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• ### $450 Tuition Credit & Official CAT Packs FREE January 15, 2019 January 15, 2019 10:00 PM PST 11:00 PM PST EMPOWERgmat is giving away the complete Official GMAT Exam Pack collection worth$100 with the 3 Month Pack ($299) • ### The winning strategy for a high GRE score January 17, 2019 January 17, 2019 08:00 AM PST 09:00 AM PST Learn the winning strategy for a high GRE score — what do people who reach a high score do differently? We're going to share insights, tips and strategies from data we've collected from over 50,000 students who used examPAL. # If x and y are non-zero integers and |x| + |y| = 32, what is  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics Author Message TAGS: ### Hide Tags Intern Joined: 13 May 2009 Posts: 18 If x and y are non-zero integers and |x| + |y| = 32, what is [#permalink] ### Show Tags 08 Aug 2009, 06:32 2 26 00:00 Difficulty: 75% (hard) Question Stats: 61% (02:21) correct 39% (02:18) wrong based on 763 sessions ### HideShow timer Statistics If x and y are non-zero integers and |x| + |y| = 32, what is xy? (1) -4x – 12y = 0 (2) |x| – |y| = 16 ##### Most Helpful Expert Reply Math Expert Joined: 02 Sep 2009 Posts: 52108 If x and y are non-zero integers and |x| + |y| = 32, what is [#permalink] ### Show Tags 03 Feb 2010, 04:07 5 6 ##### Most Helpful Community Reply Senior Manager Joined: 08 Dec 2009 Posts: 371 Re: Absolute Value [#permalink] ### Show Tags 08 Feb 2010, 11:17 9 Given: |X| + |Y| = 32, so 4 equations: -X + Y = 32 (I) X + Y = 32 (II) -X - Y = 32 (III) X - Y = 32 (IV) From (1) -4X = 12y, so X = -3Y or if X is neg, then Y is pos and vice-versa This information means equations (II) and (III) above can be eliminated. Hence, substitute X = -3Y in (I) and (IV) yields Y = -8 or 8. if Y = -8, then X = +24, so xy = -192 if Y = +8, then X = -24, so xy = -192 the same as above. (1) is true From (II) |X| - |Y| = 16 and given |X| + |Y| = 32, subtract both equations yields 2|X| = 16, so X = -8 or 8. Y is thus -24 or 24... but the combination can be the following (X,Y): (-8, 24) (-8, -24) (8, 24) (8, -24) and xy will yield either -192 or +192 _________________ kudos if you like me (or my post) ##### General Discussion Math Expert Joined: 02 Sep 2009 Posts: 52108 If x and y are non-zero integers and |x| + |y| = 32, what is [#permalink] ### Show Tags 01 Nov 2009, 04:25 5 2 If x and y are non-zero integers and |x| + |y| = 32, what is xy? (1) $$-4x - 12y = 0$$ --> $$x+3y=0$$ --> $$x=-3y$$ --> $$x$$ and $$y$$ have opposite signs --> so either $$|x|=x$$ and $$|y|=-y$$ OR $$|x|=-x$$ and $$|y|=y$$ --> either $$|x|+|y|=-x+y=3y+y=4y=32$$: $$y=8$$, $$x=-24$$, $$xy=-24*8$$ OR $$|x|+|y|=x-y=-3y-y=-4y=32$$: $$y=-8$$, $$x=24$$, $$xy=-24*8$$, same answer. Sufficient. (2) $$|x| - |y| = 16$$. Sum this one with th equations given in the stem --> $$2|x|=48$$ --> $$|x|=24$$, $$|y|=8$$. $$xy=-24*8$$ (x and y have opposite sign) or $$xy=24*8$$ (x and y have the same sign). Multiple choices. Not sufficient. Answer: A. _________________ CEO Joined: 17 Nov 2007 Posts: 3439 Concentration: Entrepreneurship, Other Schools: Chicago (Booth) - Class of 2011 GMAT 1: 750 Q50 V40 Re: Absolute Question -- Please help [#permalink] ### Show Tags 22 Mar 2010, 06:02 2 1 A 1) -4x-12y=0 --> x = -3y --> |-3y|+|y| = 32 --> |y| = 8 --> we have two solutions: (x=24, y=-8) and (x=-24, y=8). In both cases xy is the same. Sufficient 2) We don't even need to solve it. In the question and second statement we have expressions that include absolute values of both x and y. In other words, there is always at least two possible value for x and y: negative and positive. So, xy can be also negative and positive. Insufficient. It is possible to take a square but I wouldn't recommend especially for absolute value - inequality combination because it is easy to miss something. Did you see this post? It could be helpful. math-absolute-value-modulus-86462.html _________________ HOT! GMAT TOOLKIT 2 (iOS) / GMAT TOOLKIT (Android) - The OFFICIAL GMAT CLUB PREP APP, a must-have app especially if you aim at 700+ | Limited GMAT/GRE Math tutoring in Chicago Manager Joined: 13 Dec 2009 Posts: 224 Re: Absolute Question -- Please help [#permalink] ### Show Tags 22 Mar 2010, 07:01 Hey nice explanation walker. I still have one doubt. How did you reach to below conclusion. Should not we consider 4 cases here when -3y is +- and when y is +-? walker wrote: |-3y|+|y| = 32 --> |y| = 8 _________________ My debrief: done-and-dusted-730-q49-v40 CEO Joined: 17 Nov 2007 Posts: 3439 Concentration: Entrepreneurship, Other Schools: Chicago (Booth) - Class of 2011 GMAT 1: 750 Q50 V40 Re: Absolute Question -- Please help [#permalink] ### Show Tags 22 Mar 2010, 10:55 Here I use two properties: 1) |y|=|-y| 2) |ay| = a|y| if a is a non-negative number. |-3y|+|y| = 32 3|-y|+|y| = 32 3|y|+|y| = 32 4|y| = 32 |y| = 8 And only now I open a modulus: y=+/-8 Of course, we can open two modules at the beginning, use 4 cases and get the same answer. Trick here is that y and -3y have the same key point: 0. So, if y>0, -3y is negative and vice versa. In other words, y>0 and -3y>0 can't be true simultaneously and we have only 2 cases: -3y - y = 32 and 3y + y = 32 or y = +/-8 _________________ HOT! GMAT TOOLKIT 2 (iOS) / GMAT TOOLKIT (Android) - The OFFICIAL GMAT CLUB PREP APP, a must-have app especially if you aim at 700+ | Limited GMAT/GRE Math tutoring in Chicago Intern Joined: 25 Sep 2010 Posts: 16 Re: If x and y are non-zero integers and |x| + |y| = 32, what is [#permalink] ### Show Tags 29 Oct 2010, 03:53 Bunuel wrote: lbsgmat wrote: If x and y are non-zero integers and |x| + |y| = 32, what is xy? (1) -4x – 12y = 0 (2) |x| – |y| = 16 If x and y are non-zero integers and |x| + |y| = 32, what is xy? (1) $$-4x-12y=0$$ --> $$x=-3y$$ --> $$x$$ and $$y$$ have opposite signs --> so either $$|x|=x$$ and $$|y|=-y$$ OR $$|x|=-x$$ and $$|y|=y$$ --> either $$|x|+|y|=-x+y=3y+y=4y=32$$: $$y=8$$, $$x=-24$$, $$xy=-24*8$$ OR $$|x|+|y|=x-y=-3y-y=-4y=32$$: $$y=-8$$, $$x=24$$, $$xy=-24*8$$, same answer. Sufficient. (2) $$|x| - |y| = 16$$. Sum this one with th equations given in the stem --> $$2|x|=48$$ --> $$|x|=24$$, $$|y|=8$$. $$xy=-24*8$$ (x and y have opposite sign) or $$xy=24*8$$ (x and y have the same sign). Multiple choices. Not sufficient. Answer: A. hey bunnel, i know this is basic stuff, but could you explain the absolute equation |y|=-y, what does this mean, is it "y" inside the modules is negative, and "|x|+|y|=-x+y=3y+y=4y=32" how did you manage to get a negative coefficient for the "x" when it is in the module.....thanks in advance,,bunnel Math Expert Joined: 02 Sep 2009 Posts: 52108 Re: If x and y are non-zero