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If y is an even integer and x is an odd integer, which of the followin

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If y is an even integer and x is an odd integer, which of the followin  [#permalink]

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New post 13 Jun 2017, 08:47
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If y is an even integer and x is an odd integer, which of the following expressions could be an even integer?

(A) 3x + y/2
(B) (x + y)/2
(C) x + y
(D) x/4 − y/2
(E) x^2 + y^2

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If y is an even integer and x is an odd integer, which of the followin  [#permalink]

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New post Updated on: 13 Jun 2017, 09:28
Bunuel wrote:
If y is an even integer and x is an odd integer, which of the following expressions could be an even integer?

(A) 3x + y/2
(B) (x + y)/2
(C) x + y
(D) x/4 − y/2
(E) x^2 + y^2


Let \(y = 2\), \(x = 1\)

(A) \(3x + \frac{y}{2}\) = 3+ \(\frac{2}{2} = 3 + 1 = 4\) ---------- Even

(B) \(\frac{(x + y)}{2}\) = \(\frac{(1 + 2)}{2}\) = \(\frac{3}{2} = 1.5\)

(C) \(x + y = 1 + 2 = 3\)

(D) \(\frac{x}{4} − \frac{y}{2} = \frac{1}{4} - \frac{2}{2} = \frac{1}{4} - 1 = \frac{1-4}{4} = -\frac{3}{4} = -0.75\)

(E) \(x^2 + y^2 = 1^2 + 2^2 = 1 + 4 = 5\)

Answer A...

Originally posted by sashiim20 on 13 Jun 2017, 09:10.
Last edited by sashiim20 on 13 Jun 2017, 09:28, edited 1 time in total.
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If y is an even integer and x is an odd integer, which of the followin  [#permalink]

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New post 13 Jun 2017, 09:25
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1.Any even number divided by 2 will give an odd number
2.Any odd number multiplied by odd number gives another odd number.

Two odd numbers added give an even number.

Hence, Option A is the answer option!
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Re: If y is an even integer and x is an odd integer, which of the followin  [#permalink]

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New post 13 Jun 2017, 09:34
IMO A.

If x is 1 and y is 2, answer is 4 which is even
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Re: If y is an even integer and x is an odd integer, which of the followin  [#permalink]

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New post 17 Jun 2017, 03:25
pushpitkc wrote:
1.Any even number divided by 2 will give an odd number
2.Any odd number multiplied by odd number gives another odd number.

Two odd numbers added give an even number.

Hence, Option A is the answer option!



Hi!......i could not understand....If you take example of 4 divided by 2 then it will give 2 or take example of 8 divided by 2
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Re: If y is an even integer and x is an odd integer, which of the followin  [#permalink]

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New post 26 Jan 2018, 10:49
Bunuel wrote:
If y is an even integer and x is an odd integer, which of the following expressions could be an even integer?

(A) 3x + y/2
(B) (x + y)/2
(C) x + y
(D) x/4 − y/2
(E) x^2 + y^2


Notice the problem is a “could be” problem, not a “must be” problem. Let’s go through each answer choice, recalling that odd + odd = even, and odd + even = odd, and even + even = even.

A) 3x + y/2

3x is odd and y/2 could be odd (for example, if y = 6). Thus 3x + y/2 could be even.

The answer must be A. However, as an exercise, let’ verify that none of the other four choices could be even. That is, they will never be even.

B) (x + y)/2

x + y is odd and thus (x + y)/2 is not even an integer (no pun intended).

C) x + y

x + y is odd.

D) x/4 - y/2

x/4 is not an integer and y/2 is an integer, but their difference will not be an integer.

E) x^2 + y^2

x^2 is odd and y^2 is even, but their sum will be odd. Recall here that odd x odd = odd and even x even = even.

Answer: A
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Re: If y is an even integer and x is an odd integer, which of the followin  [#permalink]

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New post 26 Jan 2018, 11:59
pushpitkc wrote:
1.Any even number divided by 2 will give an odd number
2.Any odd number multiplied by odd number gives another odd number.

Two odd numbers added give an even number.

Hence, Option A is the answer option!


Hey 6 / 2 = 3 ( odd number ) but 8/2 &12/2 will give even number



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Re: If y is an even integer and x is an odd integer, which of the followin &nbs [#permalink] 26 Jan 2018, 11:59
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