Simplify the equation a bit you get :
\sqrt{X} < 2.5 ( X-2)
Now case 1: x<3
so x can only be either 1 or 2
substituting 2, \sqrt{2} < 0 ? NO
Substituting 1, \sqrt{1} < some negative value ? NO
So since we have a definite answer, A is one of the possibility. Hence, eliminate B,C and E
Now check 2nd case : x is a prime number
lets start with the simplest of prime no's 2,3
\sqrt{2} < 0? NO
\sqrt{3} < 2.5 YES
Hence, D gets ruled out as well, answer is : A
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\sqrt{X} < 2.5 ( X-2)
Now case 1: x<3
so x can only be either 1 or 2
substituting 2, \sqrt{2} < 0 ? NO
Substituting 1, \sqrt{1} < some negative value ? NO
So since we have a definite answer, A is one of the possibility. Hence, eliminate B,C and E
Now check 2nd case : x is a prime number
lets start with the simplest of prime no's 2,3
\sqrt{2} < 0? NO
\sqrt{3} < 2.5 YES
Hence, D gets ruled out as well, answer is : A
PS: Like my approach? Help me with some Kudos.
