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03 Mar 2020, 04:00
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A
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Difficulty:
5%
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Question Stats:
84% (00:48) correct
16%
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wrong
based on 335
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Is the positive integer n odd?
(1) n = 2k + 1, where k is a positive integer.
(2) 2n + 1 is an odd integer.
(1) n = 2k + 1, where k is a positive integer.
(2) 2n + 1 is an odd integer.
03 Mar 2020, 09:04
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Bunuel
Statement 1:
2k is always even. \(n\) is an even integer plus one, so it must be odd. Sufficient.
Statement 2:
This tells us 2n is even, which is always trues regardless of the parity of n. So n could be odd or even, insufficient.
Ans: A
01 Sep 2020, 07:03
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Bunuel
Target question: Is the positive integer n odd?
Statement 1: n = 2k + 1, where k is a positive integer
This is the classic definition of an odd integer.
That is, ALL odd integers can be written in the form 2k + 1, where k is a positive integer
This should make sense because, if k is an integer, then 2k will be an EVEN integer, which means 2k+1 must be an ODD integer.
In other words, n must be an odd integer
Since we can answer the target question with certainty, statement 1 is SUFFICIENT
Statement 2: 2n + 1 is an odd integer
As mentioned above, 2n + 1 will be an odd integer for ALL values of n.
Consider these two cases:
Case a: If n = 2, then 2n + 1 = 2(2) + 1 = 5, which is odd. In this case, the answer to the target question is NO, n is not odd
Case b: If n = 3, then 2n + 1 = 2(3) + 1 = 7, which is odd. In this case, the answer to the target question is YES, n is odd
Since we can’t answer the target question with certainty, statement 2 is NOT SUFFICIENT
Answer: A
Cheers,
Brent
