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Data Sufficiency: Is X an even number? I: X is divisible by 2. II: X is a prime number greater than 2.
I alone is sufficient
II alone is sufficient
Both I and II are sufficient
Neither is sufficient
I alone is sufficient
By definition, any integer divisible by 2 is an even number; prime numbers greater than 2 are always odd numbers.
By definition, any integer divisible by 2 is an even number; prime numbers greater than 2 are always odd numbers.
Analyze Statement I
Statement I says X is divisible by 2. The mathematical definition of an even number is any integer n such that n = 2k for some integer k. Since X is divisible by 2, it is by definition even. This is sufficient.
Analyze Statement II
Statement II says X is a prime number greater than 2. All prime numbers greater than 2 are odd (e.g., 3, 5, 7, 11). Therefore, X cannot be even. This statement is also sufficient to answer the question (the answer is 'No, X is not even').
B is incorrect because Statement I alone is sufficient. C is incorrect because both statements provide a definitive answer independently, not combined necessity. D is incorrect because both statements individually yield a definite conclusion.
A is correct because Statement I directly confirms the property of being an even number based on the divisibility rule for 2, making it sufficient on its own.
In Data Sufficiency, a statement is sufficient if it leads to a definitive Yes or No answer; you do not need the answer to be 'Yes' to mark a statement as sufficient.
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