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x and y are positive integers. If xy + x is odd, then which of the

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x and y are positive integers. If xy + x is odd, then which of the  [#permalink]

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New post 19 Aug 2016, 03:07
3
4
00:00
A
B
C
D
E

Difficulty:

  25% (medium)

Question Stats:

74% (01:19) correct 26% (01:48) wrong based on 259 sessions

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x and y are positive integers. If xy + x is odd, then which of the  [#permalink]

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New post 19 Aug 2016, 04:15
Bunuel wrote:
x and y are positive integers. If xy + x is odd, then which of the following must be even?

A. x
B. y
C. x + y
D. xy − x
E. x^2 − y


x y xy + x
1 2 3 odd
2 1 4 Even case
2 3 5 Even
5 2 15 odd
3 3 12 even

IMO option B is correct.

OA please..let me know if I am missing anything...
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Re: x and y are positive integers. If xy + x is odd, then which of the  [#permalink]

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New post 19 Aug 2016, 06:05
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Top Contributor
Bunuel wrote:
x and y are positive integers. If xy + x is odd, then which of the following must be even?

A. x
B. y
C. x + y
D. xy − x
E. x^2 − y


Some important rules regarding the products of evens and odds:
1. (ODD)(ODD) = ODD
2. (ODD)(EVEN) = EVEN
3. (EVEN)(EVEN) = EVEN
4. ODD +/- ODD = EVEN
5. ODD +/- EVEN = ODD
6. EVEN +/- EVEN = EVEN

As we can see from #1, IF the product of two integers is ODD, then the two integers must both be odd.

Given: xy + x is ODD
If we FACTOR xy + x, we get x(y + 1)
So, we're told that x(y + 1) is ODD
From rule #1 above, we can conclude that x is ODD and (y + 1) is ODD
If (y + 1) is odd, then we can be certain that y is EVEN

Now check the answer choices:
A. x = ODD
B. y = EVEN (done!!)
C. x + y = ODD + EVEN = ODD
D. xy − x = (ODD)(EVEN) - ODD = EVEN - ODD = ODD
E. x^2 − y = (ODD)(ODD) - EVEN = ODD - EVEN = ODD

Answer:

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Re: x and y are positive integers. If xy + x is odd, then which of the  [#permalink]

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New post 20 Aug 2016, 02:04
xy+ x= odd

Two possibilities:
(1) even + odd = odd
(2) odd + even= odd
In this case, x can not be even as it will make xy also even .
Therefore, (1) possibility present => y must be even.

Answer: B
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Re: x and y are positive integers. If xy + x is odd, then which of the  [#permalink]

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New post 22 Aug 2016, 01:33
Given that xy + x is odd, which means x(y+1) is odd.
Product of two nos. will be odd only if both the nos. are odd.
Hence x is odd, y+1 is also odd.
y+1 is odd means y is even. Answer will be B.
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Re: x and y are positive integers. If xy + x is odd, then which of the  [#permalink]

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New post 17 Apr 2017, 03:51
Option B

x & y are Positive Integers. Odd: O, Even: E & Fraction: F.
xy + x = O
i.e., x = O & y = E
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Re: x and y are positive integers. If xy + x is odd, then which of the  [#permalink]

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New post 20 Apr 2017, 16:56
1
Bunuel wrote:
x and y are positive integers. If xy + x is odd, then which of the following must be even?

A. x
B. y
C. x + y
D. xy − x
E. x^2 − y


We are given that x and y are positive integers and that xy + x is odd, or x(y + 1) is odd, which means that x is odd and y is even. Thus, y MUST be even.

Answer: B
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Re: x and y are positive integers. If xy + x is odd, then which of the  [#permalink]

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Re: x and y are positive integers. If xy + x is odd, then which of the   [#permalink] 12 May 2018, 08:34
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