We have been asked to find the value of x.

1. x^2 - 1 = x + 1
x^2 - x - 2 = 0
(x-2)(x+1) = 0
x = 2 or -1 (Insufficient)

2. x + 3 is a prime number
x could be -1,0,2 and so on. (Insufficient)

On combining the information from both the statements,
x could be -1 or 2. (Insufficient) (Option E)
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Statement One Alone:

x^2 - 1 = x + 1

x^2 - 1 = x + 1

x^2 - x - 2 = 0

(x - 2)(x + 1) = 0

x = 2 or x = -1

Statement one alone is not sufficient to answer the question.

Statement Two Alone:

x + 3 is a prime number

x could have many values; for example, x could be 2 or x could be 0. Statement two alone is not sufficient to answer the question.

Statements One and Two Together:

From statement one, we know that x is either 2 or -1. From statement two, x + 3 is a prime number. If x = 2, x + 3 = 5 is a prime number. If x = -1, x + 3 = 2 is also a prime number. Thus, we still can’t determine the value of x. The two statements together are still not sufficient to answer the question.

Answer: E
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