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

Answer: (A)

5

Answer 2

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.