GMAT Question of the Day - Daily to your Mailbox; hard ones only

 It is currently 23 Jun 2018, 07:01

### GMAT Club Daily Prep

#### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

# Events & Promotions

###### Events & Promotions in June
Open Detailed Calendar

# M22-33

Author Message
TAGS:

### Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 46295

### Show Tags

16 Sep 2014, 01:17
00:00

Difficulty:

85% (hard)

Question Stats:

41% (00:54) correct 59% (00:31) wrong based on 132 sessions

### HideShow timer Statistics

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. $$(x + 1)(y - 1)$$

_________________
Math Expert
Joined: 02 Sep 2009
Posts: 46295

### Show Tags

16 Sep 2014, 01:17
1
1
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.

_________________
Intern
Joined: 04 Mar 2010
Posts: 9

### Show Tags

18 Apr 2015, 16:16
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?
Math Expert
Joined: 02 Sep 2009
Posts: 46295

### Show Tags

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
_________________
Intern
Joined: 24 Jul 2017
Posts: 19
Location: Germany
GMAT 1: 710 Q48 V39
WE: Research (Energy and Utilities)

### Show Tags

15 Aug 2017, 16:10
Option 2 in the question looks like a Mixed fraction and not 2*(x/y)
Intern
Joined: 19 Oct 2017
Posts: 25

### Show Tags

07 Feb 2018, 06:53
Bunuel wrote:
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.

Hello. How can I know the difficulty level of this or any other quant question (part of gmat club test)?

Sent from my Redmi Note 4 using GMAT Club Forum mobile app
Math Expert
Joined: 02 Sep 2009
Posts: 46295

### Show Tags

07 Feb 2018, 06:57
HarshBazooka wrote:
Bunuel wrote:
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.

Hello. How can I know the difficulty level of this or any other quant question (part of gmat club test)?

Sent from my Redmi Note 4 using GMAT Club Forum mobile app

You can check the stats in the original post:
Attachment:
2018-02-07_1755.png

>> !!!

You do not have the required permissions to view the files attached to this post.

_________________
Intern
Joined: 11 Aug 2017
Posts: 5
WE: Account Management (Energy and Utilities)

### Show Tags

07 Feb 2018, 11:42
I used test cases and got down to two answer choices: A and D. I couldn't find an example of two even integers that disproved A?

Math Expert
Joined: 02 Sep 2009
Posts: 46295

### Show Tags

07 Feb 2018, 11:55
DouglassJensen wrote:
I used test cases and got down to two answer choices: A and D. I couldn't find an example of two even integers that disproved A?

Consider x = 2 and y = 0 --> 2^0 = 1 = odd.

(non-zero integer)^0 = 1 = odd.
_________________
Senior Manager
Joined: 31 May 2017
Posts: 282

### Show Tags

08 Feb 2018, 20:51
After initial analysis , answer choices narrowed down to A and D. The option "0" was the caveat in the choice A which made the only possible option is D.

Thanks Bunuel for clear explanation as always
_________________

Please give kudos if it helps

Resources
| | | | |

Re: M22-33   [#permalink] 08 Feb 2018, 20:51
Display posts from previous: Sort by

# M22-33

Moderators: chetan2u, Bunuel

 Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.