Yes, both the statements are fundamentally the same, but none by itself is sufficient.Vincen wrote:If x is a positive number, is x an even integer?
(1) 3x is an even integer.
(2) 5x is an even integer.
The OA is C.
Are both conditions necessary? I think (2) is the same as (1), isn't it?
Statement 1: 3x is an even integer.
Case 1: Say 3x = 6, then x = 2, even.
Case 2: Say 3x = 2, then x = 2/3, not an integer. Insufficient.
Statement 2: 5x is an even integer.
Case 1: Say 5x = 10, then x = 2, even.
Case 2: Say 5x = 2, then x = 2/5, not an integer. Insufficient.
Statement 1& 2:
Say 3x = 2a and 5x = 2b, whether a and b are positive integers.
Thus, 3/a = 5/b
=> 3b = 5a
Since a and b are positive integers, a must be a multiple of 3 and b must be a multiple of 5.
Say a = 3p, whether p is a positive integer.
Thus, x = 2a/3 = (2*3p) / 3 = 2p --> Integer. Sufficient.
The correct answer: C
Hope this helps!
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-Jay
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