“P” is the smallest positive integer such that every positive integer N greater than “P” can be written as a sum of two composite numbers. Then:
A) P = 3
B) P = 6
C) P = 10
D) P = 11

Hint:First we have to know the meaning of the composite numbers. We have to check every number by making a pair of the numbers. check that the pair is a composite number or not. We have to write a number as a sum of two composite numbers.

Complete step-by-step answer:
Given that “P” is the smallest positive integers and we have to write “P” as a sum of two composite numbers.
A composite number is a positive integer that can be formed by multiplying two smaller positive integers.
Let’s check every option
Option A) P = 3
P+1 = 3+1
4 = 2+2
4 = 3+1
They are not composite numbers
Option B) P = 6
P+1 = 6+1
7 = 2+5
7 = 3+4
None of the pair is sum of composite number
Option C) P = 10
P+1 = 10+1
11 = 2+9
11 = 3+8
11 = 4+7
11 = 5+6
None of the pair sum is composite number
Option D) P = 11
P+1 = 11+1
12 = 2+10
12 = 3+9
12 = 4+8
12 = 5+7
12 = 6+6
Here both additive pair (4,8) and (6,6) are the composite numbers.

So, the correct answer is “Option D”.

Note:Check all the options step by step and find that pairs of the number are composite numbers or not. Students mostly make the mistake in making pairs of the numbers. Try to solve the question step by step.