Instructions

Read the following scenario and answer the THREE questions that follow.

Comprehension:
GadRev is a firm 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 27

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?

Solution

The first thing we should do while solving this set is we should replace the average with the sum of the ratings as we have done in the following table:

We know that the ratings can be 1/2/3/4/5 only.

R1 has given 4 and 3 to B and D respectively and the sum of the ratings given by R1 in total is 16.

So, the sum of the ratings given by R1 to A and C is (16-4-3 = 9)

Now, this sum is only possible when he has given 4 to one of them and 5 to another.

Let's make both the cases:

Now, with this, we can derive the score given by R3 to C.

In case 1, it will be (16-4-4-5) = 3

In case 2, it will be (16-5-4-5) = 2

Now, R2 gave 3 and 4 score to A and C respectively. Hence, he would have given a sum of (16 - 3 - 4 = 9) to B and D. It could be possible when he gave 4 to one and 5 to the other one.

Hence, we can make the possible cases and sub cases: