CAT 2021 Slot 3 — DILR Question 4
Answer the next 4 questions based on the information given
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.
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?
Answer & solution
- A
3
- B
2
- C
4
1
Case 1: Only bottle contains pure P.
Now if we mix equal quantities from each of the 4 bottles, the concentration of I in the mixture = = 11.25%
∴ Testing this mixture will detect the impurities.
Case 2: 2 bottles contains pure P.
Now if we mix equal quantities from each of the 4 bottles, the concentration of I in the mixture = = 7.5%
∴ Testing this mixture will not detect the impurities.
⇒ Mix equal quantities of all 4 bottles, it I is detected then only 1 bottle contains P else 2 bottles contain P.
Hence, option (d).