There are four prime numbers written in ascending order. The product of first…
2025
There are four prime numbers written in ascending order. The product of first three is 385 and that of last three is 1001. The last number is:
- A.
9
- B.
13
- C.
15
- D.
12
Attempted by 17 students.
Show answer & explanation
Correct answer: B
Let the four prime numbers in ascending order be a, b, c, and d.
Step-by-Step Solution
Set up the equations:
The product of the first three is a * b * c = 385.
The product of the last three is b * c * d = 1001.
Prime Factorization:
Factorize 385: 5 * 77 = 5 * 7 * 11. So, a = 5, b = 7, c = 11.
Factorize 1001: 7 * 143 = 7 * 11 * 13. So, b = 7, c = 11, d = 13.
Verify:
The numbers are 5, 7, 11, and 13.
Product of first three (5 * 7 * 11) = 385. Correct.
Product of last three (7 * 11 * 13) = 1001. Correct.
The last number (d) is 13.