Four prime numbers are written in ascending order. The product of the first three is 2431 and the product of the last three is 4199. What is the first number?
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → 11
Split both products into primes. The two middle primes are common to both products; the prime left over in the first product is the first number.
\(2431=11\times13\times17\)
\(4199=13\times17\times19\)
Common primes: 13 and 17; so the four primes are 11, 13, 17, 19
The first number is 11.
Why the other options are incorrect
Option (2) 13 — Incorrect. 13 is one of the two primes common to both products, not the first number.
Option (3) 17 — Incorrect. 17 is one of the two primes common to both products, not the first number.
Option (4) 19 — Incorrect. 19 is the last (largest) of the four primes.