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There are some consecutive numbers and 'x' is the average of all the numbers, except the first number. If 'y' is the average of all the numbers, except the last number, then what is the value of x - y?
  • a)
    0
  • b)
    -1
  • c)
    1
  • d)
    2
Correct answer is option 'C'. Can you explain this answer?
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Most Upvoted Answer
There are some consecutive numbers and x is the average of all the num...
In both the cases, the number of items is the same.
Since the average is the middle number, the middle number in the first case is just one more than that in the second case.
So, x - y = 1
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Community Answer
There are some consecutive numbers and x is the average of all the num...
To solve this problem, let's assume that there are 'n' consecutive numbers.

Let the first number be 'a'. Then, the consecutive numbers would be a, a+1, a+2, ..., a+n-1.

Finding the average of all the numbers:
The sum of all the numbers would be a + (a+1) + (a+2) + ... + (a+n-1) = n*a + (1+2+3+...+(n-1))
= n*a + ((n-1)(n-1+1))/2
= n*a + (n-1)n/2

The average of all the numbers would be the sum of all the numbers divided by the total number of numbers, which is n.
So, the average is [(n*a + (n-1)n/2) / n] = a + (n-1)/2

Finding the average of all the numbers except the first number:
Now, let's find the sum of all the numbers except the first number.
The sum of all the numbers except the first number would be (a+1) + (a+2) + ... + (a+n-1) = (a+1) + (a+2) + ... + (a+n-1) + (a)
= n*a + (1+2+3+...+(n-1)) + a
= n*a + ((n-1)(n-1+1))/2 + a
= n*a + (n-1)n/2 + a

The average of all the numbers except the first number would be the sum of all the numbers except the first number divided by the total number of numbers, which is n-1.
So, the average is [(n*a + (n-1)n/2 + a) / (n-1)]

Calculating the difference between x and y:
x - y = (a + (n-1)/2) - [(n*a + (n-1)n/2 + a) / (n-1)]
= [(2a + n - 1) - (n*a + (n-1)n/2 + a)] / (n-1)
= (2a + n - 1 - na - (n-1)n/2 - a) / (n-1)
= (a + n - 1 - na - (n-1)n/2) / (n-1)
= (1 - na/2 - (n-1)n/2) / (n-1)

We need to find the value of x - y. From the given options, the correct answer is option C) 1.

Therefore, the value of x - y is 1.
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