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• ### $450 Tuition Credit & Official CAT Packs FREE December 15, 2018 December 15, 2018 10:00 PM PST 11:00 PM PST Get the complete Official GMAT Exam Pack collection worth$100 with the 3 Month Pack ($299) • ### FREE Quant Workshop by e-GMAT! December 16, 2018 December 16, 2018 07:00 AM PST 09:00 AM PST Get personalized insights on how to achieve your Target Quant Score. # In the xy plane, at what points does the graph of y=  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics Author Message TAGS: ### Hide Tags Intern Status: Tougher times ... Joined: 04 Nov 2012 Posts: 41 Location: India GMAT 1: 480 Q32 V25 WE: General Management (Manufacturing) Re: Coordinate geometry [#permalink] ### Show Tags Updated on: 23 Apr 2013, 02:31 Zarrolou wrote: kabilank87 wrote: In the xy plane at what 2 points does the graph of y = (x+a)(x+b) intersect the X - axis ? 1.a+b=-1 2.The graph intersects the y axis at (0, -6 ) The function is a parabola $$y=x^2+x(a+b)+ab$$ 1)Does $$y=x^2-x+ab$$ intersec x? It depend on ab.Not sufficient 2) Tells us that point (0,6) is on the parabol, so $$ab=-6$$. Does $$y=x^2+x(a+b)-6$$ intersect x? It depends on a+b. Not sufficient 1+2) The equation of the parabola is complete $$y=x^2-x-6$$, we can tell if it intersect x. Sufficient C Hi Zarro , In equation no 2 - How you use ab=-6. Is n't ab = +6. Will you please explain the logic behind it ? Thanks in advance. _________________ Kabilan.K Kudos is a boost to participate actively and contribute more to the forum Originally posted by kabilank87 on 23 Apr 2013, 02:27. Last edited by kabilank87 on 23 Apr 2013, 02:31, edited 1 time in total. VP Status: Far, far away! Joined: 02 Sep 2012 Posts: 1063 Location: Italy Concentration: Finance, Entrepreneurship GPA: 3.8 Re: Coordinate geometry [#permalink] ### Show Tags 23 Apr 2013, 02:31 1 kabilank87 wrote: Hi Zarro , In equation no 2 - How you replace ab with -6. Will you please explain the logic behind it ? Thanks in advance. Sure! Lets take another look at (2)The graph intersects the y axis at (0, -6 ) We know that the parabola has equation $$y=x^2+x(a+b)+ab$$, now if it intersect y in (0,-6) this point is in the parabola, so we just substitute its value (x=0,y=-6) in the equation $$-6=0^2+0(a+b)+ab$$ and we find that $$ab=-6$$ Hope it's clear now, let me know _________________ It is beyond a doubt that all our knowledge that begins with experience. Kant , Critique of Pure Reason Tips and tricks: Inequalities , Mixture | Review: MGMAT workshop Strategy: SmartGMAT v1.0 | Questions: Verbal challenge SC I-II- CR New SC set out !! , My Quant Rules for Posting in the Verbal Forum - Rules for Posting in the Quant Forum[/size][/color][/b] Senior Manager Joined: 21 Jan 2010 Posts: 261 Re: In the xy plane, at what points does the graph of y= [#permalink] ### Show Tags 24 Apr 2013, 17:10 This question is a bit tricky , if you know the following it helps : Any quadratic equation represents a parabola in the x-y domain. here , the equation is y=(x+a)(x+b) . So the roots of the equation are -a,-b . So it cuts the x axis at -a and -b. 1) a+b = 1 -> Doesn't help since we have one equation with 2 variables. 2) Gives you one set of value for x and y. So you can get an equation in a and b. Combining 1 and 2 gives the answer to A and B. C wins. Intern Joined: 28 Jun 2011 Posts: 12 Re: In the xy plane, at what points does the graph of y= [#permalink] ### Show Tags 25 May 2014, 06:25 I thought $$(x+a)(x+b) = 0$$ can be transformed to $$x^2 + ab + 2abx$$ since $$(x+y)(x+y) = x^2 + y^2 + 2xy$$ CEO Joined: 11 Sep 2015 Posts: 3238 Location: Canada Re: In the xy plane, at what points does the graph of y= [#permalink] ### Show Tags 16 Jul 2016, 11:08 Top Contributor JimmyWorld wrote: In the xy plane, at what points does the graph of y=(x+a)(x+b) intersect the x-axis? (1) a + b = -1 (2) The graph intersects the y axis at (0,-6) Target question: At which two points of the graph does y=(x+a)(x+b) intersect the x-axis? IMPORTANT ASIDE ABOUT X-INTERCEPTS: Let's examine the point where a line (or curve) crosses the x-axis. At the point of intersection, the point is on the x-axis, which means that the y-coordinate of that point is 0. So, for example, to find where the line y=2x+3 crosses the x-axis, we let y=0 and solve for x. We get: 0 = 2x+3 When we solve this for x, we get x= -3/2. So, the line y=2x+3 crosses the x-axis