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100 points for $49 worth of Veritas practice GMATs FREE VERITAS PRACTICE GMAT EXAMS Earn 10 Points Per Post Earn 10 Points Per Thanks Earn 10 Points Per Upvote ## Even Game ##### This topic has 6 member replies ## Even Game X, Y, Z, and W are integers. The expression X-Y-Z is even and the Expression Y-Z-W is odd. If X is even what must be true? (a) Y-Z must be odd. (b) W must be even. (c) W must be odd. (d) Z must be even. (e) Z must be odd DO u have a easy method to calculate this one without plugging Numbers??? OA :C Last edited by gmatmachoman on Sun Feb 21, 2010 5:41 am; edited 1 time in total Master | Next Rank: 500 Posts Joined 20 Feb 2010 Posted: 102 messages Upvotes: 10 As X is even,Y and Z both needs to be simultaneously odd or even in order to make the expression X-Y-Z even. For Y-Z-W to be odd,two cases are possible Y Z W E E O O O O In either case,W is odd. Hence,option C. Legendary Member Joined 20 Jul 2009 Posted: 1132 messages Followed by: 6 members Upvotes: 64 Test Date: 30/03/2012 Target GMAT Score: 780+ GMAT Score: 760 gmatmachoman wrote: X, Y, Z, and W are integers. The expression X-Y-Z is even and the Expression Y-Z-W is odd. If X is even what must be true? (a) Y-Z must be odd. (b) W must be even. (c) W must be odd. (d) Z must be even. (e) Z must be odd DO u have a easy method to calculate this one without plugging Numbers??? Now,X is even. That means -(Y+Z) is even.[X-(Y+Z) is even when X is even and Y+Z is even] Hence,we have 2 cases. Case 1:-Y even,Z even Case 2:-Y odd,Z odd Now, in any case Y-Z would be even only.[Even - Even =Even] Hence,W has to be odd. Hence,option C. _________________ It takes time and effort to explain, so if my comment helped you please press Thanks button Just because something is hard doesn't mean you shouldn't try,it means you should just try harder. "Keep Walking" - Johnny Walker Legendary Member Joined 21 Sep 2006 Posted: 1275 messages Followed by: 2 members Upvotes: 125 Test Date: April 2010 Target GMAT Score: 740 gmatmachoman wrote: X, Y, Z, and W are integers. The expression X-Y-Z is even and the Expression Y-Z-W is odd. If X is even what must be true? (a) Y-Z must be odd. (b) W must be even. (c) W must be odd. (d) Z must be even. (e) Z must be odd DO u have a easy method to calculate this one without plugging Numbers??? OA :C X-Y-Z is even Y-Z-W is odd The sum ; X-2Z-W is odd if X is even W is odd _________________ Always borrow money from a pessimist, he doesn't expect to be paid back. Legendary Member Joined 17 Nov 2009 Posted: 1560 messages Followed by: 5 members Upvotes: 137 Target GMAT Score: 750 gmatmachoman wrote: X, Y, Z, and W are integers. The expression X-Y-Z is even and the Expression Y-Z-W is odd. If X is even what must be true? (a) Y-Z must be odd. (b) W must be even. (c) W must be odd. (d) Z must be even. (e) Z must be odd DO u have a easy method to calculate this one without plugging Numbers??? OA :C first remeber properties even-even=even[8-6=2 for eg] odd-odd=even[9-1=8] even-odd=odd[8-3=5] now in x-y-z=even----->{even-even-even or evn-odd-odd) if y=odd---.z=odd and if y=evn------->z=even so for y-z-w to be odd if y=odd--->z=odd therfore z must be odd to get an odd value and if y=evn------>w=evn--------->w must be odd to get an odd value so in any case w is odd hence C Legendary Member Joined 20 Jul 2009 Posted: 1022 messages Followed by: 2 members Upvotes: 41 Test Date: ND Target GMAT Score: 780 GMAT Score: NA gmatmachoman wrote: X, Y, Z, and W are integers. The expression X-Y-Z is even and the Expression Y-Z-W is odd. If X is even what must be true? (a) Y-Z must be odd. (b) W must be even. (c) W must be odd. (d) Z must be even. (e) Z must be odd DO u have a easy method to calculate this one without plugging Numbers??? OA :C (O+O=E, E+E=E, O+E = O , E+O = O) X is even....X-Y-Z is also even --> Y+Z is even (E-E=E) so either both Y and Z is odd or both Y and Z is even (O+O=E, E+E=E) Now since either both Y and Z is odd or both Y and Z is even (O+O=E, E+E=E) --> Y-Z is also even. Y-Z-W is odd --> now Y-Z is even and Y-Z-W is odd so W must be odd (O+E = O , E+O = O) Hence W must be odd Ans C _________________ My Websites: www.mba.webmaggu.com - India's social Network for MBA Aspirants www.deal.webmaggu.com -India's online discount, coupon, free stuff informer. www.dictionary.webmaggu.com - A compact free online dictionary with images. Nothing is Impossible, even Impossible says I'm possible. Senior | Next Rank: 100 Posts Joined 20 Dec 2018 Posted: 33 messages The first expression is even and the second is odd, the only difference between the expressions is that the first expression has X and the second has W. 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