Question 35 Is X a whole number, if X 0?
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Question 35
Is X a whole number, if X > 0?
I. 2X is an even number.
II. 3X is an odd number.
Show answer & explanation
Statement I alone is sufficient because if 2X is even, X must be an integer, and since X > 0 it is a whole number. Statement II is not sufficient because 3X can be odd even when X is a fraction, such as X = 1/3.
Step-by-step Derivation:
Step 1: Interpret the question as asking whether X is a positive integer/whole number, given X > 0.
Step 2: Check Statement I: If 2X is an even number, then 2X = 2k for some integer k, so X = k. Thus X is an integer. Since X > 0, X is a positive whole number. Statement I alone is sufficient.
Step 3: Check Statement II: If 3X is an odd number, X need not be a whole number. For example, if 3X = 1, then X = 1/3, which is not a whole number. Therefore Statement II alone is not sufficient.
Step 4: Only Statement I is sufficient, so the correct choice is option A, i.e., 1.