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The average of three distinct positive integers is 11. What can be the maximum possible value that the greatest number of these three can take?
- a)12
- b)33
- c)30
- d)31
Correct answer is option 'C'. Can you explain this answer?
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Most Upvoted Answer
The average of three distinct positive integers is 11. What can be the...
To get the greatest possible value for one number, the other two should be as small as possible sum of the three numbers = 33.
Since the numbers are positive distinct integers, the two numbers can be 1 and 2.
So, the third will be 30, which is the maximum possible value.
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The average of three distinct positive integers is 11. What can be the...
To find the maximum possible value that the greatest number of the three distinct positive integers can take, we need to consider the average and the distinctness of the numbers.
Let's assume the three distinct positive integers as a, b, and c. We know that the average of these three numbers is 11. So, we can write the equation:
(a + b + c)/3 = 11
Simplifying the equation, we get:
a + b + c = 33
Since the integers are distinct, the greatest number among them must be less than or equal to 33. Now, we need to find the maximum possible value for the greatest number.
Let's consider the scenario where the greatest number is equal to 33. In this case, the sum of the other two numbers should be 33 - 1 - 1 = 31. However, since the integers are distinct, we cannot have two numbers adding up to 31. Hence, the greatest number cannot be 33.
Now, let's consider the scenario where the greatest number is 32. In this case, the sum of the other two numbers should be 33 - 32 = 1. Since the integers are distinct and positive, we can have the other two numbers as 1 and 2. So, the maximum possible value for the greatest number is indeed 32.
Therefore, the correct answer is option 'C' - 30.
Let's assume the three distinct positive integers as a, b, and c. We know that the average of these three numbers is 11. So, we can write the equation:
(a + b + c)/3 = 11
Simplifying the equation, we get:
a + b + c = 33
Since the integers are distinct, the greatest number among them must be less than or equal to 33. Now, we need to find the maximum possible value for the greatest number.
Let's consider the scenario where the greatest number is equal to 33. In this case, the sum of the other two numbers should be 33 - 1 - 1 = 31. However, since the integers are distinct, we cannot have two numbers adding up to 31. Hence, the greatest number cannot be 33.
Now, let's consider the scenario where the greatest number is 32. In this case, the sum of the other two numbers should be 33 - 32 = 1. Since the integers are distinct and positive, we can have the other two numbers as 1 and 2. So, the maximum possible value for the greatest number is indeed 32.
Therefore, the correct answer is option 'C' - 30.
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The average of three distinct positive integers is 11. What can be the maximum possible value that the greatest number of these three can take?a)12b)33c)30d)31Correct answer is option 'C'. Can you explain this answer?
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