Question

There are four prime numbers written in ascending order. The product of the first three numbers is 385 and that of the last three is 1001. Find the first number.
A. 5
B. 7
C. 11
D. 17

Answer 1

Hint: Consider four prime numbers be a, b, c and d. According to the given question, the product of first three prime numbers is 385 i.e abc=385 and product of last three numbers is 1001 i.e bcd=1001, then taking ratio of these numbers we get the value of a and d which is first number and last number.

Complete step-by-step answer:
Let us assume the four prime numbers to be ‘a’, ‘b’, ‘c’ and ‘d’.
As mentioned in the question, the product of the first three numbers is 385.
That is, the product of a, b and c is 385.
Therefore, abc = 385
Also, the product of the last three numbers is 1001.
That is, the product of b, c and d is 1001.
Therefore, bcd = 1001
So, \[\dfrac{abc}{bcd}=\dfrac{385}{1001}=\dfrac{5}{13}\]
Therefore, we get the value of ‘a’ and ‘d’.
That is a = 5: d = 13
Therefore, as the smallest number in the ascending order series is ‘a’ , and the value of ‘a’ is 5, so the smallest number in the ascending order series is 5.
So, the answer of the question is (a) 5.

Note: Arranging numbers in ascending order means to arrange them from smallest to largest. Prime number (or a prime) is a natural number greater than 1 that is not a product of two smaller natural numbers.Similarly we can calculate remaining numbers by substituting value of a in abc=385 we get bc=77. From this we have to find the next two prime numbers after 5 such that the product is 77, it will be 7 and 11 therefore b=7 and c=11. Substitute the value of b and c in bcd=1001 we get d= 13. Therefore the four prime numbers are 5,7,11 and 13.