integers and |x| + |y| = 32, what is [#permalink] ### Show Tags 29 Oct 2010, 04:03 2 satishreddy wrote: Bunuel wrote: lbsgmat wrote: If x and y are non-zero integers and |x| + |y| = 32, what is xy? (1) -4x – 12y = 0 (2) |x| – |y| = 16 If x and y are non-zero integers and |x| + |y| = 32, what is xy? (1) $$-4x-12y=0$$ --> $$x=-3y$$ --> $$x$$ and $$y$$ have opposite signs --> so either $$|x|=x$$ and $$|y|=-y$$ OR $$|x|=-x$$ and $$|y|=y$$ --> either $$|x|+|y|=-x+y=3y+y=4y=32$$: $$y=8$$, $$x=-24$$, $$xy=-24*8$$ OR $$|x|+|y|=x-y=-3y-y=-4y=32$$: $$y=-8$$, $$x=24$$, $$xy=-24*8$$, same answer. Sufficient. (2) $$|x| - |y| = 16$$. Sum this one with th equations given in the stem --> $$2|x|=48$$ --> $$|x|=24$$, $$|y|=8$$. $$xy=-24*8$$ (x and y have opposite sign) or $$xy=24*8$$ (x and y have the same sign). Multiple choices. Not sufficient. Answer: A. hey bunnel, i know this is basic stuff, but could you explain the absolute equation |y|=-y, what does this mean, is it "y" inside the modules is negative, and "|x|+|y|=-x+y=3y+y=4y=32" how did you manage to get a negative coefficient for the "x" when it is in the module.....thanks in advance,,bunnel Absolute value is always non-negative: $$|x|\geq{0}$$, so: When $$x\leq{0}$$ then $$|x|=-x$$ (note that in this case $$|x|=-negative=positive$$); When $$x\geq{0}$$ then $$|x|=x$$. $$x=-3y$$ implies that $$x$$ and $$y$$ have opposite sign, so when $$x$$ is negative then $$y$$ is positive. In this case (when $$x$$ is negative and $$y$$ is positive): $$|x|=-x$$ and $$|y|=y$$ and $$|x|+|y|=32$$ becomes $$-x+y=32$$. For more check: math-absolute-value-modulus-86462.html Hope it helps. _________________ SVP Status: Top MBA Admissions Consultant Joined: 24 Jul 2011 Posts: 1525 GMAT 1: 780 Q51 V48 GRE 1: Q800 V740 Re: DS-mod [#permalink] ### Show Tags 30 Jul 2011, 02:44 The question is asking us if we have enough information to determine xy if |x| + |y| = 32, and x and y are non-zero integers. From statement (1), x = -3y. Solving this with |x| + |y| = 32 gives us x=8, y =-24 or y=8, x=-24. In either case, xy is the same (-8*24 or -192). Even though we get two sets of values of x and y, their product is the same in both cases. Sufficient. From statement (2), |x| - |y| = 16. Solving |x| - |y| = 16 and |x| + |y| = 32 gives us the solution |x| = 24 and |y| = 8. => The solutions are x=24,-24 and y=8,-8. If we use x=24 and y=8, we get xy = 24*8. If we use x=-24 and y=8, we get xy=-24*8. Using just these two cases we can see that we are not getting a unique value for xy. Therefore statement (2) alone is insufficient. The answer is (A). _________________ GyanOne | Top MBA Rankings and MBA Admissions Blog Top MBA Admissions Consulting | Top MiM Admissions Consulting Premium MBA Essay Review|Best MBA Interview Preparation|Exclusive GMAT coaching Get a FREE Detailed MBA Profile Evaluation | Call us now +91 98998 31738 Senior Manager Joined: 13 May 2013 Posts: 425 Re: If x and y are non-zero integers and |x| + |y| = 32, what is [#permalink] ### Show Tags 10 Jul 2013, 13:02 2 If x and y are non-zero integers and |x| + |y| = 32, what is xy? (1) -4x – 12y = 0 -4x = 12y x = -3y |x| + |y| = 32 |-3y| + |y| = 32 4y = 32 y=8 x = -3y x = -3(8) x=-24 xy = (-24)*(8) SUFFICIENT (2) |x| – |y| = 16 |x| – |y| = 16 |x| + |y| = 32 2|x|=48 |x|=24 x=24, x=-24 x=24 |x| – |y| = 16 |24| - |y| = 16 24 - |y| = 16 - |y| = -8 |y| = 8 y=8 OR y=-8 If x is 24, y could = 8 or -8 meaning xy could be positive or negative. INSUFFICIENT (A) Manager Joined: 30 May 2013 Posts: 155 Location: India Concentration: Entrepreneurship, General Management GPA: 3.82 Re: If x and y are non-zero integers [#permalink] ### Show Tags 21 Sep 2013, 22:32 Bunuel wrote: devinawilliam83 wrote: If x and y are non-zero integers and |x| + |y| = 32, what is xy? (1) -4x – 12y = 0 (2) |x| – |y| = 16 please explain how A is sufficient I got C. on solving A i get 2 possible values of x and y and thus 2 values of XY If x and y are non-zero integers and |x| + |y| = 32, what is xy? (1) $$-4x - 12y = 0$$ --> $$x+3y=0$$ --> $$x=-3y$$ --> $$x$$ and $$y$$ have opposite signs --> so either $$|x|=x$$ and $$|y|=-y$$ OR $$|x|=-x$$ and $$|y|=y$$ --> either $$|x|+|y|=-x+y=3y+y=4y=32$$: $$y=8$$, $$x=-24$$, $$xy=-24*8$$ OR $$|x|+|y|=x-y=-3y-y=-4y=32$$: $$y=-8$$, $$x=24$$, $$xy=-24*8$$, same answer. Sufficient. (2) $$|x| - |y| = 16$$. Sum this one with th equations given in the stem --> $$2|x|=48$$ --> $$|x|=24$$, $$|y|=8$$. $$xy=-24*8$$ (x and y have opposite sign) or $$xy=24*8$$ (x and y have the same sign). Multiple choices. Not sufficient. Answer: A. Hi Bunel, i have a doubt in ur explanation |x|+|y|=32 For this the modulus sign wont have four cases? (-x,+y), (+x,-y), (+x,+y), (-x,-y) Please clarify me. Thanks in Advance, Rrsnathan. Math Expert Joined: 02 Sep 2009 Posts: 52108 Re: If x and y are non-zero integers [#permalink] ### Show Tags 22 Sep 2013, 03:35 rrsnathan wrote: Bunuel wrote: devinawilliam83 wrote: If x and y are non-zero integers and |x| + |y| = 32, what is xy? (1) -4x – 12y = 0 (2) |x| – |y| = 16 please explain how A is sufficient I got C. on solving A i get 2 possible values of x and y and thus 2 values of XY If x and y are non-zero integers and |x| + |y| = 32, what is xy? (1) $$-4x - 12y = 0$$ --> $$x+3y=0$$ --> $$x=-3y$$ --> $$x$$ and $$y$$ have opposite signs --> so either $$|x|=x$$ and $$|y|=-y$$ OR $$|x|=-x$$ and $$|y|=y$$ --> either $$|x|+|y|=-x+y=3y+y=4y=32$$: $$y=8$$, $$x=-24$$, $$xy=-24*8$$ OR $$|x|+|y|=x-y=-3y-y=-4y=32$$: $$y=-8$$, $$x=24$$, $$xy=-24*8$$, same answer. Sufficient. (2) $$|x| - |y| = 16$$. Sum this one with th equations given in the stem --> $$2|x|=48$$ --> $$|x|=24$$, $$|y|=8$$. $$xy=-24*8$$ (x and y have opposite sign) or $$xy=24*8$$ (x and y have the same sign). Multiple choices. Not sufficient. Answer: A. Hi Bunel, i have a doubt in ur explanation |x|+|y|=32 For this the modulus sign wont have four cases? (-x,+y), (+x,-y), (+x,+y), (-x,-y) Please clarify me. Thanks in Advance, Rrsnathan. Generally yes. But from $$x=-3y$$ we can get that $$x$$ and $$y$$ have opposite signs, so we are left only with two cases (+, -) or (-, +). Hope it's clear. _________________ Intern Joined: 30 Apr 2010 Posts: 20 Re: If x and y are non-zero integers and |x| + |y| = 32, what is [#permalink] ### Show Tags 17 Oct 2013, 07:45 3 If x and y are non-zero integers and |x| + |y| = 32, what is xy? (1) -4x – 12y = 0 (2) |x| – |y| = 16 (1) -4x - 12y = 0 multiply by (-1) 4x + 12y = 0 4(x + 3y) = 0 x + 3y = 0 we are also told that |x| + |y| = 32, so the only values for x and y that satisfy both equations are x = 24 y = -8 or x = -24 y = 8 in both cases xy is the same (-24)(8) = (24)(-8) ==> Sufficient. (2) |x| - |y| = 16 multiple values for xy