Question

The sum of 8 consecutive odd numbers is 256. Also average of four consecutive even numbers is 100. What is the sum of the smallest odd number and second largest even number?

Answer 1

Given: The sum of 8 consecutive odd numbers is 256. Also average of four consecutive even numbers is 100.

To find: What is the sum of the smallest odd number and second largest even number?

Solution:

• Now we have given that the sum of 8 consecutive odd numbers is 256.

• Let the 8 consecutive odd numbers are x, x+2, x+4, x+6, x+8, x+10, x+12, x+14.

• The sum is:

                    x + x+2 + x+4 + x+6 + x+8+  x+10+ x+12+x+14 = 256

                    8x + 56 = 256

                    8x = 200

                    x = 200/8

                    x = 25

• So the sum of smallest odd number is 25.

• Now we have given that average of four consecutive even numbers is 100, so:

                    y + y+2 + y+4 + y+6  / 4 = 100

                    y + y+2 + y+4 + y+6 = 400

                    4y + 12 = 400

                    4y = 388

                    y = 388/4

                    y = 97

• So the value of y is 97, then the second largest even number is y + 4 = 101

• The sum of smallest odd number and second largest even number is :

                    101 + 25 = 126

Answer:

                So the sum of smallest odd number and second largest even number is 126.