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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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New post 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


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(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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New post 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.

The best answer is D.
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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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New post 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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If x and y are integers and x − y is odd, which of the following must  [#permalink]

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New post 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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New post 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.

Answer: D
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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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