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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 ## Inequality tagged by: ##### This topic has 3 expert replies and 27 member replies Goto page Newbie | Next Rank: 10 Posts Joined 30 Apr 2011 Posted: 5 messages I agree that the answer is E. if XY=0, x or y has to be 0. If X is 0, Y can e +1 or -1. If Y is 0, X can be +1 or -1 as well. There are always two solutions. We cannot conclude that X+Y=1 because it can also equal -1 as well Master | Next Rank: 500 Posts Joined 30 Dec 2008 Posted: 111 messages Upvotes: 28 Test Date: 10/24/2011 GMAT Score: 770 The question stem gives the fact that x^2 + y^2 = 1, visually this is a circle with radius 1, centered at the origin. See the drawing below. The question stem asks whether x + y = 1 also, or y = -x + 1. This is a line with -1 slope, y-intercept of 1, and x-intercept of 1. The only two points that these two equations intersect are (0,1) and (1,0). Rephrase the question: "Is (x,y) equal to either (0,1) or (1,0)?" Statement 1) This statement says that visually, the point lies on one of the axes. Although both (0,1) and (1,0) satisfy this constraint, there are two additional points on the original circle that do not satisfy x + y = 1, namely (-1,0) and (0,-1). Insufficient. Statement 2) This statement says that the points lie on the x axis. There is still point (-1,0) that does not satisfy x + y = 1, but (1,0) satisfies. Insufficient. Statement 1 does not add any information to statement 2, so even combined they are insufficient. E Attachments This post contains an attachment. You must be logged in to download/view this file. Please login or register as a user. Legendary Member Joined 23 Dec 2011 Posted: 626 messages Followed by: 10 members Upvotes: 31 Test Date: June Target GMAT Score: 750 Given: x^2+y^2 = 1 To find: x+y = 1? S1. xy = 0 => (x+y)^2 = 1 => x+y = +/- 1 Not sufficient. S2. y = 0 => x^2 = 1 => x = +/-1, x+y = +/-1 Not Sufficient Comb. Similar to S1. Not Sufficient (E) is the answer. _________________ Follow your passion, Success as perceived by others shall follow you Newbie | Next Rank: 10 Posts Joined 27 May 2011 Posted: 6 messages use plugig that satisfies first statement x=-1/y=0 x+y =-1 x=1/y=0 x+y=1 so not sufficient The same plugin helps to proove that 2nd statement is not sufficient:-) The same plugin helps to proove that statement 1+statement 2 is not sufficient,hence answer E. Master | Next Rank: 500 Posts Joined 29 Mar 2012 Posted: 308 messages Followed by: 3 members Upvotes: 16 Target GMAT Score: 750 2 is clearly Insufficient ! 1 comes down to (x+y)^2=+1 -> (x+y)= +1 or -1. So, Insufficient ! Take away : Square root of (+1) = +1 or -1 Senior | Next Rank: 100 Posts Joined 24 Jun 2012 Posted: 97 messages Target GMAT Score: 700+ E Uff held patience to apply the values of x = 1 and -1 or would have chosen C Newbie | Next Rank: 10 Posts Joined 27 Oct 2012 Posted: 8 messages Upvotes: 1 If x^2 + y^2 =1, is x + y =1? (1) xy =0 (2) y = 0 IMO: E the question says x^2+y^2=1 which means either of the one should be one and the other a zero, which means for if x+y=1,then one of them is 1 and the other a zero Looking at statements: 1) it says xy=0, for this to be true either both can be zero or one of them 1 and the other zero, as both being zero can be ruled out as the question stem says the squaring of both x+y=1, but one of them could also be negative which makes it insufficient 2)It says y=0, nothing can be said about the other same reasons x could be 1 or -1, Combined still insufficient same reasons x=-1 or 1 Answer has to be E Master | Next Rank: 500 Posts Joined 08 Jan 2013 Posted: 171 messages Upvotes: 1 E in answEr. (x+y)^2=x^2+y^2+2*x*y Master | Next Rank: 500 Posts Joined 16 Jul 2013 Posted: 234 messages Upvotes: 9 Target GMAT Score: 700+ +1 E Newbie | Next Rank: 10 Posts Joined 12 Sep 2013 Posted: 5 messages This is the case where doing work before the statements is very useful. Notice there are four options. X=0, Y=1. X=1, Y=0. X=-1, Y=0 and X=0, Y=-1. First statement: This is not helpful because in all four of our cases xy=0. (Note: there are other cases but these do not work with this first statement. ie: x=1/2, y=sqrt(3)/2. Second statement: With this statement we can eliminate cases where X=0 But y=-1 or 1. Not sufficient Together: We still do not know if y=1 or y=-1. E Master | Next Rank: 500 Posts Joined 20 Sep 2014 Posted: 164 messages Upvotes: 1 Target GMAT Score: 650 If x^2 + y^2 = 1, is x + y = 1? 1. xy = 0 2. y = 0 IMO: E Reason (1) xy = 0 if x = 1 then 1^2 +0^2 = 1 if y = 1 then 0^2 + 1^2 = 1 i.e. x+y = 1+0 = 1 or 0+1 = 1 but if x = -1 then -1^2 + 0^2 = 1 x+y = -1+0 = -1 not sufficient (2) y = 0 x^2 + y^2 = 1 => 1^2 + 0^2 = 1 x+y = 1+0 = 1 if x = -1 -1^2 + 0^2 = 1 x+y = -1+0 = -1 Not sufficient _________________ Hard work brings success! Legendary Member Joined 12 May 2015 Posted: 518 messages Upvotes: 10 Test Date: 3 Oct Target GMAT Score: 750 pradeepkaushal9518 wrote: x^2+y^2=1 1.xy is zero hence either x=0 or y =0 but its not sufficent 2.y=0 so x^2+y^2=1 x^2+0=1 x^2=1 so X=1 so x+y=1 sufficeint So B If X^2 =1 X can be +/- 1 x + y =-1 Not Sufficient. Legendary Member Joined 12 May 2015 Posted: 518 messages Upvotes: 10 Test Date: 3 Oct Target GMAT Score: 750 I will go with E. X + y can be +/- 1 Legendary Member Joined 12 May 2015 Posted: 518 messages Upvotes: 10 Test Date: 3 Oct Target GMAT Score: 750 I will go with E. X + y can be +/- 1 Junior | Next Rank: 30 Posts Joined 13 Jul 2013 Posted: 14 messages Upvotes: 1 Target GMAT Score: 700 ANS : E Hint : 1= -1x-1 or 1x1 • 5 Day FREE Trial Study Smarter, Not Harder Available with Beat the GMAT members only code • Free Veritas GMAT Class Experience Lesson 1 Live Free Available with Beat the GMAT members only code • 5-Day Free Trial 5-day free, full-access trial TTP Quant Available with Beat the GMAT members only code • Award-winning private GMAT tutoring Register now and save up to$200

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