CAT 2025 Lesson : Interpretative Tables - Case 4

Details for Questions 14 to 17 are provided below

A company administers a written test comprising of three sections of 20 marks each – Data Interpretation (DI), Written English (WE) and General Awareness (GA), for recruitment. A composite score for a candidate (out of 80) is calculated by doubling her marks in DI and adding it to the sum of her marks in the other two sections. Candidates who score less than 70% marks in two or more sections are disqualified. From among the rest, the four with the highest composite scores are recruited. If four or less candidates qualify, all who qualify are recruited.

Ten candidates appeared for the written test. Their marks in the test are given in the table below. Some marks in the table are missing, but the following facts are known:
1. No two candidates had the same composite score.
2. Ajay was the unique highest scorer in WE.
3. Among the four recruited, Geeta had the lowest composite score.
4. Indu was recruited.
5. Danish, Harini, and Indu had scored the same marks in GA.
6. Indu and Jatin both scored 100% in exactly one section and Jatin’s composite score was 10 more than Indu’s.


[CAT 2018 S1]

14) Which of the following statements MUST be true?
1. Jatin's composite score was more than that of Danish.
2. Indu scored less than Chetna in DI.
3. Jatin scored more than Indu in GA.

(1) Only 1
(2) Only 2
(3) Both 2 and 3
(4) Both 1 and 2

15) Which of the following statements MUST be FALSE?

(1) Bala scored same as Jatin in DI
(2) Bala’s composite score was less than that of Ester
(3) Chetna scored more than Bala in DI
(4) Harini’s composite score was less than that of Falak

16) If all the candidates except Ajay and Danish had different marks in DI, and Bala's composite score was less than Chetna's composite score, then what is the maximum marks that Bala could have scored in DI?

17) If all the candidates scored different marks in WE then what is the maximum marks that Harini could have scored in WE?

Solution

Case Solution:

We have to form a table with a total column as point 1 says that the composite score of each candidate is unique.

Total composite score = 2 $\times$ DI + WE + GA

⇒ By point 2, Ajay's marks in WE will be 19 or 20 and total will be 51 or 52.

⇒ From point 6, we can conclude that Jatin's DI marks is 20 and the total composite score is 70. Then Indu's total composite score is 60.

⇒ Danish, Harini, and Indu scored the same marks in GA and it should be 20, because by point 4 & 6 Indu should score 20 in one section and also got recruited. Therefore, if Indu gets 20 marks in DI, then Indu's marks in GA will be 12 and Indu will not be recruited.

⇒ As Danish's total composite score is 51, then Ajay's total composite score will be 52.

⇒ Since Geeta was also recruited and her total composite score is the least among those who got recruited, it should be greater than 52. The only possible total composite score for Geeta is 53 and marks in WE is 19.



14)

⇒ With the data from the table we can say that both 1 and 2 are true

Answer: (4) Both 1 and 2

15)

Let us consider the options.

Option (1): Jatin and Bala could not get the same marks in DI because Bala's total composite score will then be 60, which will be equal to Indu’s total composite score. As two people cannot have the same total composite score, this will be definitely false.

Option (2): Bala could get a maximum of 18 marks in DI. With this his total composite score will be 56, so Bala's composite score can be less than Ester’s total composite score. This can be true.

Option (3) As Bala's maximum marks in DI could be 18, so this can be true.

Option (4): As we don’t know Harini's marks in WE, his/her composite score could have been more than or less than Falak’s composite score. So this can be true.

Answer: (1) Bala scored same as Jatin in DI.

16)

⇒ Bala cannot score 20, 19, 15 or 14 because each candidate scored different marks. And Bala cannot score 18 or 17, because then Bala’s total composite score will be greater or equal to the total composite score of Cheta. So the maximum possible score is 13.

Answer: 13

17)

⇒ If Harini’s marks in WE is 17, the total composite score will be 47. This is eliminated as Falak’s total composite score. So the next maximum marks is 14.

Answer: 14

Answer:
14) (4) Both 1 and 2
15) (1) Bala scored same as Jatin in DI
16) 13
17) 14