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Math Expert V
Joined: 02 Sep 2009
Posts: 60647
If x and y are integers and x − y is odd, which of the following must  [#permalink]

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1
9 00:00

Difficulty:   5% (low)

Question Stats: 80% (01:08) correct 20% (01:15) wrong based on 631 sessions

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If x and y are integers and x − y is odd, which of the following must be true?

I. xy is even.
II. x^2 + y^2 is odd.
II. (x + y)^2 is even.

A. I only
B. II only
C. III only
D. I and II only
E. I, II, and III

NEW question from GMAT® Quantitative Review 2019

(PS01120)

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VP  D
Joined: 31 Oct 2013
Posts: 1493
Concentration: Accounting, Finance
GPA: 3.68
WE: Analyst (Accounting)
If x and y are integers and x − y is odd, which of the following must  [#permalink]

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Bunuel wrote:
If x and y are integers and x − y is odd, which of the following must be true?

I. xy is even.
II. x^2 + y^2 is odd.
II. (x + y)^2 is even.

A. I only
B. II only
C. III only
D. I and II only
E. I, II, and III

NEW question from GMAT® Quantitative Review 2019

(PS01120)

Given

x - y = odd

In this case either x or y must be even and another must be odd.

I. xy = even. True . (3*2)= 6

II.$$x^2 + y^2 = odd$$. True. $$(2)^2 + (3)^2 = 13$$

III. $$(3+2)^2 = 25$$ . False.

Intern  B
Joined: 22 Dec 2010
Posts: 13
Location: India
GMAT 1: 750 Q49 V44 GPA: 3.7
Re: If x and y are integers and x − y is odd, which of the following must  [#permalink]

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D...odd-even or even-odd is odd...
I. One is even so xy will be even
II. Odd+even is odd/ even +odd is odd
III... Odd+even is odd ...sqaure can't be even ..will be odd

Sent from my MI MAX 2 using GMAT Club Forum mobile app
VP  D
Joined: 09 Mar 2016
Posts: 1223
If x and y are integers and x − y is odd, which of the following must  [#permalink]

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Bunuel wrote:
If x and y are integers and x − y is odd, which of the following must be true?

I. xy is even.
II. x^2 + y^2 is odd.
II. (x + y)^2 is even.

A. I only
B. II only
C. III only
D. I and II only
E. I, II, and III

NEW question from GMAT® Quantitative Review 2019

(PS01120)

IMO D must be correct answer Let X = 7 and Y = 2

I. xy is even ( 7*2 = 14 ) correct II. x^2 + y^2 is odd. $$7^2+2^2 = 53$$ TRUE

II. (x + y)^2 is even. $$(7+ 2)^2 = 49+4 =53$$ FALSE

EDIT
Target Test Prep Representative V
Status: Founder & CEO
Affiliations: Target Test Prep
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Posts: 9142
Location: United States (CA)
Re: If x and y are integers and x − y is odd, which of the following must  [#permalink]

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1
Bunuel wrote:
If x and y are integers and x − y is odd, which of the following must be true?

I. xy is even.
II. x^2 + y^2 is odd.
II. (x + y)^2 is even.

A. I only
B. II only
C. III only
D. I and II only
E. I, II, and III

The only way to get an odd sum or difference of two integers is if one integer is odd and the other integer is even. Since x - y is odd, then x is even and y is odd OR x is odd and y is even.

We recall that even x odd = even. Thus, xy must be even. Thus, Roman numeral I is true.

Since odd + even = odd, we see that x^2 + y^2 must be odd, and (x + y)^2 must be odd. Thus, Roman numeral II is true and Roman numeral III is false.

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Director  G
Joined: 19 Oct 2013
Posts: 511
Location: Kuwait
GPA: 3.2
WE: Engineering (Real Estate)
Re: If x and y are integers and x − y is odd, which of the following must  [#permalink]

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Bunuel wrote:
If x and y are integers and x − y is odd, which of the following must be true?

I. xy is even.
II. x^2 + y^2 is odd.
II. (x + y)^2 is even.

A. I only
B. II only
C. III only
D. I and II only
E. I, II, and III

NEW question from GMAT® Quantitative Review 2019

(PS01120)

Can be solved much faster and without any substitution if we know that even - odd = odd. From this we know that one number must be even. What applies to subtraction in terms of even/odd applies to addition.

even * odd = even

Having a power does not change whether the number is odd or even.

only I and II are true.
Manager  B
Joined: 10 Sep 2019
Posts: 54
Location: India
Concentration: Social Entrepreneurship, Healthcare
GMAT 1: 690 Q49 V34
GPA: 2.6
WE: Project Management (Non-Profit and Government)
Re: If x and y are integers and x − y is odd, which of the following must  [#permalink]

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Input numbers 3&2 and 5&2.

Smash D
e-GMAT Representative V
Joined: 04 Jan 2015
Posts: 3222
Re: If x and y are integers and x − y is odd, which of the following must  [#permalink]

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Given
• x and y are integers and x − y is odd
o One of x and y is even and another is odd.

To find
• The correct option.

Approach and Working out

I – xy is even
• Multiplication of one even and one integer is always even.

II - x^2 + y^2 is odd.
• Even ^2 + Odd^2 = Even + Odd = Odd

III - (x + y)^2 is even.
• Odd^2 = Odd
• Not true

Thus, option D is the correct answer.

_________________ Re: If x and y are integers and x − y is odd, which of the following must   [#permalink] 25 Nov 2019, 20:24
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