Question

There are four prime numbers written in ascending order. The product of the first three is 385 and that of the last three is 1001. The first number is

• A. 5
• B. 7
• C. 11
• D. 17

Answer 1

The Correct Option is A

The correct option is (A): 5
Explanation: To solve this problem, we first need to identify the four prime numbers based on the information given.
1. Let the four prime numbers be \( p_1, p_2, p_3, p_4 \) in ascending order.
2. We know that:
- \( p_1 \times p_2 \times p_3 = 385 \)
  - \( p_2 \times p_3 \times p_4 = 1001 \)
Step 1: Factor 385
The prime factorization of 385 is:
\[385 = 5 \times 7 \times 11\]
Thus, we can set:
- \( p_1 = 5 \)
- \( p_2 = 7 \)
- \( p_3 = 11 \)
Step 2: Find \( p_4 \)
Now we need to find \( p_4 \) using the second equation:
\[p_2 \times p_3 \times p_4 = 1001\]
Substituting the values of \( p_2 \) and \( p_3 \):
\[7 \times 11 \times p_4 = 1001\]
Calculating \( 7 \times 11 \):
\[77 \times p_4 = 1001\]
To find \( p_4 \):
\[p_4 = \frac{1001}{77} = 13\]
Conclusion
The four prime numbers in ascending order are \( 5, 7, 11, \) and \( 13 \). Thus, the first number is 5.