Question

Three distinct prime numbers add up to 392. What is the minimum difference between the larger two of the given three prime numbers?
4
6
8
10

Answer 1

Answer:

6

Step-by-step explanation:

392 = 2 + 5 + 383

392 = 2 + 11 + 377

Difference between 383 - 377 = 6

Answer 2

Given: Three distinct prime numbers add up to 392.

To find The minimum difference between the larger two of the given three prime numbers.

Solution: Prime numbers are the numbers that can be divided by the number itself and the number one.

Distinct Prime numbers or a pair of distinct prime numbers are prime numbers say a,b, and a≠b. If we multiply a pair of distinct prime numbers, we get a number that is composite.

Now from above, three distinct prime numbers add up to 392.

So, 392 can be written as:

392=2+7+383 [∵ from 2 to 7, 3 and 5 are also prime numbers but if we add  them with 2 and subtract it from 392, then we do not get a larger prime  number.]

 392=2+11+379

Now if we add 2+13+377=392 which is also a possible case, but it is written in the question the minimum difference. So, we subtract [383-377=6], which is not minimum according to option, and if we subtract [379-377=2], which is not given in option.

∴ The minimum difference = 383-379

                                               = 4

Hence, the minimum difference between the larger two of the given three prime numbers is 4.