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If |x – 9/2| = 5/2, and if y is the median of a set of p

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If |x – 9/2| = 5/2, and if y is the median of a set of p [#permalink] New post 18 Apr 2010, 15:27
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If |x – 9/2| = 5/2, and if y is the median of a set of p consecutive integers, where p is odd, which of the following must be true?

I. xyp is odd
II. xy(p^2 + p) is even
III. x^2y^2p^2 is even

A. II only
B. III only
C. I and III
D. II and III
E. I, II, and III
[Reveal] Spoiler: OA

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Last edited by Bunuel on 06 Jul 2013, 11:27, edited 3 times in total.
Edited the question and added the OA
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Re: MGMAT question [#permalink] New post 18 Apr 2010, 15:51
A - II only

P^2+P will always be even because p is odd adding an odd to an odd is even.

x can be 2 or 7 so it can be odd or even which makes it impossible for I or III to always be true
also, y can be odd or even

-ANy time an even number is in a multiple the product is even.
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Re: MGMAT question [#permalink] New post 18 Apr 2010, 18:12
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mads wrote:
If |x – (9/2) | = 5/2 , and if y is the median of a set of p consecutive integers, where p is odd, which of the following must be true?

I. xypis odd

II. xy(p^2 + p) is even

III. x^2y^2p^2 is even

A. II only
B. III only
C. I and III
D. II and III
E. I, II, and III


x is in range of 2 and 7 so it can be even or odd
y is median of set of odd integers so it can be even or odd
p is given as odd
using above information only II for sure can be inferred as even.
other two, either can be even or odd
correct response is A.
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Re: MGMAT question [#permalink] New post 06 Jul 2013, 11:16
einstein10 wrote:
mads wrote:
If |x – (9/2) | = 5/2 , and if y is the median of a set of p consecutive integers, where p is odd, which of the following must be true?

I. xypis odd

II. xy(p^2 + p) is even

III. x^2y^2p^2 is even

A. II only
B. III only
C. I and III
D. II and III
E. I, II, and III


x is in range of 2 and 7 so it can be even or odd
y is median of set of odd integers so it can be even or odd
p is given as odd
using above information only II for sure can be inferred as even.
other two, either can be even or odd
correct response is A.



X is not between 2 and 7. X is either 2 or 7.
But the rest of the explanation is correct I believe.
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Re: If |x – 9/2| = 5/2, and if y is the median of a set of p [#permalink] New post 21 Jul 2014, 22:25
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Re: If |x – 9/2| = 5/2, and if y is the median of a set of p   [#permalink] 21 Jul 2014, 22:25
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