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# M22-33

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Math Expert
Joined: 02 Sep 2009
Posts: 41884

Kudos [?]: 128932 [0], given: 12183

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16 Sep 2014, 01:17
00:00

Difficulty:

45% (medium)

Question Stats:

55% (01:27) correct 45% (00:38) wrong based on 31 sessions

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If $$x$$ and $$y$$ are even integers, which of the following must also be an even integer?

A. $$x^y$$
B. $$2\frac{x}{y}$$
C. $$\frac{x - y}{x + y}$$
D. $$\frac{x^2 - y^2}{2}$$
E. $$(x + 1)(y - 1)$$
[Reveal] Spoiler: OA

_________________

Kudos [?]: 128932 [0], given: 12183

Math Expert
Joined: 02 Sep 2009
Posts: 41884

Kudos [?]: 128932 [0], given: 12183

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16 Sep 2014, 01:17
Official Solution:

If $$x$$ and $$y$$ are even integers, which of the following must also be an even integer?

A. $$x^y$$
B. $$2\frac{x}{y}$$
C. $$\frac{x - y}{x + y}$$
D. $$\frac{x^2 - y^2}{2}$$
E. $$(x + 1)(y - 1)$$

$$\frac{x^2 - y^2}{2} = \frac{(x - y)(x + y)}{2} = \frac{even*even}{2} = even*integer = even$$.

$$x^y$$ is 1 if $$y = 0$$ and $$x$$ is positive.

$$2*\frac{x}{y}$$ is 1 if $$x = 2$$ and $$y = 4$$.

$$\frac{x - y}{x + y}$$ might not be an integer at all.

$$(x + 1)(y - 1)$$ is always odd.

_________________

Kudos [?]: 128932 [0], given: 12183

Intern
Joined: 04 Mar 2010
Posts: 9

Kudos [?]: 20 [0], given: 1

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18 Apr 2015, 16:16
1
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Here, if x=y (Question didn't say that x and y are different, so we can consider this use case as well), then option (D) becomes 0/2 =0, which is not an even integer. Can you please let me know your thoughts on this?

Kudos [?]: 20 [0], given: 1

Math Expert
Joined: 02 Sep 2009
Posts: 41884

Kudos [?]: 128932 [0], given: 12183

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19 Apr 2015, 03:47
reddyMBA wrote:
Here, if x=y (Question didn't say that x and y are different, so we can consider this use case as well), then option (D) becomes 0/2 =0, which is not an even integer. Can you please let me know your thoughts on this?

You should brush up fundamentals before attempting questions.

ZERO:

1. 0 is an integer.

2. 0 is an even integer. An even number is an integer that is "evenly divisible" by 2, i.e., divisible by 2 without a remainder and as zero is evenly divisible by 2 then it must be even.

3. 0 is neither positive nor negative integer (the only one of this kind).

4. 0 is divisible by EVERY integer except 0 itself.

Check more here: tips-and-hints-for-specific-quant-topics-with-examples-172096.html#p1371030
_________________

Kudos [?]: 128932 [0], given: 12183

Intern
Joined: 24 Jul 2017
Posts: 7

Kudos [?]: 7 [0], given: 10

Location: Germany
GMAT 1: 710 Q48 V39
WE: Research (Energy and Utilities)

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15 Aug 2017, 16:10
Option 2 in the question looks like a Mixed fraction and not 2*(x/y)

Kudos [?]: 7 [0], given: 10

Re: M22-33   [#permalink] 15 Aug 2017, 16:10
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# M22-33

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