CAT 2018 Slot 1 — DILR Question 9
Answer the following question based on the information given 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:
- No two candidates had the same composite score.
- Ajay was the unique highest scorer in WE.
- Among the four recruited, Geeta had the lowest composite score.
- Indu was recruited.
- Danish, Harini, and Indu had scored the same marks the in GA.
- Indu and Jatin both scored 100% in exactly one section and Jatin’s composite score was 10 more than Indu’s.
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Which of the following statements MUST be true?
- Jatin's composite score was more than that of Danish.
- Indu scored less than Chetna in DI.
- Jatin scored more than Indu in GA.
Answer & solution
Both 1 and 2
- B
Both 2 and 3
- C
Only 1
- D
Only 2
70% of 20 = 14
Qualified candidate score 14 or more marks in two or more sections.
Composite scores of few students:
Chetna: 2(19) + 4 + 12 = 54
Ester: 2(12) + 18 + 16 = 58
Falak: 2(15) + 7 + 10 = 47
From (6), Jatin scored 20 marks in DI. Therefore, his Composite score is 2(20) + 16 + 14 = 70
Therefore, Indu’s Composite score = 60
If Indu scored 20 marks in DI, her score in GA = 60 – 2(20) – 8 = 12.
In this case, Indu scored less than 70% in WE and GA. But from (4) Indu was recruited. Therefore, this case is not valid. This means she must have scored 100% marks in GA i.e., 20 marks in GA.
∴ indu's marks (out of 20) in DI =
= 16
From (5), Danish and Harini also scored 20 marks in GA.
Therefore, his Composite score = 2(8) + 15 + 20 = 51
From (2), Ajay must have scored more than 18 marks. Assuming his score in WE as 19, composite score would be 2(8) + 19 + 16 = 51. This cannot be true as Danish’s composite score was 51. Thus, Ajay’s score in WE = 20 and his composite score 2(8) + 20 + 16 = 52.
Bala, Chetna and Falak scored less than 70% marks in at least two sections and hence were disqualified.
From (4), Geeta had the lowest score. Maximum composite score of Harini = 2(5) + 20 + 20 = 50
Ajay(52), Danish(51), Ester(58), Indu(60) and Jatin(70) are definitely qualified.
So, Ester(58), Indu(60) and Jatin(70) were top three scorers. Geeta must have scored more than 52 marks. Therefore marks scored by her in WE ≥ 53 – 2(14) − 6 i.e., marks scored by her in WE ≥ 19
If she had scored 20 marks in WE, her composite marks would be 2(14) + 20 + 6 = 54
But Chetna’s composite score = 54. So, Geeta’s marks in WE = 19 and her composite score = 53
Thus we have
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‘a’ denotes marks of Harini in WE while ‘d’ denote marks of Bala in DI.
Jatin’s composite score = 70 and Danish’s composite score = 51
Thus, statement 1 is true.
Indu’s score in DI = 16 and Chetna’s score in DI = 19
Thus, statement 2 is true.
Jatin’s score in GA = 14 and Indu’s score in GA = 20
Thus, statement 3 is false.
Hence, option (a).