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If x and y are different integers and x^2 = xy, which of the [#permalink]
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21 Feb 2014, 01:00
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The Official Guide For GMAT® Quantitative Review, 2ND EditionIf x and y are different integers and x^2 = xy, which of the following must be true? I. x = 0 II. y = 0 III. x = y (A) l only (B) II only (C) III only (D) I and III only (E) I, II, and III Problem Solving Question: 106 Category: Arithmetic; Algebra Operations on rational numbers; Seconddegree equations Page: 75 Difficulty: 600 GMAT Club is introducing a new project: The Official Guide For GMAT® Quantitative Review, 2ND Edition  Quantitative Questions ProjectEach week we'll be posting several questions from The Official Guide For GMAT® Quantitative Review, 2ND Edition and then after couple of days we'll provide Official Answer (OA) to them along with a slution. We'll be glad if you participate in development of this project: 1. Please provide your solutions to the questions; 2. Please vote for the best solutions by pressing Kudos button; 3. Please vote for the questions themselves by pressing Kudos button; 4. Please share your views on difficulty level of the questions, so that we have most precise evaluation. Thank you!
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Re: If x and y are different integers and x^2 = xy, which of the [#permalink]
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21 Feb 2014, 01:01
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Re: If x and y are different integers and x^2 = xy, which of the [#permalink]
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21 Feb 2014, 02:18
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Given Facts  1. x and y are different integers 2. x^2 = xy
I  x=0 then x^2 = 0 and xy = 0 , for any value of y thus x^2 = xy  True for any value of y
II  y = 0 if x=1 then x^2 = 1 and xy = 0 Thus x^2 not equal to xy and thus not true for any value of x
III  x = y x^2 = (y)^2 = y^2 xy = (y)*(y)=y^2 Thus x^2 not equal to xy and thus not true for any value of x,y
Hence since I only is true for all values Option (A) is the correct answer.



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Re: If x and y are different integers and x^2 = xy, which of the [#permalink]
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21 Feb 2014, 09:35
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If x and y are different integers and x^2 = xy, which of the following must be true?
I. x = 0 II. y = 0 III. x = y
Sol.: From the question stem, x^2 – xy = 0 x ( x – y) = 0 ⇨ Either x = 0 or x = y Since x and y are two different integers, => x= 0. Hence (A)



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Re: If x and y are different integers and x^2 = xy, which of the [#permalink]
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09 Apr 2018, 08:13
Bunuel wrote: SOLUTION
If x and y are different integers and x^2 = xy, which of the following must be true?
I. x = 0 II. y = 0 III. x = y
(A) l only (B) II only (C) III only (D) I and III only (E) I, II, and III
\(x^2=xy\) > \(x(xy)=0\) > either \(x=0\) or \(x=y\) but as given that \(x\) and \(y\) are different numbers than the second option is out and we have: \(x=0\). So only I is always true (in fact because of the same reason that \(x\) and \(y\) are different numbers II and III are never true).
Answer: A. Bunuel why this option is not valid III. x = y if y = 2 and x= y > x = 2 then \(2^2 = (2*)(2)\) > \(4 =4\) can you explain ? pleaese



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If x and y are different integers and x^2 = xy, which of the [#permalink]
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09 Apr 2018, 08:26
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dave13 wrote: Bunuel wrote: SOLUTION
If x and y are different integers and x^2 = xy, which of the following must be true?
I. x = 0 II. y = 0 III. x = y
(A) l only (B) II only (C) III only (D) I and III only (E) I, II, and III
\(x^2=xy\) > \(x(xy)=0\) > either \(x=0\) or \(x=y\) but as given that \(x\) and \(y\) are different numbers than the second option is out and we have: \(x=0\). So only I is always true (in fact because of the same reason that \(x\) and \(y\) are different numbers II and III are never true).
Answer: A. Bunuel why this option is not valid III. x = y if y = 2 and x= y > x = 2 then \(2^2 = (2*)(2)\) > \(4 =4\) can you explain ? pleaese This does not make sense. If y = 2 and x = y, then x = (2) = 2. What x= y has to do with this? x = y is not possible at all because the stem says that x and y are different integers... Also, the question asks which of the following MUST be true not COULD be true. Even if there would exist x and y, for which x = y, would satisfy the stem, still this would not be sufficient to say that III MUST be true. MUST be true means true for ALL possible values, not for some specific values only. Finally, you should be careful with brackets. It's math, they DO matter. 2^2 means (2^2) = 4, while (2)^2 = 4.
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New to the Math Forum? Please read this: Ultimate GMAT Quantitative Megathread  All You Need for Quant  PLEASE READ AND FOLLOW: 12 Rules for Posting!!! Resources: GMAT Math Book  Triangles  Polygons  Coordinate Geometry  Factorials  Circles  Number Theory  Remainders; 8. Overlapping Sets  PDF of Math Book; 10. Remainders  GMAT Prep Software Analysis  SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS)  Tricky questions from previous years.
Collection of Questions: PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.
What are GMAT Club Tests? Extrahard Quant Tests with Brilliant Analytics




If x and y are different integers and x^2 = xy, which of the
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