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08 Jan 2024, 07:50
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A
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
95%
(hard)
Question Stats:
52% (02:00) correct
48%
(01:53)
wrong
based on 907
sessions
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Date
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Not Attempted Yet
If n is an even integer, which of the following must also be an even integer?
I. (n^2 - 4)/4
II. (n^2 + 2n)/4
III. (n^2 + 4n)/4
(A) II only
(B) III only
(C) I and II only
(D) II and III only
(E) I, II and III
GMAT-Club-Forum-mchcwqrq.png [ 48.02 KiB | Viewed 4393 times ]
I. (n^2 - 4)/4
II. (n^2 + 2n)/4
III. (n^2 + 4n)/4
(A) II only
(B) III only
(C) I and II only
(D) II and III only
(E) I, II and III
Attachment:
GMAT-Club-Forum-mchcwqrq.png [ 48.02 KiB | Viewed 4393 times ]
10 Jan 2024, 07:13
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JoeAa
Yes.
N being even means
N=2K where K is any integer.
So plugging in to each option:
I. (4K^2-4)/4 = K^2-1. If K is an even number so is K^2 making the expression odd, so eliminate I.
II. (N^2+2N)/4 = (4K^2+4K)/4
= K^2 +K. If K is odd, so is K^2 and adding two odd numbers is even. If K is even, so is K^2, so the expression is always even.
III. (N^2+4N)/4 =
(4K^2+8K)/4 = K^2 + 2K =
K(K+2). If K is odd, so is K+2 and two odd numbers multiplied is always odd, so eliminate III.
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21 Mar 2024, 00:27
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This question is of the format - If condition, then what MUST be true. In Quant, such questions can be asked in the context of Number Properties or Algebra concepts. In this question, the context is Number Properties.
To answer this question comfortably, one needs to completely understand the condition presented. And then one needs to carefully simplify the choices presented – one at a time. So, one clear faltering point is if the student rushes through this processing.
Other faltering points in this question include drawing incorrect inferences – such as incorrectly infering that a number divided by 4 is always even – This happens if the student fails to consider all cases.
Watch the solution and identify which step you faltered at.
To answer this question comfortably, one needs to completely understand the condition presented. And then one needs to carefully simplify the choices presented – one at a time. So, one clear faltering point is if the student rushes through this processing.
Other faltering points in this question include drawing incorrect inferences – such as incorrectly infering that a number divided by 4 is always even – This happens if the student fails to consider all cases.
Watch the solution and identify which step you faltered at.
