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The average of 1088 real numbers is zero. At most how many of them can be negative?
- a)544
- b)88
- c)1087
- d)100
Correct answer is option 'C'. Can you explain this answer?
Verified Answer
The average of 1088 real numbers is zero. At most how many of them can...
We know, Average of quantities = sum of all quantities/no. of quantities
The average of 1088 numbers is zero.
So, the summation of 1088 numbers = 1088 × 0 = 0
If the summation of 1087 numbers = - (1088th number) then only summation of 1088 number will be zero.
∴ Out of 1088 numbers, at most 1087 numbers may be greater than zero.
The average of 1088 numbers is zero.
So, the summation of 1088 numbers = 1088 × 0 = 0
If the summation of 1087 numbers = - (1088th number) then only summation of 1088 number will be zero.
∴ Out of 1088 numbers, at most 1087 numbers may be greater than zero.
Most Upvoted Answer
The average of 1088 real numbers is zero. At most how many of them can...
Understanding the Problem:
The average of 1088 real numbers is zero, which means the sum of all the numbers is zero. We need to determine the maximum number of negative numbers among these 1088 numbers.
Solution:
Assume the number of negative numbers to be x:
- Let the sum of all the positive numbers be P.
- Let the sum of all the negative numbers be N.
- Given that the total sum of all numbers is zero.
Equation:
P - N = 0
P = N
Maximum number of negative numbers:
- The sum of all the negative numbers is equal to the sum of all the positive numbers.
- So, to maximize the number of negative numbers, we need to make the sum of positive numbers as small as possible.
- The sum of 1088 numbers is zero, so we can have 1087 positive numbers and 1 negative number to maintain the sum as zero.
- Therefore, at most 1087 numbers can be negative.
Therefore, the correct answer is option C) 1087.
The average of 1088 real numbers is zero, which means the sum of all the numbers is zero. We need to determine the maximum number of negative numbers among these 1088 numbers.
Solution:
Assume the number of negative numbers to be x:
- Let the sum of all the positive numbers be P.
- Let the sum of all the negative numbers be N.
- Given that the total sum of all numbers is zero.
Equation:
P - N = 0
P = N
Maximum number of negative numbers:
- The sum of all the negative numbers is equal to the sum of all the positive numbers.
- So, to maximize the number of negative numbers, we need to make the sum of positive numbers as small as possible.
- The sum of 1088 numbers is zero, so we can have 1087 positive numbers and 1 negative number to maintain the sum as zero.
- Therefore, at most 1087 numbers can be negative.
Therefore, the correct answer is option C) 1087.
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The average of 1088 real numbers is zero. At most how many of them can be negative?a)544b)88c)1087d)100Correct answer is option 'C'. Can you explain this answer?
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