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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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29 Jul 2018, 23:26
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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, 00:08
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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30 Jul 2018, 00:12
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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30 Jul 2018, 01:55
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, 17:54
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.

Answer: 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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16 Oct 2018, 13:02
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.
Re: If x and y are integers and x − y is odd, which of the following must   [#permalink] 16 Oct 2018, 13:02
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If x and y are integers and x − y is odd, which of the following must

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