CAT 2018 Question Paper | CAT LR DI

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CAT DILR : CAT 2018 Question Paper Slot 1

Set 1 : Written Test

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.

Question 3 : 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? [TITA]

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Video Explanation

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Explanatory Answer

Method of solving this CAT Question on CAT DILR

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.

Ajay was the unique highest scorer in WE.


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.
Indu and Jatin both scored 100% in exactly one section and Jatin’s composite score was 10 more than Indu’s.
Now, if Indu had scored 100% in DI, then her CS would be 20 × 2 + 8 + x = 60 or, x should be 12.
Now, this is a problem as Indu could have less than 70% in 2 sections and so would not have been selected.
So, x = 20.
Indu and Jatin are in. The highest CS Geeta can get is 54, so Ester is also in.
Ajay could not have scored 19 in WE as his CS would then become 51 same as Danish.
So, Ajay should have scored 20 in WE resulting in an CS of 52.


Geeta should have scored a CS of more than 52 so she should have scored 19 or 20 in WE. But Ajay was the unique highest scorer in WE.
So, Geeta should have score 19 in WE.
Let us assume Bala scored x in DI. His CS would be 2x + 20. We know 2x + 20 < 56 or, x < 18.
x = 17 gives Bala a CS of 54 which Chetna has scored.
x cannot be 16, 15 or 14 because Indu, Falak and Geetha have those scores.
x = 13 gives us a CS score of 46 which thankfully no one has.

The question is "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? [TITA]"

Hence, the answer is 13 marks

 

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