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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] New post 21 Feb 2014, 00:00
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A
B
C
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E

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  25% (medium)

Question Stats:

73% (01:59) correct 27% (01:03) wrong based on 101 sessions
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] New post 21 Feb 2014, 00:01
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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.
_________________

NEW TO MATH FORUM? PLEASE READ THIS: ALL YOU NEED FOR QUANT!!!

PLEASE READ AND FOLLOW: 11 Rules for Posting!!!

RESOURCES: [GMAT MATH BOOK]; 1. Triangles; 2. Polygons; 3. Coordinate Geometry; 4. Factorials; 5. Circles; 6. Number Theory; 7. Remainders; 8. Overlapping Sets; 9. PDF of Math Book; 10. Remainders; 11. GMAT Prep Software Analysis NEW!!!; 12. SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) NEW!!!; 12. Tricky questions from previous years. NEW!!!;

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.


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Re: If x and y are different integers and x^2 = xy, which of the [#permalink] New post 21 Feb 2014, 01:18
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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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GMAT Date: 09-27-2014
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Re: If x and y are different integers and x^2 = xy, which of the [#permalink] New post 21 Feb 2014, 08:35
1
This post received
KUDOS
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] New post 22 Feb 2014, 05:14
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 MATH FORUM? PLEASE READ THIS: ALL YOU NEED FOR QUANT!!!

PLEASE READ AND FOLLOW: 11 Rules for Posting!!!

RESOURCES: [GMAT MATH BOOK]; 1. Triangles; 2. Polygons; 3. Coordinate Geometry; 4. Factorials; 5. Circles; 6. Number Theory; 7. Remainders; 8. Overlapping Sets; 9. PDF of Math Book; 10. Remainders; 11. GMAT Prep Software Analysis NEW!!!; 12. SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) NEW!!!; 12. Tricky questions from previous years. NEW!!!;

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?
25 extra-hard Quant Tests

Get the best GMAT Prep Resources with GMAT Club Premium Membership

Re: If x and y are different integers and x^2 = xy, which of the   [#permalink] 22 Feb 2014, 05:14
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