Times and square
Roger multiplies two consecutive integers and squares the result. Can you find the last two digits of his new number?
Age
14 to 16
Challenge level
Problem
Roger picks two consecutive integers, one of which ends in a 5.
He multiplies the integers together and then squares the result.
What are the last two digits of his answer?
This problem is taken from the UKMT Mathematical Challenges.
Student Solutions
Answer: 00
__ 5, __6 or __ 4, __ 5
__ 5 $\times$ __ 6 = __ 0 , __ 4 $\times$ __ 5 = __ 0 (multiples of 10)
__ 0 $\times$ __ 0 = __ 0 0 (the square of a multiple of 10 is a multiple of 100)