If x is an odd number, x^2 must be odd => (x^2+1) must be even.

By the same logic, (x+5) is even. As addition of two odd numbers results in an even number.

Multiplication of two even numbers results in an even number. Thus (x^2+1)(x+5) is an even number.

Satetment (1) is SUFFICIENT.

And for (2), each prime factor of x^2 is greater than 7 implies that 2 is not a prime factor of x^2 and in turn 2 is not a prime factor of x. (As all the prime factors of x^2 are also prime factors of x)

That means x is composed of 11, 13, 17, 19, 23 etc (Prime numbers greater than 7).

Therefore x is an odd number => Equivalent to statement (1).

Statement (2) is SUFFICIENT.

The correct answer is D.

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Thanks & Regards,

Anaira Mitch