The average of five consecutive natural numbers is 50. What is the product of the smallest and the largest of the numbers?
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → 2496
For an odd number of consecutive numbers, the average is the middle number, because the numbers are spread evenly on both sides of it.
The middle (third) number is 50, so the numbers are 48, 49, 50, 51, 52
Smallest × largest \(=48\times52=2496\)
Tip: \(48\times52=(50-2)(50+2)=50^2-2^2=2500-4\). A product of two numbers equally spaced about a round number is quickest found as a difference of squares.