Multiple choice

Passage

Directions: 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 1is 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.

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. 10 ml

  2. 1 ml

  3. 10 ml or more

  4. Less than 1 ml
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

The test detects impurity if the concentration is >= 10%. Mixing 5ml of P (0% impurity) and 5ml of B (x% impurity) results in 10ml with (5/10)*x = 0.5x% impurity. Since the test detects impurity, 0.5x >= 10, so x >= 20%. 20% of 50ml is 10ml.

AI explanation

The testing device detects impurity only if the mixture contains at least 10% impurity. When 5 ml from bottle A (which is pure) is mixed with 5 ml from bottle B, the resulting 10 ml mixture tests positive for impurity, meaning it has at least 1 ml of impurity. Since this 1 ml of impurity must come entirely from the 5 ml taken from bottle B, the concentration of impurity in bottle B itself must be at least 20%. Because bottle B holds 50 ml, a 20% concentration means it must contain 10 ml or more of impurity.

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