Problem: The population of Nosuch Junction at one time was a perfect square. Later, with an increase of , the population was one more than a perfect square. Now, with an additional increase of , the population is again a perfect square. The original population is a multiple of:
Answer Choices:
A.
B.
C.
D.
E.
Solution:
Let be the original population. Then , , and .
Subtract the first equation from the second to obtain or or or . Try and ; to satisfy these equations , a multiple of . Furthermore, and . With either of the other two sets of factors you obtain a value of N which satisfies the first and second conditions of the problem, but not the third.