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# If x and y are integers and xy2 is a positive odd integer,

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Joined: 31 Oct 2007
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If x and y are integers and xy2 is a positive odd integer,  [#permalink]

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05 Mar 2008, 04:05
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100% (01:53) correct 0% (00:00) wrong based on 32 sessions

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16. If x and y are integers and xy2 is a positive odd integer, which of the following must be true?
Ⅰ. xy is positive.
Ⅱ. xy is odd.
Ⅲ. x + y is even.
(A) Ⅰ only
(B) Ⅱ only
(C) Ⅲ only
(D) Ⅰ and Ⅱ
(E) Ⅱ and Ⅲ

Care to explain?

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Jimmy Low, Frankfurt, Germany
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Posts: 466
Re: 1000PS: Section 2 Question 16  [#permalink]

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05 Mar 2008, 07:47
jimmylow wrote:
Care to explain?

maybe you could first explain what you mean by xy2? is it (x*y)^2?
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Joined: 29 Aug 2007
Posts: 1939
Re: 1000PS: Section 2 Question 16  [#permalink]

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05 Mar 2008, 07:51
jimmylow wrote:
16. If x and y are integers and xy2 is a positive odd integer, which of the following must be true?
Ⅰ. xy is positive.
Ⅱ. xy is odd.
Ⅲ. x + y is even.
(A) Ⅰ only
(B) Ⅱ only
(C) Ⅲ only
(D) Ⅰ and Ⅱ
(E) Ⅱ and Ⅲ

Care to explain?

if xy2 = xy^2, I, II and III.
if xy2 = (xy)^2, II and III.
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Joined: 31 Oct 2007
Posts: 93
Location: Frankfurt, Germany
Re: 1000PS: Section 2 Question 16  [#permalink]

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05 Mar 2008, 08:11
maratikus wrote:
jimmylow wrote:
Care to explain?

maybe you could first explain what you mean by xy2? is it (x*y)^2?

My apology. It should read x * y^2
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Manager
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Re: 1000PS: Section 2 Question 16  [#permalink]

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05 Mar 2008, 08:12
GMAT TIGER wrote:
jimmylow wrote:
16. If x and y are integers and xy2 is a positive odd integer, which of the following must be true?
Ⅰ. xy is positive.
Ⅱ. xy is odd.
Ⅲ. x + y is even.
(A) Ⅰ only
(B) Ⅱ only
(C) Ⅲ only
(D) Ⅰ and Ⅱ
(E) Ⅱ and Ⅲ

Care to explain?

if xy2 = xy^2, I, II and III.
if xy2 = (xy)^2, II and III.

Tiger, pls explain this - if xy2 = xy^2, I, II and III.
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Jimmy Low, Frankfurt, Germany
Blog: http://mytrainmaster.wordpress.com
GMAT Malaysia: http://gmatmalaysia.blogspot.com
Senior Manager
Joined: 01 Jan 2008
Posts: 466
Re: 1000PS: Section 2 Question 16  [#permalink]

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05 Mar 2008, 08:21
1
jimmylow wrote:
16. If x and y are integers and xy2 is a positive odd integer, which of the following must be true?
Ⅰ. xy is positive.
Ⅱ. xy is odd.
Ⅲ. x + y is even.
(A) Ⅰ only
(B) Ⅱ only
(C) Ⅲ only
(D) Ⅰ and Ⅱ
(E) Ⅱ and Ⅲ

Care to explain?

since x*y^2 is positive odd -> x is odd, x is positive, y is odd

I is not always true: (x,y) = (1,1) and (1,-1)
II is true because both numbers are odd
III is true because both numbers are odd

E
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Joined: 29 Aug 2007
Posts: 1939
Re: 1000PS: Section 2 Question 16  [#permalink]

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05 Mar 2008, 09:15
jimmylow wrote:
GMAT TIGER wrote:
jimmylow wrote:
16. If x and y are integers and xy2 is a positive odd integer, which of the following must be true?Ⅰ. xy is positive.Ⅱ. xy is odd.Ⅲ. x + y is even.

(A) Ⅰ only
(B) Ⅱ only
(C) Ⅲ only
(D) Ⅰ and Ⅱ
(E) Ⅱ and ⅢCare to explain?

if xy2 = xy^2, I, II and III.if xy2 = (xy)^2, II and III.

Tiger, pls explain this - if xy2 = xy^2, I, II and III.

I. agree with above.

II. Since x and y are integers and xy^2 is a positive odd integer, xy must be an odd integer. Since xy^2 is an odd integer, if either or x or y is even, xy^2 cannot be odd.

III. Since x and y are integers and xy^2 is a positive odd integer, (x+y) must be an even intger. from II, we know x and y both are odd integer. sum of two odd integer is even.

So II, III.
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Joined: 12 Feb 2008
Posts: 128
Re: 1000PS: Section 2 Question 16  [#permalink]

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05 Mar 2008, 11:46
maratikus wrote:
jimmylow wrote:
16. If x and y are integers and xy2 is a positive odd integer, which of the following must be true?
Ⅰ. xy is positive.
Ⅱ. xy is odd.
Ⅲ. x + y is even.
(A) Ⅰ only
(B) Ⅱ only
(C) Ⅲ only
(D) Ⅰ and Ⅱ
(E) Ⅱ and Ⅲ

Care to explain?

since x*y^2 is positive odd -> x is odd, x is positive, y is odd

I is not always true: (x,y) = (1,1) and (1,-1)
II is true because both numbers are odd
III is true because both numbers are odd

E

First take a look at what is given.
from xy^2 >0 and being prime we know that X and Y have to be both odd.
from here:

Ⅰ. xy is positive. y can be + or -
Ⅱ. xy is odd. Odd x Odd = Odd
Ⅲ. x + y is even odd +odd = even

E!!

--== Message from the GMAT Club Team ==--

THERE IS LIKELY A BETTER DISCUSSION OF THIS EXACT QUESTION.
This discussion does not meet community quality standards. It has been retired.

If you would like to discuss this question please re-post it in the respective forum. Thank you!

To review the GMAT Club's Forums Posting Guidelines, please follow these links: Quantitative | Verbal Please note - we may remove posts that do not follow our posting guidelines. Thank you.
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Re: If x and y are integers and xy2 is a positive odd integer,  [#permalink]

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17 Sep 2018, 01:37
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Re: If x and y are integers and xy2 is a positive odd integer,   [#permalink] 17 Sep 2018, 01:37
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