Pearl writes down seven consecutive integers, and adds them up. The sum of the integers is equal to 6 times the largest of the seven integers. What is the smallest integer that Pearl wrote down?

Easy...

If we let the smallest integer = x then the sum of all the integers is:

x + x + 1 + x + 2 + x + 3 + x + 4 + x + 5 + x + 6 = 6(x+6)

Simplifying we get:

7x + 21 = 6x + 36

x = 15

So the smallest integer is 15.

(Please tell me if this answer is incorrect)