GMAT Changed on April 16th - Read about the latest changes here

 It is currently 24 May 2018, 18:35

### 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

# M25-35

Author Message
TAGS:

### Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 45367

### Show Tags

16 Sep 2014, 01:24
Expert's post
2
This post was
BOOKMARKED
00:00

Difficulty:

35% (medium)

Question Stats:

64% (01:01) correct 36% (00:53) wrong based on 220 sessions

### HideShow timer Statistics

If $$m$$ and $$n$$ are positive integers, then is $$m$$ an even integer?

(1) $$\frac{m}{n}$$ is an odd integer.

(2) $$m + n$$ is an even integer.

_________________
Math Expert
Joined: 02 Sep 2009
Posts: 45367

### Show Tags

16 Sep 2014, 01:24
Expert's post
1
This post was
BOOKMARKED
Official Solution:

(1) $$\frac{m}{n}$$ is an odd integer. Hence $$m=n*\text{odd}$$. Now, if $$n=\text{odd}$$ then $$m=\text{odd}$$ but if $$n=\text{even}$$ then $$m=\text{even}$$. Not sufficient.

(2) $$m+n$$ is an even integer. Either both are odd or both are even. Not sufficient.

(1)+(2) Still the same two cases are possible: either both are odd (for example $$m=3$$ and $$n=1$$) or both are even (for example $$m=2$$ and $$n=2$$). Not sufficient.

_________________
Senior Manager
Status: Math is psycho-logical
Joined: 07 Apr 2014
Posts: 423
Location: Netherlands
GMAT Date: 02-11-2015
WE: Psychology and Counseling (Other)

### Show Tags

30 Dec 2014, 09:02
Hey,

I didn't understand your point about [1]. This part in specific: Hence m=n*odd.

[1] says that m/n is odd and an integer. This should mean that m is a multiple of n, otherwise it wouldn't be an integer, right?
So, in order to have an integer as the answer, both m and n should be even or odd, with m>n.
But, since we now that it is odd, then both m and n should be odd, sth like 9/3=3. Which means that both m and n are odd, so we get that m is an odd integer and not an even integer. So, this is sufficient.

Where am I making the mistake..?
Math Expert
Joined: 02 Sep 2009
Posts: 45367

### Show Tags

31 Dec 2014, 04:52
pacifist85 wrote:
Hey,

I didn't understand your point about [1]. This part in specific: Hence m=n*odd.

[1] says that m/n is odd and an integer. This should mean that m is a multiple of n, otherwise it wouldn't be an integer, right?
So, in order to have an integer as the answer, both m and n should be even or odd, with m>n.
But, since we now that it is odd, then both m and n should be odd, sth like 9/3=3. Which means that both m and n are odd, so we get that m is an odd integer and not an even integer. So, this is sufficient.

Where am I making the mistake..?

This is very simple: $$\frac{m}{n}$$ is an odd integer --> $$\frac{m}{n}=odd$$ --> $$m=n*\text{odd}$$. If $$n=\text{odd}$$ then $$m=\text{odd}$$ (for example m=n=1) but if $$n=\text{even}$$ then $$m=\text{even}$$ (for example m=n=2). Not sufficient.
_________________
Senior Manager
Status: Math is psycho-logical
Joined: 07 Apr 2014
Posts: 423
Location: Netherlands
GMAT Date: 02-11-2015
WE: Psychology and Counseling (Other)

### Show Tags

31 Dec 2014, 05:23
Hmmm, I just saw my mistake. For some reason, I didn't think of options such as 10/2=5, 6/2=3, but only such as 4/2=2, 8/2=4. So, because my examples were of even numbers ending in another even number, I rejected the possibility of the integers being even. This is why picking numbers can sometimes be tricky...

Thank you.
Manager
Joined: 02 Jan 2016
Posts: 52

### Show Tags

12 May 2018, 23:29
Hi Bunuel,

I applied the generalized approach, Even No.* Even No. or Even No. * Odd No. = Even No.
The same outcomes are also applicable for division too, Because I had read about this rule somewhere, So I assumed, here as the outcome of Division is Odd, both No.s have to be Odd.

Is this rule for division correct ?
Math Expert
Joined: 02 Sep 2009
Posts: 45367

### Show Tags

13 May 2018, 00:34
hero_with_1000_faces wrote:
Hi Bunuel,

I applied the generalized approach, Even No.* Even No. or Even No. * Odd No. = Even No.
The same outcomes are also applicable for division too, Because I had read about this rule somewhere, So I assumed, here as the outcome of Division is Odd, both No.s have to be Odd.

Is this rule for division correct ?

Even/Even might be even, odd or not an integer at all. For example, 4/2 = 2 = even, 2/2 = 1 = odd, 2/4 = 1/2 = not an integer.

Even/odd might be even, or not an integer at all. For example, 6/3 = 2 = even, 4/3 = not an integer.

Odd/even is not an integer.

Odd/odd is either an odd integer or not an integer at all. 49/7 = 7 = odd and 7/49 is not an integer.
_________________
Re: M25-35   [#permalink] 13 May 2018, 00:34
Display posts from previous: Sort by

# M25-35

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®.