Four prime numbers are arranged in ascending order. The product of the first three numbers is 255 and that of the last three is 1955. The largest prime number is:
Show answer & explanation
Correct answer: A
Explanation
The correct answer is Option 1 i.e. 23.
Let the prime numbers be a, b, c, and d, where a < b < c < d.
The product of the first three numbers
⇒ abc = 255 = 3 × 5 × 17
The product of the last three numbers
⇒ bcd = 1955 = 5 × 17 × 23
Dividing the product of the last three numbers by the product of the first three numbers
⇒ bcd/abc = 1955/255 = 5 × 17 × 23/5 × 3 × 17 = 23/3
⇒ d = 23 and a = 3
Hence,
The largest prime number = d = 23