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 the in GA.
6. Indu and Jatin both scored 100% in exactly one section and Jatin’s composite score was 10 more than Indu’s.
|Candidate||Mark Out of 20|
If all the candidates scored different marks in WE then what is the maximum marks that Harini could have scored in WE?
Given that Indu was recruited and scored 100% in exactly one section, and Jatin also scored 100% in exactly one section, we can determine Jatin's scores.
Therefore, we can find the composite score as:
Assuming Indu scores 20 in Data Interpretation (DI), Indu's score in General Awareness (GA) would be . However, in this case, Indu would not qualify. Therefore, Indu must have scored 20 in GA.
Hence, Ajay’s score:
(As Ajay scores either 19 or 20 in DI, the composite score cannot be 51)
Below table can be calculated:
|Candidate||Marks Out of 20||Composite Score|
Ajay was the unique highest scorer in WE.
This means that Ajay scored the most marks in WE, and no other candidate scored the same marks as him in WE.
Case 1: Geeta scored 19 marks in WE.
If Geeta scored 19 marks in WE, then Ajay must have scored 20 marks in DI. This is because Ajay's composite score is the highest, and if he scored 19 marks in DI, his composite score would be the same as Danish's.
Case 2: Geeta scored 18 marks in WE.
If Geeta scored 18 marks in WE, then Ajay could have scored either 19 or 20 marks in DI. However, if Ajay scored 20 marks in DI, his composite score would be the same as Geeta's. Therefore, Ajay could not have scored 20 marks in DI. If Ajay scored 19 marks in DI, his composite score would be the same as Danish's. Therefore, Ajay could not have scored 19 marks in DI either.
It is given that all the candidates scored different marks in WE.
This means that Harini cannot have scored the same marks in WE as any of the other candidates. Since Ajay, Geeta, and Ester have already scored 20, 19, and 18 marks in WE, respectively, the maximum marks that Harini could have scored in WE is 17. However, if Harini scored 17 marks in WE, her composite score would be the same as Falak's. Therefore, Harini could not have scored 17 marks in WE either.
Therefore, the maximum marks that Harini could have scored in WE is 14.
This is the largest possible score that Harini could have gotten in WE without having the same score as another candidate.