# CAT Model Paper 3 Questions and Answers with Explanation Part 9

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__Directions for question 46 - 48: answer the questions based on the following data__.

GTV Foodies is a group who is searching for talent via a contest called “Cognitive Digestion” . It visits various cities and in each city conducts contests. The details of the contest in the city Bhukkarnagar are provided below.

The contest is conducted in multiple stages. Each stage has a different value (points) assigned to it, which can also be negative. The difference in points between any two consecutive stages is 1. The contestants keep on moving from one stage to another, not necessarily in any order.

The total points of each stage are defined as the product of the ‘Points Value’ assigned to it and the number of contestants in that stage. When contestants move from one stage to another, the total points of each stage change as explained below.

For example, say the points assigned for stage is , and 4 contestants enter and 6 contestants exit stage X. Then, points will be added to and points will be subtracted from the already existing points for stage X.

4 stages, A, E, I, O, out of many stages; occur together but not necessarily in the same order. The following questions deal with the movement of contestants between these stages.

However, to conceal the scores from the contestants, the judges code the movements of the contestants in the following way: they mention a 4 letter word, whose middle 2 letters denote the stages and the extremes denote the number of candidates. For example, PQRS would mean P contestants have gone from stage Q to stage R and S candidates have gone from stage R to stage Q, where P and S are the numbers corresponding to the position of the letters in the English alphabet.

Moreover, the judges not only mention the words alone but do the same in a sentence.

For the movements mentioned, the following sentence was quoted.

Sunny Deol said, “To roam about in a coat having a coin in the pocket in front of a lion is to eat pies and meat on the mountain peak in vain.”

Q: 46. If the value of level O is zero, what is the minimum total change in points after the movement among these 4 stages?

(A)

(B)

(C)

(D) Cannot be determined

Ans: A

Solution

The 4 lettered words are deol, said, roam, coat, coin, lion, pies, meat, peak, vain.

The table below shows the number corresponding to the alphabets denoting the movements.

Based on the above table, we make another table representing the movement of contestants in and out of these four stages.

Let us assume that the points for the stages A, E, I, O are respectively.

Therefore, total change

Given s = 0, min total change happens when we assign the following values to the stages

Then as per the Equation

Total points

Option (A)

Q: 47. If the points for the 4 stages are and 0 respectively, what is the total change in points?

(A)

(B)

(C)

(D) Cannot be determined

Ans: B

Solution

The 4 lettered words are deol, said, roam, coat, coin, lion, pies, meat, peak, vain.

The table below shows the number corresponding to the alphabets denoting the movements.

Based on the above table, we make another table representing the movement of contestants in and out of these four stages.

Let us assume that the points for the stages A, E, I, O are p, q, r, s respectively.

Therefore, total change

Since the points for the stages are mentioned, we can directly put them in the equation.

.

Hence a change of

Option (B)

Q: 48. What is the maximum possible change in the total points possible after the movement in these 4 stages?

(A)

(B)

(C)

(D) Cannot be determined

Ans: A

Solution

The 4 lettered words are deol, said, roam, coat, coin, lion, pies, meat, and peak, vain.

The table below shows the number corresponding to the alphabets denoting the movements.

Based on the above table, we make another table representing the movement of contestants in and out of these four stages.

Let us assume that the points for the stages A, E, I, O are p, q, r, s respectively.

Therefore, total change

=

To maximize the total change, we assume

Hence .