The difference between two numbers is 4 and their average is 6. The product of these numbers is:
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → 32
An average of 6 for two numbers means their sum is \(2\times6=12\). With the sum and the difference known, adding the two equations gives the larger number.
\(x+y=12\) (1)
\(x-y=4\) (2)
Adding (1) and (2), the \(y\) terms cancel: \(2x=16\), so \(x=8\) and \(y=4\)
Product \(=8\times4=32\)
Shortcut: The two numbers lie half the difference on either side of their average, so they are \(6\pm2\) and their product is \(6^2-2^2=36-4=32\).