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

 It is currently 14 Dec 2018, 18:23

### 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 December
PrevNext
SuMoTuWeThFrSa
2526272829301
2345678
9101112131415
16171819202122
23242526272829
303112345
Open Detailed Calendar
• ### Typical Day of a UCLA MBA Student - Recording of Webinar with UCLA Adcom and Student

December 14, 2018

December 14, 2018

10:00 PM PST

11:00 PM PST

Carolyn and Brett - nicely explained what is the typical day of a UCLA student. I am posting below recording of the webinar for those who could't attend this session.
• ### Free GMAT Strategy Webinar

December 15, 2018

December 15, 2018

07:00 AM PST

09:00 AM PST

Aiming to score 760+? Attend this FREE session to learn how to Define your GMAT Strategy, Create your Study Plan and Master the Core Skills to excel on the GMAT.

# If a and b are positive integers such that a-b and a/b are

Author Message
Manager
Joined: 23 Nov 2008
Posts: 73
If a and b are positive integers such that a-b and a/b are  [#permalink]

### Show Tags

Updated on: 14 Sep 2014, 14:39
3
10
00:00

Difficulty:

95% (hard)

Question Stats:

51% (01:11) correct 49% (01:47) wrong based on 250 sessions

### HideShow timer Statistics

If a and b are positive integers such that a-b and a/b are both even integers, which of the following must be an odd integer?

A. a/2
B. b/2
C. (a+b)/2
D. (a+2)/2
E. (b+2)/2

I dont understand the answer choices here.
If I substitute 8 and 4 for a and b, i get both D&E as odd.
If I assume D&E to be even, both A and B need to be odd.
I just gave up and guessed C (not saying C is the OA)

OPEN DISCUSSION OF THIS QUESTION IS HERE: if-a-and-b-are-positive-integers-such-that-a-b-and-a-b-are-88108.html

Originally posted by twilight on 25 Nov 2008, 05:00.
Last edited by Bunuel on 14 Sep 2014, 14:39, edited 1 time in total.
Renamed the topic, edited the question, added the OA and moved to PS forum.
Manager
Joined: 15 Oct 2008
Posts: 90
Re: If a and b are positive integers such that a-b and a/b are  [#permalink]

### Show Tags

25 Nov 2008, 05:33
twilight wrote:
If a and b are positive integers such that a-b and a/b are both even integers, which of the following must be an odd integer?

A. a/2
B. b/2
C. (a+b)/2
D. (a+2)/2
E. (b+2)/2

I dont understand the answer choices here.
If I substitute 8 and 4 for a and b, i get both D&E as odd.
If I assume D&E to be even, both A and B need to be odd.
I just gave up and guessed C (not saying C is the OA)

I do not have the answer yet but I would like to comment on your reasoning. I think D and E can be odd or even, even when a and b are even. If you take a = 6, then you will have (6+2)/2 = 4 even. Or you can take b = 10, then you will have (10+2)/2 = 6 even.
Manager
Joined: 23 Nov 2008
Posts: 73
Re: If a and b are positive integers such that a-b and a/b are  [#permalink]

### Show Tags

25 Nov 2008, 05:36
Agree with you.
What I was poitning out there (with the 8 and 4 example) was that for two even numbers that satisfy the question, I get a situation where two of the choices are potentials answers.

---edit---
but I see the flaw in my reasoning here, since the question asks for a 'must be odd' response, so substitution is not the right way to go.
Manager
Joined: 18 Nov 2008
Posts: 103
Re: If a and b are positive integers such that a-b and a/b are  [#permalink]

### Show Tags

Updated on: 25 Nov 2008, 12:27
good question, and it initially confussed me

to satisfy a-b and a/b are both even integers, a and b should be both even.

A - a can be 2 (a/2=1) or 4 (a/2=2) Out
B - the same as A Out
C - (4+2)/2 = 3 or (8+4)/2=6
E - The same as in A,B

Thus, only D satisfies, because a can't be equal to 2

Originally posted by atletikos on 25 Nov 2008, 05:48.
Last edited by atletikos on 25 Nov 2008, 12:27, edited 1 time in total.
Manager
Joined: 23 Nov 2008
Posts: 73
Re: If a and b are positive integers such that a-b and a/b are  [#permalink]

### Show Tags

25 Nov 2008, 06:29
I did not consider that 'a' must not be 2, which is true and your explantion makes sense.

However, theres nothing stopping a from being say a 6 - and in that case (a+2)/2 would be even, and hence would not agree with the requirement of 'must be odd'..

what say?
Current Student
Joined: 28 Dec 2004
Posts: 3232
Location: New York City
Schools: Wharton'11 HBS'12
Re: If a and b are positive integers such that a-b and a/b are  [#permalink]

### Show Tags

25 Nov 2008, 07:18
I get D too...basically A >2 and could be of the form 2*N...so 2*n/2=n+1 is always odd.
Manager
Joined: 05 Jul 2008
Posts: 130
GMAT 2: 740 Q51 V38
Re: If a and b are positive integers such that a-b and a/b are  [#permalink]

### Show Tags

25 Nov 2008, 07:25
2
1
twilight wrote:
If a and b are positive integers such that a-b and a/b are both even integers, which of the following must be an odd integer?

