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If both x and y are positive even integers, then which of the followin
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Updated on: 19 Nov 2018, 11:22
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64% (00:30) correct 36% (00:38) wrong based on 89 sessions
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If both x and y are positive even integers, then which of the following expressions must also be even? I. \(y^{x − 1}\) II. \(y – 1\) III. \(\frac{x}{2}\) (A) I only (B) II only (C) III only (D) I and III only (E) I, II, and III Source: Nova GMATDifficulty Level: 600
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Originally posted by SajjadAhmad on 01 Jan 2017, 11:36.
Last edited by SajjadAhmad on 19 Nov 2018, 11:22, edited 1 time in total.



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Re: If both x and y are positive even integers, then which of the followin
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01 Jan 2017, 12:14
SajjadAhmad wrote: If both x and y are positive even integers, then which of the following expressions must also be even?
I. yx−1 II. y – 1 III. x/2
(A) I only (B) II only (C) III only (D) I and III only (E) I, II, and III I think the question is of bad quality . It is given that both x and y are positive even integers . take x = 2 and y =4 then 1 . yx 1 ==> 8  1 = 7 (odd) 2. y1 ==> 41 = 3 (odd) 3. x/2 = 2/2 =1 (odd) so, no expression will be even



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Re: If both x and y are positive even integers, then which of the followin
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02 Jan 2017, 02:26
sb0541 wrote: SajjadAhmad wrote: If both x and y are positive even integers, then which of the following expressions must also be even?
I. yx−1 II. y – 1 III. x/2
(A) I only (B) II only (C) III only (D) I and III only (E) I, II, and III I think the question is of bad quality . It is given that both x and y are positive even integers . take x = 2 and y =4 then 1 . yx 1 ==> 8  1 = 7 (odd) 2. y1 ==> 41 = 3 (odd) 3. x/2 = 2/2 =1 (odd) so, no expression will be even I too reached the same conclusion! Sent from my 2014818 using GMAT Club Forum mobile app



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Re: If both x and y are positive even integers, then which of the followin
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05 Jan 2017, 09:49
SajjadAhmad wrote: If both x and y are positive even integers, then which of the following expressions must also be even?
I. \(yx − 1\)
II. \(y – 1\)
III. \(\frac{x}{2}\)
(A) I only (B) II only (C) III only (D) I and III only (E) I, II, and III Dear SajjadAhmad, My friend, I wonder if you posted the question correctly. For expression I, you have yx  1which, of course, would be odd if both x & y were even. Did you mean: y(x  1)That would be even, so long as y is even. Is this what you meant? Mike
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Re: If both x and y are positive even integers, then which of the followin
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05 Jan 2017, 09:55
mikemcgarry wrote: SajjadAhmad wrote: If both x and y are positive even integers, then which of the following expressions must also be even?
I. \(yx − 1\)
II. \(y – 1\)
III. \(\frac{x}{2}\)
(A) I only (B) II only (C) III only (D) I and III only (E) I, II, and III Dear SajjadAhmad, My friend, I wonder if you posted the question correctly. For expression I, you have yx  1which, of course, would be odd if both x & y were even. Did you mean: y(x  1)That would be even, so long as y is even. Is this what you meant? Mike Sir, source of this question is NOVA GMAT , i randomly try to solve the question but can not, so i have posted it here ... official answer was given at the end of the question which i didnt understand
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Re: If both x and y are positive even integers, then which of the followin
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05 Jan 2017, 10:21
IMHO with the same opinion... The question can be something like this  Quote: If both x and y are positive even integers, then which of the following expressions can also be even? Rest is fine, MUST be even should never be correct...
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Re: If both x and y are positive even integers, then which of the followin
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05 Jan 2017, 10:41
SajjadAhmad wrote: Sir,
source of this question is NOVA GMAT , i randomly try to solve the question but can not, so i have posted it here ... official answer was given at the end of the question which i didnt understand Dear SajjadAhmad, My friend, please give the exact name of the book (as NOVA has a few different GMAT books), the edition, and the exact page number & problem number. There's a deep problem here and I want to see it in the published book for myself. Thank you, Mike
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Re: If both x and y are positive even integers, then which of the followin
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05 Jan 2017, 10:52
mikemcgarry wrote: SajjadAhmad wrote: Sir,
source of this question is NOVA GMAT , i randomly try to solve the question but can not, so i have posted it here ... official answer was given at the end of the question which i didnt understand Dear SajjadAhmad, My friend, please give the exact name of the book (as NOVA has a few different GMAT books), the edition, and the exact page number & problem number. There's a deep problem here and I want to see it in the published book for myself. Thank you, Mike Here is detail Nova GMAT Prep Course ISBN 1–889057–27–4 Page no.25/614 Question no. 13
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Re: If both x and y are positive even integers, then which of the followin
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05 Jan 2017, 11:07
SajjadAhmad wrote: Here is detail
Nova GMAT Prep Course ISBN 1–889057–27–4
Page no.25/614 Question no. 13 Dear SajjadAhmad, Thank you! Thank you! Thank you! My friend, it's always important to include precise locations of anything that confuses you, because it's always possible that a GMAT expert will notice something you didn't. In this particular case, you miscopied expression I. You wrote: I. \(xy  1\)Instead, on that NOVA book, the problem clearly has: I. \(x^{y  1}\)I corrected this in the problem above. The expression (y  1) is not a multiplied factor: instead, it's the exponent of x. You see, if y is a positive even integer, it has to be 2 or greater, so (y  1) will be some positive odd number. If x is an even integer, then any positive power of it also has to be even. This is why (I) has to be even and why the answer is (A). Does all this make sense? Mike
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Re: If both x and y are positive even integers, then which of the followin
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05 Jan 2017, 11:27
mikemcgarry wrote: SajjadAhmad wrote: Here is detail
Nova GMAT Prep Course ISBN 1–889057–27–4
Page no.25/614 Question no. 13 Dear SajjadAhmad, Thank you! Thank you! Thank you! My friend, it's always important to include precise locations of anything that confuses you, because it's always possible that a GMAT expert will notice something you didn't. In this particular case, you miscopied expression I. You wrote: I. \(xy  1\)Instead, on that NOVA book, the problem clearly has: I. \(x^{y  1}\)I corrected this in the problem above. The expression (y  1) is not a multiplied factor: instead, it's the exponent of x. You see, if y is a positive even integer, it has to be 2 or greater, so (y  1) will be some positive odd number. If x is an even integer, then any positive power of it also has to be even. This is why (I) has to be even and why the answer is (A). Does all this make sense? Mike Thank you very Much for this favor and really really sorry for inconvenience and trouble due to my fault. So nice of you Regards
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Re: If both x and y are positive even integers, then which of the followin
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19 Jan 2017, 03:45
Such a wonderful question. Here is my solution to this one >
We are told that x and y are even. So the least value of both would be 2.
We need to see if the given statement is even or not. Statement 1> y^x1 Here as y is even y^x1 would always be even as the least value of x is two. Hence this is always even. Statement 2> y1 even  odd=> Odd. Hence this statement is always odd. Statement 3> This statement might be even/odd e.g > x=2 => 2/2 is odd x=4 => 4/2 is even.
Hence only 1 must be odd. Hence A.
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Re: If both x and y are positive even integers, then which of the followin
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17 Apr 2017, 02:20
Option Ax & y are Even Positive integers. Odd: O, Even: E & Fraction: F. I. \(y^{x−1}\) = \(E^{E1}\) = E II. \(y– 1\) = E  1 = O III. \(\frac{x}{2}\) = E or O
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