The product of two positive whole numbers is 403 and their difference is 18. What is the bigger number?
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → 31
The two numbers are factors of 403 that differ by 18, so 403 is split into its prime factors and the factor pairs are listed.
\(403=13\times31\)
Factor pairs: \(1\times403\), \(13\times31\)
Only \(31-13=18\)
The numbers are 13 and 31, so the bigger number is 31.
Why the other options are incorrect
Option (1) 403 — Incorrect. \(403\div403=1\), and \(403-1=402\), not 18.
Option (2) 13 — Incorrect. 13 is the smaller of the two numbers.
Option (3) 49 — Incorrect. 49 does not divide 403 exactly, so it cannot be one of the numbers.