A set of consecutive positive integers beginning with 1

Asked by admin @ 17/08/2021 in Math viewed by 284 People

A set of consecutive positive integers beginning with 1 is written on the blackboard. A student came and erased one number. The average of the remaining numbers is 35(7/17). What was the number erased?

A) 7
B) 8
C) 9
D) none of these

Answered by admin @ 17/08/2021

Given: A set of consecutive positive integers beginning with 1 is written on the blackboard

To find: What was the number erased?

Solution:

Now we have given that a student came and erased one number. The average of the remaining numbers is 35(7/17).

The sum will be an integer as all of the values are Integers.

So the sum will be the product of number and average.

The average is 35 + 7/17.

The number of integers must be a multiple of 17

Now for any evenly spaced set, average is always equal to median.

Now the number of integers = 4 x 17 = 68

Sum = 68 x (35 + 7/17) = 2408.

Now for original set:

68 integers remain after one of the integers is removed, then the original set will contain 69 integers.

Sum of the first n positive integers = (n)(n+1)
/2

69 x 70 / 2

2415.

So now, removed integer will be:

original sum - sum after one integer is removed

2415 - 2408 = 7

Answer:

So the erased number is 7.

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