Question

If the sum and difference of two numbers is 20 and 8 respectively, then the difference between their squares shall be:

• A. 56
• B. 160
• C. 28
• D. 180
• E. 12

Hint:

Difference of squares formula: $a^2 - b^2 = (a-(b)(a+(b)$. Use this to avoid calculating squares individually.

Answer 1

The Correct Option is B

Step 1:
Let the numbers be \(x\) and \(y\), with \(x > y\).
Sum: \(x + y = 20\)
Difference: \(x - y = 8\)

Step 2:
Adding: \(2x = 28 \implies x = 14\), then \(y = 6\)

Step 3:
Difference of squares = \(x^2 - y^2 = (x - y)(x + y) = 8 \times 20 = 160\)

Step 4:
Final Answer: 160