A. a/2
B. b/2
C. (a+b)/2
D. (a+2)/2
E. (b+2)/2

I dont understand the answer choices here.
If I substitute 8 and 4 for a and b, i get both D&E as odd.
If I assume D&E to be even, both A and B need to be odd.
I just gave up and guessed C (not saying C is the OA)

7-t66732
I think this prob and yours are the same.
a/b is even so a must be even
a+b is even so b must be even
a/b is even while b is even so a must be a multiple of 4.
a is a multiple of 4 => a+2 is not a multiple of 4. => (a+2)/2 must be odd.
Manager
Joined: 23 Nov 2008
Posts: 73
Re: If a and b are positive integers such that a-b and a/b are  [#permalink]

### Show Tags

25 Nov 2008, 07:38
fresinha12 wrote:
I get D too...basically A >2 and could be of the form 2*N...so 2*n/2=n+1 is always odd.

But if N is odd (which it can be), then 2*n/2=n+1 will be even?
Manager
Joined: 23 Nov 2008
Posts: 73
Re: If a and b are positive integers such that a-b and a/b are  [#permalink]

### Show Tags

25 Nov 2008, 07:40
DavidArchuleta wrote:

7-t66732
I think this prob and yours are the same.
a/b is even so a must be even
a+b is even so b must be even
a/b is even while b is even so a must be a multiple of 4.
a is a multiple of 4 => a+2 is not a multiple of 4. => (a+2)/2 must be odd.

ah yes!
thats perfect, thanks.
Current Student
Joined: 28 Dec 2004
Posts: 3232
Location: New York City
Schools: Wharton'11 HBS'12
Re: If a and b are positive integers such that a-b and a/b are  [#permalink]

### Show Tags

25 Nov 2008, 07:41
twilight wrote:
fresinha12 wrote:
I get D too...basically A >2 and could be of the form 2*N...so 2*n/2=n+1 is always odd.

But if N is odd (which it can be), then 2*n/2=n+1 will be even?

this is not possible sinc a/b is an even integer which means N is even..
VP
Joined: 05 Jul 2008
Posts: 1274
Re: If a and b are positive integers such that a-b and a/b are  [#permalink]

### Show Tags

25 Nov 2008, 20:31
DavidArchuleta wrote:
twilight wrote:
If a and b are positive integers such that a-b and a/b are both even integers, which of the following must be an odd integer?

A. a/2
B. b/2
C. (a+b)/2
D. (a+2)/2
E. (b+2)/2

I dont understand the answer choices here.
If I substitute 8 and 4 for a and b, i get both D&E as odd.
If I assume D&E to be even, both A and B need to be odd.
I just gave up and guessed C (not saying C is the OA)

7-t66732
I think this prob and yours are the same.
a/b is even so a must be even
a+b is even so b must be even
a/b is even while b is even so a must be a multiple of 4.
a is a multiple of 4 => a+2 is not a multiple of 4. => (a+2)/2 must be odd.

+1 David. Good explanation
Manager
Joined: 05 May 2005
Posts: 76
Re: If a and b are positive integers such that a-b and a/b are  [#permalink]

### Show Tags

28 Nov 2008, 19:08
You may use substitution:

Initially substitute a and b with 8 and 2 respectively.
a = 8
b = 2

8 - 2 = even number
8/2 = even number

so these numbers satisfy requirements

a) a/2: 8/2 = 4 EVEN

b) b/2: 4/2 = 2 EVEN

c) (a+b)/2: (8+4)/2 = 6 EVEN

d) (a+2)/2: (8+2)/2 = 5 ODD
substitute another set (a=4 & b=2) for check
(4+2)/2 = 3 Again, ODD

e) (b+2)/2: (4+2)/2 = 3 ODD
substitute another set (a=4 & b=2) for check
(2+2)/2 = 2 EVEN

Math Expert
Joined: 02 Sep 2009
Posts: 51215
Re: If a and b are positive integers such that a-b and a/b are  [#permalink]

### Show Tags

14 Sep 2014, 14:39
5
10
twilight wrote:
If a and b are positive integers such that a-b and a/b are both even integers, which of the following must be an odd integer?

A. a/2
B. b/2
C. (a+b)/2
D. (a+2)/2
E. (b+2)/2

I dont understand the answer choices here.
If I substitute 8 and 4 for a and b, i get both D&E as odd.
If I assume D&E to be even, both A and B need to be odd.
I just gave up and guessed C (not saying C is the OA)

$$a-b$$ even --> either both even or both odd

$$\frac{a}{b}$$ even --> either both even or $$a$$ is even and $$b$$ is odd.

As both statements are true --> $$a$$ and $$b$$ must be even.

As $$\frac{a}{b}$$ is an even integer --> $$a$$ must be multiple of 4.

Options A is always even.
Options B can be even or odd.
Options C can be even or odd.
Options D: $$\frac{a+2}{2}=\frac{a}{2}+1$$, as $$a$$ is multiple of $$4$$, $$\frac{a}{2}$$ is even integer --> even+1=odd. Hence option D is always odd.
Options E can be even, odd.

OPEN DISCUSSION OF THIS QUESTION IS HERE: if-a-and-b-are-positive-integers-such-that-a-b-and-a-b-are-88108.html
_________________
Non-Human User
Joined: 09 Sep 2013
Posts: 9162
Re: If a and b are positive integers such that a-b and a/b are  [#permalink]

### Show Tags

10 Aug 2018, 17:45
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________
Re: If a and b are positive integers such that a-b and a/b are &nbs [#permalink] 10 Aug 2018, 17:45
Display posts from previous: Sort by