possible, for example x = 24 y = 8 or x = -24 y = 8 ==> Not sufficient. Answer: A Senior Manager Joined: 17 Sep 2013 Posts: 339 Concentration: Strategy, General Management GMAT 1: 730 Q51 V38 WE: Analyst (Consulting) Re: If x and y are non-zero integers [#permalink] ### Show Tags 02 May 2014, 02:44 Bunuel wrote: devinawilliam83 wrote: If x and y are non-zero integers and |x| + |y| = 32, what is xy? (1) -4x – 12y = 0 (2) |x| – |y| = 16 please explain how A is sufficient I got C. on solving A i get 2 possible values of x and y and thus 2 values of XY If x and y are non-zero integers and |x| + |y| = 32, what is xy? (1) $$-4x - 12y = 0$$ --> $$x+3y=0$$ --> $$x=-3y$$ --> $$x$$ and $$y$$ have opposite signs --> so either $$|x|=x$$ and $$|y|=-y$$ OR $$|x|=-x$$ and $$|y|=y$$ --> either $$|x|+|y|=-x+y=3y+y=4y=32$$: $$y=8$$, $$x=-24$$, $$xy=-24*8$$ OR $$|x|+|y|=x-y=-3y-y=-4y=32$$: $$y=-8$$, $$x=24$$, $$xy=-24*8$$, same answer. Sufficient. (2) $$|x| - |y| = 16$$. Sum this one with th equations given in the stem --> $$2|x|=48$$ --> $$|x|=24$$, $$|y|=8$$. $$xy=-24*8$$ (x and y have opposite sign) or $$xy=24*8$$ (x and y have the same sign). Multiple choices. Not sufficient. Answer: A. Where did I go wrong.. |x| - |y| = 32 --> |-3y| - |y| = 32 --> 3y - |y| = 32 --> |y| = 32- 3y y= -(32 - 3y)--> y= 16 y= 32 - 3y --> y= 8 Guess I am wrong here...But I dont understand why...Absolute value confuses me a lot...been thru GMAT CLub Book...not sufficient I guess _________________ Appreciate the efforts...KUDOS for all Don't let an extra chromosome get you down.. Math Expert Joined: 02 Sep 2009 Posts: 52108 Re: If x and y are non-zero integers [#permalink] ### Show Tags 02 May 2014, 09:21 1 JusTLucK04 wrote: Bunuel wrote: devinawilliam83 wrote: If x and y are non-zero integers and |x| + |y| = 32, what is xy? (1) -4x – 12y = 0 (2) |x| – |y| = 16 please explain how A is sufficient I got C. on solving A i get 2 possible values of x and y and thus 2 values of XY If x and y are non-zero integers and |x| + |y| = 32, what is xy? (1) $$-4x - 12y = 0$$ --> $$x+3y=0$$ --> $$x=-3y$$ --> $$x$$ and $$y$$ have opposite signs --> so either $$|x|=x$$ and $$|y|=-y$$ OR $$|x|=-x$$ and $$|y|=y$$ --> either $$|x|+|y|=-x+y=3y+y=4y=32$$: $$y=8$$, $$x=-24$$, $$xy=-24*8$$ OR $$|x|+|y|=x-y=-3y-y=-4y=32$$: $$y=-8$$, $$x=24$$, $$xy=-24*8$$, same answer. Sufficient. (2) $$|x| - |y| = 16$$. Sum this one with th equations given in the stem --> $$2|x|=48$$ --> $$|x|=24$$, $$|y|=8$$. $$xy=-24*8$$ (x and y have opposite sign) or $$xy=24*8$$ (x and y have the same sign). Multiple choices. Not sufficient. Answer: A. Where did I go wrong.. |x| - |y| = 32 --> |-3y| - |y| = 32 --> 3y - |y| = 32 --> |y| = 32- 3y y= -(32 - 3y)--> y= 16 y= 32 - 3y --> y= 8 Guess I am wrong here...But I dont understand why...Absolute value confuses me a lot...been thru GMAT CLub Book...not sufficient I guess It's $$|x| + |y| = 32$$, not |x| - |y| = 32. From (1): $$x=-3y$$ --> $$|x| + |y| = 32$$ --> $$|-3y| + |y| = 32$$ --> $$3|y| + |y| = 32$$ --> $$4|y|=32$$ --> $$|y|=8$$ --> $$y=8$$ or $$y=-8$$. If $$y=8$$, then $$x=-3y=-24$$ --> $$xy=(-24)8$$. If $$y=-8$$, then $$x=-3y=24$$ --> $$xy=24(-8)$$. Both cases give the same value of xy. Hope it's clear. _________________ Manager Joined: 20 Jan 2014 Posts: 142 Location: India Concentration: Technology, Marketing Re: If x and y are non-zero