at (-3/2, 0) Likewise, to determine the point where y = (x + a)(x + b) crosses the x axis, let y=0 and solve for x. We get: 0 = (x + a)(x + b), which means x=-a or x=-b This means that y = (x + a)(x + b) crosses the x axis at (-a, 0) and (-b, 0) So, to solve this question, we need the values of a and b Aside: y = (x + a)(x + b) is actually a parabola. This explains why it crosses the x axis at TWO points. Now let's rephrase the target question... REPHRASED target question: What are the values of a and b? Statement 1: a + b = -1 There's no way we can use this to determine the values of a and b. Since we can answer the target question with certainty, statement 1 is NOT SUFFICIENT Statement 2: The line intercepts the y axis at (0,-6) This tells us that when x = 0, y = -6 When we plug x = 0 and y = -6 into the equation y = (x + a)(x + b), we get -6 = (0 + a)(0 + b), which tells us that ab=-6 In other words, statement 2 is a fancy way to tell us that ab = -6 Since there's no way we can use this information to determine the values of a and b, statement 2 is NOT SUFFICIENT Statements 1 and 2 combined: Statement 1 tells us that a+b = -1 Statement 2 tells us that ab = -6 Rewrite equation 1 as a = -1 - b Then take equation 2 and replace a with (-1 - b) to get: (-1 - b)(b) = -6 Expand: -b - b^2 = -6 Set equal to zero: b^2 + b - 6 = 0 Factor: (b+3)(b-2) = 0 So, b= -3 or b= 2 When b = -3, a = 2 and when b = 2, a = -3 In both cases, the two points of intersection are (3, 0) and (-2, 0) Since we can answer the target question with certainty, the combined statements are SUFFICIENT Answer = RELATED VIDEOS _________________ Test confidently with gmatprepnow.com Senior Manager Joined: 02 Mar 2012 Posts: 310 Schools: Schulich '16 Re: In the xy plane, at what points does the graph of y= [#permalink] ### Show Tags 16 Jul 2016, 23:14 Answer is C my thinking is diff here you are given a quadratic equation of the form x^2+(a+b)x + ab 1)gives u sum of roots.insuff 2) gives u product of roots.iinsuff so easy C Manager Joined: 22 Feb 2016 Posts: 91 Location: India Concentration: Economics, Healthcare GMAT 1: 690 Q42 V47 GMAT 2: 710 Q47 V39 GPA: 3.57 Re: In the xy plane, at what points does the graph of y= [#permalink] ### Show Tags 14 Oct 2016, 20:12 This boils down to the classic case of sum of roots and product of roots. the equation is y=x^2+(a+B)x+ab where a+b is the sum of the roots and ab is the product of the roots. Statement 1: sum of roots= -1 NS Statement 2: product of roots=-6 NS Combining 1 & 2 we get the desired result. EMPOWERgmat Instructor Status: GMAT Assassin/Co-Founder Affiliations: EMPOWERgmat Joined: 19 Dec 2014 Posts: 13087 Location: United States (CA) GMAT 1: 800 Q51 V49 GRE 1: Q170 V170 Re: In the xy plane, at what points does the graph of y= [#permalink] ### Show Tags 25 Feb 2018, 14:39 Hi All, Like most questions on the GMAT, this question can be approached in a number of different ways. There's actually a great Algebra pattern/shortcut built into this question: We given the equation Y = (X+A)(X+B) and we're asked at what 2 points the graph will intersect with the X-axis. This essentially comes down to the A and B. If we know their values, then we can answer the question. It's also worth noting that since we're multiplying, you can "flip-flop" the values of A and B and you'd have the same solution. For example: (X+1)(X+2) is the same as (X+2)(X+1)…... 1) A + B = -1 There's no way to determine the exact values for A and B with this information. IF... A = 0, B = -1 A = 100, B = -101 Etc. Different numbers for A and B would lead to different solutions. Fact 1 is INSUFFICIENT 2) The graph intersects the Y-axis at (0, -6). Now we have one of the points on the graph. Plugging it into the original equation gives us…. -6 = (0+A)(0+B) -6 = AB We have the same situation as in Fact 1: more than 1 possible solution. A = 1, B = -6 A = 2, B = -3 Etc. Fact 2 is INSUFFICIENT Combined, we have… A + B = -1 AB = -6 Here's where things get interesting. This is a "system" of equations, so we CAN solve it...the "catch" is that the answers would "flip flop": If you did do the math, you'd have A = -3, B = 2 OR A = 2, B = -3 Since this is a graphing question, these two options provide the SAME solution. 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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13 Dec 2018, 08:18
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