A number is increased by 120, and the result becomes a perfect square. The original number lies between two consecutive square numbers, 625 and 676. Find the original number.
Show answer & explanation
Correct answer: C
Explanation
Let's assume the original number = x.
Given: x + 120 is a perfect square.
And x lies between 625 and 676.
625 = 25² and 676 = 26².
Meanwhile, let's check that 664 is the only perfect number:
664 + 120 = 784
and 784 = 28² (perfect square).
Therefore, the original number = 664.