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If positive integers x and y are not both odd, which of the

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If positive integers x and y are not both odd, which of the  [#permalink]

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New post 10 Jan 2014, 07:04
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The Official Guide For GMAT® Quantitative Review, 2ND Edition

If positive integers x and y are not both odd, which of the following must be even?

(A) xy
(B) x + y
(C) x - y
(D) x + y -1
(E) 2(x + y) - 1

Problem Solving
Question: 31
Category: Arithmetic Properties of numbers
Page: 65
Difficulty: 600


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Re: If positive integers x and y are not both odd, which of the  [#permalink]

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New post 10 Jan 2014, 07:04
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Re: If positive integers x and y are not both odd, which of the  [#permalink]

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New post 10 Jan 2014, 11:01
Bunuel wrote:
The Official Guide For GMAT® Quantitative Review, 2ND Edition

If positive integers x and y are not both odd, which of the following must be even?

(A) xy
(B) x + y
(C) x - y
(D) x + y -1
(E) 2(x + y) - 1



If x and y are both odd, either one of them is odd or both are even.
In any case xy will always have a factor of 2 and hence even - Option A)
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Re: If positive integers x and y are not both odd, which of the  [#permalink]

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New post 11 Jan 2014, 06:52
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Re: If positive integers x and y are not both odd, which of the  [#permalink]

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New post 11 Jan 2014, 09:47
Answer A

xy where either x or y is even : even x any number =even

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Re: If positive integers x and y are not both odd, which of the  [#permalink]

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New post 11 Jan 2014, 11:40
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Even +/- odd= odd
Even +/- even= even
Odd +/- odd = even

Even * even= even
Even * odd= even
Odd * odd= odd

X & Y could be both even or one odd and one even=> x*y= even always.
Ans.A

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Re: If positive integers x and y are not both odd, which of the  [#permalink]

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New post 18 Mar 2014, 05:17
Bunuel wrote:
SOLUTION

If positive integers x and y are not both odd, which of the following must be even?

(A) xy
(B) x + y
(C) x - y
(D) x + y -1
(E) 2(x + y) - 1

Positive integers x and y are NOT both odd, means that either both x and y are even or one is even and the other one is odd. In either case xy must be even.

Answer: A.


I am sorry but i disagree as x and y are not both odd means that either one of them is odd i.e. x or y is odd which implies the one that is not odd is even. so basically x is odd and y is even or x is even and y is odd.
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Re: If positive integers x and y are not both odd, which of the  [#permalink]

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New post 18 Mar 2014, 05:33
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havoc7860 wrote:
Bunuel wrote:
SOLUTION

If positive integers x and y are not both odd, which of the following must be even?

(A) xy
(B) x + y
(C) x - y
(D) x + y -1
(E) 2(x + y) - 1

Positive integers x and y are NOT both odd, means that either both x and y are even or one is even and the other one is odd. In either case xy must be even.

Answer: A.


I am sorry but i disagree as x and y are not both odd means that either one of them is odd i.e. x or y is odd which implies the one that is not odd is even. so basically x is odd and y is even or x is even and y is odd.


Nope. x and y are not both odd means that:

(i) Both x and y are even;
OR:
(ii) One of x or y is even, the other odd.
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Re: If positive integers x and y are not both odd, which of the  [#permalink]

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New post 19 Jan 2017, 05:32
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Re: If positive integers x and y are not both odd, which of the  [#permalink]

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New post 19 Jan 2017, 16:52
E x E or E x O = Even
2x3 or 2x2 = E
A
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Re: If positive integers x and y are not both odd, which of the  [#permalink]

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New post 17 Apr 2017, 03:36
Option A

x = Odd & Y = Even "or" x = Even & y = Odd "or" x = Even & y = Even. Odd: O, Even: E & Fraction: F.

(A) xy =O*E = E*O = E
(B) x + y = O + E = E + O = O
(C) x - y = E - O or O - E or E - E = O or O or E
(D) x + y -1 = O + E - 1 or E + O - 1 or E + E -1 = O -1 or O - 1 or E - 1 = E or E or O
(E) 2(x + y) - 1 = 2(O+E) - 1 = E - 1 = O
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If positive integers x and y are not both odd, which of the  [#permalink]

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New post 29 Apr 2017, 08:34
Bunuel wrote
Quote:
If positive integers x and y are not both odd, which of the following must be even?

(A) xy
(B) x + y
(C) x - y
(D) x + y -1
(E) 2(x + y) - 1


I took a mostly similar approach, but also tested values, which often help me to track on even and odd rules.

If x and y are not both odd:

O O is NOT a possibility - list the possibilities that ARE allowed
E E okay.
E O, or O E, okay.

So 1) x and y are both even; or 2) one is odd and the other is even.

And: What if x and y ARE both odd?

Property often tested: only odd * odd = odd. Just one even factor means product is even.

Here we have at least one even factor and possibly two. E x O = E, E x E = E. Answer A jumped out.

Decided to test values to be sure. Eliminated three choices with x=4, y=3

(A) xy: 4 x 3 =12. Even. Because I think this is the answer, I try the other possibility: both x and y are even. If x=4 and y=2, xy=8. Both answers, even. KEEP

(B) (x+y): 4 + 3 = 7. Odd. Eliminate.

(C) (x-y): 4-3=1. Odd. Eliminate.

(D) (x+ y-1): 4+3-1=6, even. Keep for the moment. I want to see whether or not I can eliminate E before I pick new numbers.

(E) 2(x+y)-1: 3+4=7, 2(7) - 1 = 13. Odd. Eliminate.

Left with A and D, but haven't tried different variables for D. Use different numbers, both even. If x=4 and y=2, 4+2-1=5. Odd. Eliminate. Answer A
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Re: If positive integers x and y are not both odd, which of the  [#permalink]

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Re: If positive integers x and y are not both odd, which of the   [#permalink] 08 Jul 2018, 12:43
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