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• ### $450 Tuition Credit & Official CAT Packs FREE November 15, 2018 November 15, 2018 10:00 PM MST 11:00 PM MST EMPOWERgmat is giving away the complete Official GMAT Exam Pack collection worth$100 with the 3 Month Pack ($299) • ### Free GMAT Strategy Webinar November 17, 2018 November 17, 2018 07:00 AM PST 09:00 AM PST Nov. 17, 7 AM PST. Aiming to score 760+? Attend this FREE session to learn how to Define your GMAT Strategy, Create your Study Plan and Master the Core Skills to excel on the GMAT. # Is z an even integer?  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics Author Message TAGS: ### Hide Tags Math Expert Joined: 02 Aug 2009 Posts: 7028 Is z an even integer? [#permalink] ### Show Tags Updated on: 30 Apr 2017, 02:37 00:00 Difficulty: 75% (hard) Question Stats: 40% (01:28) correct 60% (00:58) wrong based on 70 sessions ### HideShow timer Statistics Is z an even integer? (1) $$z^2$$ is an even integer. (2) y*z is an even integer, where z and y are integers. _________________ 1) Absolute modulus : http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372 2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html 3) effects of arithmetic operations : https://gmatclub.com/forum/effects-of-arithmetic-operations-on-fractions-269413.html GMAT online Tutor Originally posted by chetan2u on 29 Apr 2017, 08:09. Last edited by Bunuel on 30 Apr 2017, 02:37, edited 1 time in total. Renamed the topic and edited the question. Intern Joined: 02 Mar 2017 Posts: 8 Re: Is z an even integer? [#permalink] ### Show Tags 29 Apr 2017, 08:13 Statement 1 alone is sufficient and statement 2 is not sufficient. Sent from my iPhone using GMAT Club Forum Math Expert Joined: 02 Aug 2009 Posts: 7028 Re: Is z an even integer? [#permalink] ### Show Tags 29 Apr 2017, 08:27 1 Munch wrote: Statement 1 alone is sufficient and statement 2 is not sufficient. Sent from my iPhone using GMAT Club Forum Hi, What if z is √2... $$z^2=2$$ and thus an even integer but z is not an even integer. _________________ 1) Absolute modulus : http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372 2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html 3) effects of arithmetic operations : https://gmatclub.com/forum/effects-of-arithmetic-operations-on-fractions-269413.html GMAT online Tutor Retired Moderator Joined: 05 Jul 2006 Posts: 1726 Re: Is z an even integer? [#permalink] ### Show Tags 29 Apr 2017, 14:03 chetan2u wrote: Is z an even integer? 1) $$z^2$$ is an even integer. 2) y*z is an even integer, where z and y are integers. from 1 z could be a radical ... insuff from 2 if y is even integer and no idea about z... insuff both z is an integer and z^2 is even thus z is even...C Intern Joined: 25 Dec 2016 Posts: 17 Re: Is z an even integer? [#permalink] ### Show Tags 29 Apr 2017, 21:37 Statement 1: Z can be sqrt2 insufficient Statement 2 : Not Unique answer. Both we can derive unique answer that Z is an integer and even Current Student Joined: 12 Aug 2015 Posts: 2633 Schools: Boston U '20 (M) GRE 1: Q169 V154 Re: Is z an even integer? [#permalink] ### Show Tags 29 Apr 2017, 22:09 Even/Odd Questions are one of my favourite. So much to learn. Here is what i did on this one -> Firstly => The most important step in any even/odd question before we move to the individual statements is check whether the involved numbers are integers or not. We are not told that z is an integer. Lets roll--> Statement 1 => z^2 is even If z is an integer => z would be even. But what if z=$$√12$$ ? z^2 is even But $$√12$$ isnt even. Not sufficient. Statement 2 => So y and z are integers. yz= even So at-least one out of y or z must be even. So if y is even => z can be even or odd. Not sufficient. Combing the two statements => As z is an integer and z^2 is even => z must be even. Property in action =>Positive exponent does not affect the even/odd nature of any integer. Hence C is sufficient. SMASH THAT C. _________________ MBA Financing:- INDIAN PUBLIC BANKS vs PRODIGY FINANCE! Getting into HOLLYWOOD with an MBA! The MOST AFFORDABLE MBA programs! STONECOLD's BRUTAL Mock Tests for GMAT-Quant(700+) AVERAGE GRE Scores At The Top Business Schools! Senior CR Moderator Status: Long way to go! Joined: 10 Oct 2016 Posts: 1378 Location: Viet Nam Re: Is z an even integer? [#permalink] ### Show Tags 30 Apr 2017, 03:12 chetan2u wrote: Is z an even integer? (1) $$z^2$$ is an even integer. (2) y*z is an even integer, where z and y are integers. (1) $$z^2$$ is an even integer. $$z^2=2 \implies z=\sqrt{2}$$ is not an even integer. $$z^2=4 \implies z=2$$ is an even integer. Hence (1) is insufficient. (2) $$y$$ and $$z$$ are both integers. Since $$y \times z$$ is even, $$y$$ or $$z$$ or both must be even. If $$y$$ is odd, then $$z$$ must be even. If $$y$$ is even, then $$z$$ could be odd. Hence, insufficient. Cobine (1) and (2), we have $$z$$ is an integer and $$z^2$$ is even. Hence $$z$$ must be even. Sufficient. The answer is C. _________________ EMPOWERgmat Instructor Status: GMAT Assassin/Co-Founder Affiliations: EMPOWERgmat Joined: 19 Dec 2014 Posts: 12853 Location: United States (CA) GMAT 1: 800 Q51 V49 GRE 1: Q170 V170 Re: Is z an even integer? [#permalink] ### Show Tags 10 Dec 2017, 14:17 1 Hi All, We're asked if Z is an EVEN INTEGER. This is a YES/NO question. We can solve it by TESTing VALUES. 1) Z^2 is an EVEN integer. IF... Z^2 = 2, then Z = (root2) and the answer to the question is NO. Z^2 = 4, then Z = 2 and the answer to the question is YES. Fact 1 is INSUFFICIENT 2) (Y)(Z) is an EVEN integer and Z and Y are INTEGERS IF... Y = 1 and Z = 2, then the answer to the question is YES. Y = 2 and Z = 1, then the answer to the question is NO. Fact 2 is INSUFFICIENT Combined, we know... Y and Z are INTEGERS Z^2 is an EVEN integer The ONLY way to square an INTEGER and end up with an EVEN integer is if you started with an EVEN integer. Fact 2 tells us that Z MUST be an integer, so Z MUST be even and the answer to the question is ALWAYS YES. Combined, SUFFICIENT Final Answer: GMAT assassins aren't born, they're made, Rich _________________ 760+: Learn What GMAT Assassins Do to Score at the Highest Levels Contact Rich at: Rich.C@empowergmat.com # Rich Cohen Co-Founder & GMAT Assassin Special Offer: Save$75 + GMAT Club Tests Free
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Re: Is z an even integer? &nbs [#permalink] 10 Dec 2017, 14:17
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