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# If x and y are integers and x − y is odd, which of the following must

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If x and y are integers and x − y is odd, which of the following must  [#permalink]

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30 Jul 2018, 00:26
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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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If x and y are integers and x − y is odd, which of the following must  [#permalink]

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30 Jul 2018, 01:08
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.

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Joined: 22 Dec 2010
Posts: 8
Re: If x and y are integers and x − y is odd, which of the following must  [#permalink]

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30 Jul 2018, 01:12
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

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Posts: 766
If x and y are integers and x − y is odd, which of the following must  [#permalink]

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30 Jul 2018, 02:55
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

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Re: If x and y are integers and x − y is odd, which of the following must  [#permalink]

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10 Aug 2018, 18:54
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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Re: If x and y are integers and x − y is odd, which of the following must &nbs [#permalink] 10 Aug 2018, 18:54
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