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Year

CAT 2021

Section

Data

Topic

Quant Based LR

Difficulty

Hard

Question

Slot-3

Read the passage and answer the questions below.

Passage:

Each of the bottles mentioned in this question contains 50 ml of liquid. The liquid in any bottle can be 100%100 \% pure content (P)(\mathrm{P}) or can have certain amount of impurity (I)(\mathrm{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%P80 \% \mathrm{P} and 20%I20 \% \mathrm{I}. If content from bottle 1 is tested, it will be found out that it contains only PP. 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 1

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 II. If it is known that bottle AA contains only PP, what BEST can be concluded about the volume of I in bottle B?

1 ml

Less than 1 ml

10 ml

10 ml or more

Question 2

There are four bottles. Each bottle is known to contain only PP or only I. They will be considered to be "collectively ready for dIspatch" 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 dIspatch"?

Question 3

There are four bottles. It is known that three of these bottles contain only PP, while the remaining one contains 80%P80 \% \mathrm{P} and 20%I20 \% \mathrm{I}. What is the minimum number of tests required to definitely identify the bottle containing some amount of II ?

Question 4

There are four bottles. It is known that either one or two of these bottles contain(s) only PP, while the remaining ones contain 85%P85 \% \mathrm{P} and 15%I15 \% \mathrm{I}. What is the minimum number of tests required to ascertain the exact number of bottles containing only PP ?

4

2

3

1

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