CAT 2018 Question Paper | CAT LR DI

CAT Questions

This is a classic question from the grid-based set that got rolled out in the CAT 2018 question paper. Here, you are required to find the highest overall score among the eight institutions. It can be categorized as an easy-medium level difficulty. Try your hands on this beautiful problem and ace your CAT preparation online.

CAT DILR : CAT 2018 Question Paper Slot 2

Set 1: College Accreditation

An agency entrusted to accredit colleges looks at four parameters: faculty quality (F), reputation (R), placement quality (P), and infrastructure (I). The four parameters are used to arrive at an overall score, which the agency uses to give an accreditation to the colleges. In each parameter, there are five possible letter grades given, each carrying certain points: A (50 points), B (40 points), C (30 points), D (20 points), and F (0 points). The overall score for a college is the weighted sum of the points scored in the four parameters. The weights of the parameters are 0.1, 0.2, 0.3 and 0.4 in some order, but the order is not disclosed.

Accreditation is awarded based on the following scheme:



Eight colleges apply for accreditation, and receive the following grades in the four parameters (F, R, P, and I):



It is further known that in terms of overall scores:
1. High Q is better than Best Ed.
2. Best Ed is better than Cosmopolitan.
3. Education Aid is better than A-one.

Question 3 : What is the highest overall score among the eight colleges? [TITA]

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Video Explanation

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Explanatory Answer

Method of solving this CAT Question on CAT DILR

Let us look at this one at a time. Statement 1 does not give us clear comparables, let us start with statement 2.

Ratings in F and P are identical, so we can infer that Weightage for R > Weightage for I.
R > I.
Now, let us move to statement 3.

Ratings in F and R are identical, so we can infer that Weightage for I > Weightage for P.
I > P.
Now, let us combine these two inferences – we get R > I > P.

Now, let us look at Statement 1.
Scores in P are identical. Best Ed has gotten better scores in F and R and a worse score in I.
Further Best Ed has gotten better score by one grade in F and R, but worse score by two grades in I.
So, Best Ed’s better score in two grades is more than offset by High Q’s better score in one parameter.

High Q is -1 in F and R, but +2 in I. We know that weightage given for R > I.
So, the -1 in R has a great impact, so the -1 in F should have much lower impact.
In other words, weightage for F should be small and that for I should be high.

Let us account for R > I > P first.
Of the 4 possibilities, we can easily eliminate the last one as F cannot be 0.4.
F cannot be 0.3 either, so the 3rd one can also be eliminated.

Even if F were 0.2, High Q would not be higher than Best End – the two scores would be equal.
So, the weightages have to be F = 0.1, R = 0.4, P = 0.2 and I = 0.3.
So, the weightages are as follows.


From the above table, we can see that the highest overall score among the eight colleges is 48.

The question is "What is the highest overall score among the eight colleges? [TITA]"

Hence, the answer is 48