The product of two positive whole numbers is 368 and their difference is 7. What is the bigger number?
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → 23
The two numbers are factors of 368 that differ by 7, so 368 is split into its prime factors and the factor pairs are listed.
\(368=2^{4}\times23\)
Factor pairs: \(1\times368\), \(2\times184\), \(4\times92\), \(8\times46\), \(16\times23\)
Only \(23-16=7\)
The numbers are 16 and 23, so the bigger number is 23.
Why the other options are incorrect
Option (1) 16 — Incorrect. 16 is the smaller of the two numbers.
Option (2) 30 — Incorrect. 30 does not divide 368 exactly, so it cannot be one of the numbers.
Option (3) 46 — Incorrect. \(368\div46=8\), and \(46-8=38\), not 7.