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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?
Correct answer is '2'. Can you explain this answer?
Most Upvoted Answer
There are four bottles. It is known that three of these bottles conta...
Introduction:
In this problem, we are given four bottles and our objective is to identify the bottle containing some amount of I. Three of the bottles contain only P (which means they do not contain any I), while the remaining one contains a mixture of 80% P and 20% I. We need to determine the minimum number of tests required to definitively identify the bottle containing I.
Approach:
To solve this problem efficiently, we can use a combination of two tests. Let's understand the approach step-by-step:
Test 1:
- For the first test, we will take a small amount of liquid from the first bottle, a large amount from the second bottle, and the same amount from the third and fourth bottles.
- The purpose of this test is to determine whether the bottle containing I is the one from which we took a small amount of liquid.
- Let's denote the bottles as A, B, C, and D.
- Now, there are three possible outcomes of this test:
1. If the mixture from the first bottle and the mixture from the second bottle are the same, then the bottle containing I can only be either A or B.
2. If the mixture from the third bottle is the same as the first two mixtures, then the bottle containing I can only be C.
3. If the mixture from the fourth bottle is the same as the first two mixtures, then the bottle containing I can only be D.
Test 2:
- For the second test, we will take a small amount of liquid from the bottle that we identified in the first test as the potential bottle containing I (either A, B, C, or D), and a large amount from one of the other bottles.
- The purpose of this test is to confirm whether the bottle identified in the first test actually contains I or not.
- If the mixture from the second test is different from the first two mixtures, then the bottle identified in the first test is the one containing I. Otherwise, the bottle containing I is the other one.
Minimum number of tests:
By using the combination of the above two tests, we can definitively identify the bottle containing I in just two tests. The first test helps narrow down the possibilities to two bottles, and the second test confirms the presence of I in one of those bottles.
Therefore, the minimum number of tests required to definitely identify the bottle containing some amount of I is 2.
In this problem, we are given four bottles and our objective is to identify the bottle containing some amount of I. Three of the bottles contain only P (which means they do not contain any I), while the remaining one contains a mixture of 80% P and 20% I. We need to determine the minimum number of tests required to definitively identify the bottle containing I.
Approach:
To solve this problem efficiently, we can use a combination of two tests. Let's understand the approach step-by-step:
Test 1:
- For the first test, we will take a small amount of liquid from the first bottle, a large amount from the second bottle, and the same amount from the third and fourth bottles.
- The purpose of this test is to determine whether the bottle containing I is the one from which we took a small amount of liquid.
- Let's denote the bottles as A, B, C, and D.
- Now, there are three possible outcomes of this test:
1. If the mixture from the first bottle and the mixture from the second bottle are the same, then the bottle containing I can only be either A or B.
2. If the mixture from the third bottle is the same as the first two mixtures, then the bottle containing I can only be C.
3. If the mixture from the fourth bottle is the same as the first two mixtures, then the bottle containing I can only be D.
Test 2:
- For the second test, we will take a small amount of liquid from the bottle that we identified in the first test as the potential bottle containing I (either A, B, C, or D), and a large amount from one of the other bottles.
- The purpose of this test is to confirm whether the bottle identified in the first test actually contains I or not.
- If the mixture from the second test is different from the first two mixtures, then the bottle identified in the first test is the one containing I. Otherwise, the bottle containing I is the other one.
Minimum number of tests:
By using the combination of the above two tests, we can definitively identify the bottle containing I in just two tests. The first test helps narrow down the possibilities to two bottles, and the second test confirms the presence of I in one of those bottles.
Therefore, the minimum number of tests required to definitely identify the bottle containing some amount of I is 2.
Community Answer
There are four bottles. It is known that three of these bottles conta...
The percentage concentration of the impure solution is 80 percent.
When equal volumes of all four solutions are mixed.
Considering 10 ml of each we have impurity to be 2ml/40ml. The impurity concentration is less than 10 percent and hence cannot be recognized.
Similarly when equal volumes of one impure and 2 pure solutions are mixed.
The impurity in the solution is 2ml/30ml which is less than 10 percent and hence cannot be recognized.
Hence for detecting the impure solution we must use equal volumes of 2 solutions at a time.
Considering the three pure solutions to be P and the impure solution to be I.
P, P, P, I.
Considering equal volumes of solution from the bottle one bottle of P, and I. Testing this would recognize the impurity.
After this consider one bottle among the other 2 P bottles which are left and test this with one among the previously tested P, I.
If the one considered is I it will detect the impurity and confirms the bottle to be I.
If the one considered is P it will fail to detect the impurity and hence the other bottle will be I.
Hence a minimum of two tests are required to identify the bottle with the impurity.
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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?Correct answer is '2'. Can you explain this answer?
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