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# If x and y are integers and x^2*y is a negative odd integer, which of

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Math Expert
Joined: 02 Sep 2009
Posts: 52295
If x and y are integers and x^2*y is a negative odd integer, which of  [#permalink]

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06 Dec 2016, 06:20
1
2
00:00

Difficulty:

45% (medium)

Question Stats:

64% (01:41) correct 36% (01:50) wrong based on 183 sessions

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If x and y are integers and x^2*y is a negative odd integer, which of the following must be true?

I. xy^2 is odd.
II. xy is negative.
III. x + y is even.

A. I only
B. III only
C. I and II only
D. I and III only
E. I, II, and III

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Joined: 25 Oct 2016
Posts: 1
Re: If x and y are integers and x^2*y is a negative odd integer, which of  [#permalink]

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06 Dec 2016, 17:27
x^2*y = negative odd integer

inference:
1. Odd * Odd = Odd
2. y is negative odd integer
3. x is odd (since its squared, the result is positive - so x could be either positive or negative).

Statement I - xy is odd, so is its sqaure - statement must be true
Statement II - xy may or may not be negative - statement may be true but NOT must
Statement III - x and y are odd, so Odd + Odd = Even - statement must be true

Answer is D - I and III only
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Re: If x and y are integers and x^2*y is a negative odd integer, which of  [#permalink]

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19 Jan 2017, 10:55
1
Great Question.
Here is what i did in this one ->

We are told that x^2*y<0
Hence x≠0 and y≠0
So as x^2 is always greater than 0.
Hence y<0.
Also as x^2*y is odd => x and y must be both odd.

Option 1->xy^2=> odd*odd^2=> odd.
True.
Option 2-> xy will be negative for x being positive and xy will be positive for x being negative.
Hence this statement is not always true.
Option 3->
x+y=> odd+odd=> even.
Hence this is True.

So the correct answer is D.

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Re: If x and y are integers and x^2*y is a negative odd integer, which of  [#permalink]

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17 Apr 2017, 03:44
Option D

x & y are integers such that x^2*y = Negative Odd integer.
i.e., y = Negative Odd integer & x = Negative or Positive Odd integer

I. xy^2 is odd. = True
II. xy is negative. = +ve or -ve
III. x + y is even. = True
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Re: If x and y are integers and x^2*y is a negative odd integer, which of  [#permalink]

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20 Apr 2017, 15:46
1
Bunuel wrote:
If x and y are integers and x^2*y is a negative odd integer, which of the following must be true?

I. xy^2 is odd.
II. xy is negative.
III. x + y is even.

A. I only
B. III only
C. I and II only
D. I and III only
E. I, II, and III

We are given that x and y are integers and that x^2*y is a negative odd integer. First, recall that odd x odd = odd. This means that x is odd, that x^2 is odd, and that y is odd.Second, we see that since x^2 is positive, then y must be negative, in order for the product x^2*y to be negative. With these facts in mind, we can now analyze each Roman numeral.

I. xy^2 is odd

Since both x and y must be odd, xy^2 is odd. Roman numeral I must be true.

II. xy is negative.

We determined that y must be negative, but we don’t have information about whether x is positive or negative. Roman numeral II does not have to be true.

III. x + y is even.

Recall that odd + odd = even. Since both x and y must be odd, we know that x + y must be even. Roman numeral III must be true.

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Re: If x and y are integers and x^2*y is a negative odd integer, which of &nbs [#permalink] 20 Apr 2017, 15:46
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