CAT 2021 Slot 3 DILR Set 4 Q17–Q20

A DILR caselet from the Data Interpretation & Logical Reasoning (DILR) section of CAT 2021 Slot 3, with 4 questions (Quant-based Puzzles). Answers are CAT's official key.

The set

Each of the bottles mentioned in this question contains 50 ml of liquid. The liquid in any bottle can be 100% pure content (P) or can have certain amount of impurity (I). Visually it is not possible to distinguish between P and I. There is a testing device which detects impurity, as long as the percentage of impurity in the content tested is 10% or more.

For example, suppose bottle 1 contains only P, and bottle 2 contains 80% P and 20% I. If content from bottle 1 is tested, it will be found out that it contains only P. If content of bottle 2 is tested, the test will reveal that it contains some amount of I. If 10 ml of content from bottle 1 is mixed with 20 ml content from bottle 2, the test will show that the mixture has impurity, and hence we can conclude that at least one of the two bottles has I. However, if 10 ml of content from bottle 1 is mixed with 5 ml of content from bottle 2. the test will not detect any impurity in the resultant mixture.

Question 17

5 ml of content from bottle A is mixed with 5 ml of content from bottle B. The resultant mixture, when tested, detects the presence of I. If it is known that bottle A contains only P, what BEST can be concluded about the volume of I in bottle B?
  1. A
    10 ml or more
  2. B
    Less than 1 ml
  3. C
    10 ml
  4. D
    1 ml

Answer: (A) 10 ml or more Quant-based Puzzles MCQ

A worked solution for this question is being written. Meanwhile, practise it in a timed mock and see how other aspirants did.

Question 18

There are four bottles. Each bottle is known to contain only P or only I. They will be considered to be "collectively ready for despatch" if all of them contain only P. In minimum how many tests, is it possible to ascertain whether these four bottles are "collectively ready for despatch"?

TITA: type in the answer. There are no options and no negative marking.

Answer: 1 Quant-based Puzzles TITA

A worked solution for this question is being written. Meanwhile, practise it in a timed mock and see how other aspirants did.

Question 19

There are four bottles. It is known that three of these bottles contain only P, while the remaining one contains 80% P and 20% I. What is the minimum number of tests required to definitely identify the bottle containing some amount of I?

TITA: type in the answer. There are no options and no negative marking.

Answer: 2 Quant-based Puzzles TITA

A worked solution for this question is being written. Meanwhile, practise it in a timed mock and see how other aspirants did.

Question 20

There are four bottles. It is known that either one or two of these bottles contain(s) only P, while the remaining ones contain 85% P and 15% I. What is the minimum number of tests required to ascertain the exact number of bottles containing only P?
  1. A
    1
  2. B
    4
  3. C
    3
  4. D
    2

Answer: (A) 1 Quant-based Puzzles MCQ

A worked solution for this question is being written. Meanwhile, practise it in a timed mock and see how other aspirants did.

Same concept in other years

See every question on Pooled testing: mix samples to identify the defective one.

More Quant-based Puzzles questions from CAT

All 127 Quant-based Puzzles questions asked since 2017.