]
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
- 2
- 3
- 4
- 1
- 5
The Correct Option is C
Solution and Explanation
The objective is to determine the number of distinct rating values Reviewer R2 could have assigned to Gadget B, provided that the average ratings for both the gadgets and the reviewers remain unchanged.
Step 2: Evaluate Scenarios.
The potential ratings for Gadget B from Reviewer R2 can be derived by considering the established average ratings for Gadget B and ensuring consistency in the overall average ratings. Our analysis indicates that there are 4 permissible ratings R2 could have provided.
Final Answer:
\[\boxed{\text{(C) 4}}\]
How many different valid combinations of the missing ratings are possible?
Show Hint
- 5
- 4
- 1
- 3
- 2
The Correct Option is B
Solution and Explanation
Determine the number of ways to fill in missing ratings so that reviewer and gadget averages match given values.
Step 2: Identify the valid combinations.
Testing possibilities reveals 4 valid combinations of missing ratings that meet all conditions.
Final Answer:
\[ \boxed{\text{(B) 4}} \]
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