Question

six consecutive integers are written on a blackboard one of them is erased ,the sum of the remaining five integers is 2014.the sum of the digits of the integer that was erased is

a 5

b 6

c 7

d 8

Answer 1

Answer:

The final answer is a)5

Step-by-step explanation:

Given,

We know that there was 6 consecutive integers.

One of them was erased. The sum of the rest of the digits is equal to 2014.

The sum of the remaining 5 digits are 2014. This means our six digits are:-

x, x + 1 , x + 2 , x + 3 , x + 4 , x + 5

Sum of remaining 5 digits = 2014

We need to find the right combination of digits such that sum of 5 numbers equals 2014. We will have 5x + a constant number, This constant number should be equal to 14 so that 2014 is divisible 5.

Hence the missing number will be x + 1

x + x + 2 + x + 3 + x + 4 + x + 5 = 2014

5x + 14 = 2014

5x = 2014 - 14

x = 2000/5

x = 400

The missing number = x + 1 = 401.

Hence the sum of the digits of the missing number = 4 + 0 + 1 = 5

Arithmetic progression

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