Question

Help John solve this mathematical puzzle:

The difference between two numbers is 1. If so, what will the difference between their squares be?

• A. Same as the sum of the numbers
• B. 1
• C. Same as the product of the numbers
• D. Cannot be determined

Answer 1

The correct option is A Same as the sum of the numbers

Let the numbers be a and b.

$⟹a–b=1$

Now, the difference between the squares of these numbers will be:

$a^2–b^2$
$=(a+b)\times (a–b)$
$=(a+b)\times 1$
$=(a+b)$

Hence, the difference between the squares of the two numbers will be the same as the sum of the numbers.