Four prime numbers are written in ascending order. The product of the first three is 385 and the product of the last three is 1001. What is the first number?
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → 5
A number has only one way of being written as a product of primes, so factorising both products shows the four primes directly.
\(385=5\times7\times11\), so the first three primes are 5, 7, 11
\(1001=7\times11\times13\), so the last three primes are 7, 11, 13
The four primes in ascending order: 5, 7, 11, 13
The first number is 5.