The product of two positive whole numbers is 493 and their difference is 12. What is the bigger number?
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → 29
The two numbers are factors of 493 that differ by 12, so 493 is split into its prime factors and the factor pairs are listed.
\(493=17\times29\)
Factor pairs: \(1\times493\), \(17\times29\)
Only \(29-17=12\)
The numbers are 17 and 29, so the bigger number is 29.
Why the other options are incorrect
Option (1) 493 — Incorrect. \(493\div493=1\), and \(493-1=492\), not 12.
Option (2) 17 — Incorrect. 17 is the smaller of the two numbers.
Option (4) 41 — Incorrect. 41 does not divide 493 exactly, so it cannot be one of the numbers.