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

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

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New post 05 Mar 2008, 03:05
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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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Re: 1000PS: Section 2 Question 16  [#permalink]

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New post 05 Mar 2008, 06:47
jimmylow wrote:
Care to explain?


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

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New post 05 Mar 2008, 06:51
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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Re: 1000PS: Section 2 Question 16  [#permalink]

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New post 05 Mar 2008, 07:11
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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Re: 1000PS: Section 2 Question 16  [#permalink]

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New post 05 Mar 2008, 07:12
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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Re: 1000PS: Section 2 Question 16  [#permalink]

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New post 05 Mar 2008, 07:21
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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Re: 1000PS: Section 2 Question 16  [#permalink]

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New post 05 Mar 2008, 08:15
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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Re: 1000PS: Section 2 Question 16  [#permalink]

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New post 05 Mar 2008, 10:46
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 ==--

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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!

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Re: If x and y are integers and xy2 is a positive odd integer,  [#permalink]

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Re: If x and y are integers and xy2 is a positive odd integer, &nbs [#permalink] 17 Sep 2018, 00:37
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