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

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If x and y are different integers and x^2 = xy, which of the [#permalink]

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The Official Guide For GMAT® Quantitative Review, 2ND Edition

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

Problem Solving
Question: 106
Category: Arithmetic; Algebra Operations on rational numbers; Second-degree equations
Page: 75
Difficulty: 600


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Re: If x and y are different integers and x^2 = xy, which of the [#permalink]

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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

\(x^2=xy\) --> \(x(x-y)=0\) --> 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.
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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

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Re: If x and y are different integers and x^2 = xy, which of the [#permalink]

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New post 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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New post 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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New post 22 Feb 2014, 06:14
Expert's post
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

\(x^2=xy\) --> \(x(x-y)=0\) --> 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.
_________________

New to the Math Forum?
Please read this: 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?
Extra-hard Quant Tests with Brilliant Analytics

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Re: If x and y are different integers and x^2 = xy, which of the [#permalink]

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Re: If x and y are different integers and x^2 = xy, which of the   [#permalink] 28 Sep 2015, 21:11
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