Answer:

c. 17

Explanation (Why  "c.17" ?):

• 1 + 7 = 8 ,therefore, it satisfies the first and second condition.

Conditions:

1st Condition:

• I'm a Prime Number
• Meaning the number should have only 2 factors. (1 and Itself)

2nd Condition:

• I'm a prime number my digits add up to 8
• Meaning "x + y = 8"

3rd Condition:

• I'm a factors of 34 but am not a factor of 36
• Meaning it should be the following numbers "1, 2, 17 and 34"

Explanation (Why not "a." "b." or "d."):

• Although 2 is a Prime number, it has only 1 digit and doesn't satisfy the first, second and third condition.

• Although 9 is a Prime number, it has only 1 digit and doesn't satisfy the first, second and third condition.

• 34 is a composite number meaning it doesn't satisfy the first condition, adding the digits doesn't give you the sum of 8 meaning it doesn't satisfy the 2nd condition.

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