integers and |x| + |y| = 32, what is [#permalink] ### Show Tags 01 Oct 2014, 07:41 Note that one need not determine the values of both x and y to solve this problem; the value of product xy will suffice. (1) SUFFICIENT: Statement (1) can be rephrased as follows: -4x – 12y = 0 -4x = 12y x = -3y If x and y are non-zero integers, we can deduce that they must have opposite signs: one positive, and the other negative. Therefore, this last equation could be rephrased as |x| = 3|y| We don’t know whether x or y is negative, but we do know that they have the opposite signs. Converting both variables to absolute value cancels the negative sign in the expression x = -3y. We are left with two equations and two unknowns, where the unknowns are |x| and |y|: |x| + |y| = 32 |x| – 3|y| = 0 Subtracting the second equation from the first yields 4|y| = 32 |y| = 8 Substituting 8 for |y| in the original equation, we can easily determine that |x| = 24. Because we know that one of either x or y is negative and the other positive, xy must be the negative product of |x| and |y|, or -8(24) = -192. (2) INSUFFICIENT: Statement (2) also provides two equations with two unknowns: |x| + |y| = 32 |x| - |y| = 16 Solving these equations allows us to determine the values of |x| and |y|: |x| = 24 and |y| = 8. However, this gives no information about the sign of x or y. The product xy could either be -192 or 192. The correct answer is A. _________________ Consider +1 Kudos Please EMPOWERgmat Instructor Status: GMAT Assassin/Co-Founder Affiliations: EMPOWERgmat Joined: 19 Dec 2014 Posts: 13325 Location: United States (CA) GMAT 1: 800 Q51 V49 GRE 1: Q170 V170 Re: If x and y are non-zero integers and |x| + |y| = 32, what is [#permalink] ### Show Tags 25 May 2015, 22:04 1 Hi All, This question has some interesting 'pattern-matching shortcuts' built into it that you can take advantage of IF you take enough notes. We're told that X and Y are NON-0 INTEGERS and |X| + |Y| = 32. We're asked for the value of (X)(Y). Before dealing with the two Facts, it's worth noting that the prompt provides a significant limitation on the possible values of X and Y. Since the absolute values will turn negative results into positive ones, and the variables CANNOT be 0, there really are NOT that many possible values for X and Y. +-1 and +-31 +-2 and +-30 +-3 and +-29 Etc. We can use this to our advantage when dealing with the two Facts.... Fact 1: -4X - 12Y = 0 Here, we can do some algebra to simplify the equation... -4X = 12Y -X = 3Y This tells us that one variable MUST be POSITIVE and one MUST be NEGATIVE. When we include the absolute value equation given in the prompt, we know that one absolute value must be 3 times the value of the other.... That leaves us with two options for X and Y.... X = +24 and Y = -8 or X = -24 and Y = +8 Either way, we get the SAME PRODUCT: -192 Fact 1 is SUFFICIENT Fact 2: |X| – |Y| = 16 Here, we can use the work we did in Fact 1 to save us some time (and help us create some new possibilities)... IF... X = +24, Y = -8, the answer to the question is -192 IF... X = +24, Y = +8, the answer to the question is +192 Fact 2 is INSUFFICIENT 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: If x and y are non-zero integers and |x| + |y| = 32, what is &nbs [#permalink] 02 May 2018, 06:57
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