integers

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naaga: Master | Next Rank: 500 Posts; Posts: 129; Joined: Mon Dec 15, 2008 11:43 pm; Location: Hyderabad; Thanked: 2 times

by naaga » Sat Feb 14, 2009 5:52 am

. If x and y are integers and xy2 is a positive odd integer, which of the following must be true?
Ⅰ. xy is positive.
Ⅱ. xy is odd.
Ⅲ. x + y is even.
folks please explain how many statements of the above are sufficient to answer the question..

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Source: Beat The GMAT — Problem Solving | Sat Feb 14, 2009 5:52 am

sureshbala: Master | Next Rank: 500 Posts; Posts: 319; Joined: Wed Feb 04, 2009 10:32 amFollowed by: 9 members; Location: Delhi; Thanked: 84 times

by sureshbala » Sat Feb 14, 2009 6:07 am

I will take it as (xy)^2 is positive and odd.

(xy)^2 is always positive either xy is positive or negative.

So I need not be true.

(xy)^2 will be odd provided xy is odd, which means both x and y are odd.

So II must be true.

Also if x and y both are odd, x+y must be even. So III also must be true.

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Etoiles: Newbie | Next Rank: 10 Posts; Posts: 3; Joined: Sun Feb 08, 2009 3:53 pm

Re: integers

by Etoiles » Sat Feb 14, 2009 10:34 am

naaga wrote:. If x and y are integers and xy2 is a positive odd integer, which of the following must be true?
Ⅰ. xy is positive.
Ⅱ. xy is odd.
Ⅲ. x + y is even.
folks please explain how many statements of the above are sufficient to answer the question..

let 's start
xy2 is a positive odd
xy must be odd
so x+y are odd why ? Because what ever time even is even so no even here
both are odd adding 2 odd give even
but we can't say that both are positive since -X- = + so we know they have the same sign

so the sum is even xy odd
that 's all

when there is a will there is a way ... believe in yourself ... kind regards

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Bidisha800: Master | Next Rank: 500 Posts; Posts: 344; Joined: Sun Sep 28, 2008 11:00 amFollowed by: 1 member; Location: USA; Thanked: 6 times

by Bidisha800 » Sat Feb 14, 2009 11:32 am

II & III

Drill baby drill !

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earth@work: Master | Next Rank: 500 Posts; Posts: 248; Joined: Mon Aug 11, 2008 9:51 am; Thanked: 13 times

by earth@work » Sat Feb 14, 2009 6:55 pm

II & III
(XY)^2 is odd means both x & y are odd
now 4 possibilities:
1) x (positive) & y (negative)
2) x (positive) & y (positive)
3) x (negative) & y (negative)
4) x (negative) & y (positive)
this means I is not always true

II - odd x odd = odd ..true
III - odd + odd = even ....true

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