Last visit was: 21 Nov 2024, 15:57 It is currently 21 Nov 2024, 15:57

Close

GRE Prep 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
Your Progress

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

Practice
Pays

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

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.

Close

Request Expert Reply

Confirm Cancel
avatar
Intern
Intern
Joined: 15 Sep 2017
Posts: 34
Own Kudos [?]: 136 [32]
Given Kudos: 0
Send PM
Most Helpful Expert Reply
Verbal Expert
Joined: 18 Apr 2015
Posts: 30003
Own Kudos [?]: 36338 [12]
Given Kudos: 25927
Send PM
General Discussion
avatar
Intern
Intern
Joined: 27 Aug 2018
Posts: 36
Own Kudos [?]: 30 [2]
Given Kudos: 0
Send PM
avatar
Intern
Intern
Joined: 15 Sep 2017
Posts: 34
Own Kudos [?]: 136 [0]
Given Kudos: 0
Send PM
Re: If a and b are positive integers [#permalink]
Nomad wrote:
The answers are D and E.

Since a-b = even and a/b = even, then both a and b are positive even integers.

We can rewrite D as a/2 + 2/2. a/2 will always be even, 2/2 = 1. Even+1 = Odd.

The same for E


Yeah, I too got same doubt,Just posted the question with same answer as in material.
avatar
Intern
Intern
Joined: 27 Aug 2018
Posts: 36
Own Kudos [?]: 30 [0]
Given Kudos: 0
Send PM
Re: If a and b are positive integers [#permalink]
AchyuthReddy wrote:
Nomad wrote:
The answers are D and E.

Since a-b = even and a/b = even, then both a and b are positive even integers.

We can rewrite D as a/2 + 2/2. a/2 will always be even, 2/2 = 1. Even+1 = Odd.

The same for E


Yeah, I too got same doubt,Just posted the question with same answer as in material.


Actually, @Carcass solution is the correct one. I did not consider if b=2. That is a mistake
avatar
Manager
Manager
Joined: 19 Mar 2018
Posts: 64
Own Kudos [?]: 37 [0]
Given Kudos: 0
Send PM
Re: If a and b are positive integers [#permalink]
How is E wrong?
if a = 4, b = 2

then b--> 2+2/2 = 2 which is even?
Please explain what is wrong here?
avatar
Intern
Intern
Joined: 27 Oct 2018
Posts: 49
Own Kudos [?]: 37 [0]
Given Kudos: 0
Send PM
Re: If a and b are positive integers [#permalink]
1
a must be greater than 2 in a way a/b is even.
b can be 2 also in which case b+2/2 is NOT odd
avatar
Intern
Intern
Joined: 11 Aug 2019
Posts: 2
Own Kudos [?]: 1 [0]
Given Kudos: 0
Send PM
Re: If a and b are positive integers [#permalink]
Carcass wrote:
\(a-b\) 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.


Answer: D.

Hope this helps. The answer is one and only.

Regards


what if a=12 and b=4?
then a/b will not be even. plz explain. thanks in advance
avatar
Intern
Intern
Joined: 16 Feb 2021
Posts: 1
Own Kudos [?]: 1 [1]
Given Kudos: 4
Send PM
Re: If a and b are positive integers [#permalink]
1
Triti wrote:
Carcass wrote:
\(a-b\) 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.


Answer: D.

Hope this helps. The answer is one and only.

Regards


what if a=12 and b=4?
then a/b will not be even. plz explain. thanks in advance


Here in the question it is give a/b is even and a-b is even.
So both a and b should be even and also 'a' can be only multiple of 4.
'b' can be only those numbers where the ratio remains even.
so if you consider a=12, b can be = 2, 6 only.
Intern
Intern
Joined: 30 Oct 2021
Posts: 30
Own Kudos [?]: 10 [0]
Given Kudos: 25
Send PM
Re: If a and b are positive integers [#permalink]
What are some number properties that I have to keep in mind for the division?
Verbal Expert
Joined: 18 Apr 2015
Posts: 30003
Own Kudos [?]: 36338 [0]
Given Kudos: 25927
Send PM
Re: If a and b are positive integers [#permalink]
Expert Reply
Greprep911 wrote:
What are some number properties that I have to keep in mind for the division?


Sir what do you mean ? for the division ??
Intern
Intern
Joined: 30 Oct 2021
Posts: 30
Own Kudos [?]: 10 [0]
Given Kudos: 25
Send PM
Re: If a and b are positive integers [#permalink]
There are certain properties for addition, subtraction and multiplication like: If you add even + even = result is even and if 2 is multiple of anything, the result is an even number. Are there any such properties for division too?
Verbal Expert
Joined: 18 Apr 2015
Posts: 30003
Own Kudos [?]: 36338 [0]
Given Kudos: 25927
Send PM
Re: If a and b are positive integers [#permalink]
Expert Reply
Greprep911 wrote:
There are certain properties for addition, subtraction and multiplication like: If you add even + even = result is even and if 2 is multiple of anything, the result is an even number. Are there any such properties for division too?


Here read please

Basic number properties https://gre.myprepclub.com/forum/gre-math- ... 24947.html
Advanced https://gre.myprepclub.com/forum/gre-quant ... tml#p51913

Please also take a look at the sticky and announcements posts under every section here on the board. All the notions for the GRE are listed in evidence

regards
Manager
Manager
Joined: 24 Jan 2021
Posts: 62
Own Kudos [?]: 80 [1]
Given Kudos: 898
Send PM
Re: If a and b are positive integers [#permalink]
1
Greprep911 wrote:
There are certain properties for addition, subtraction and multiplication like: If you add even + even = result is even and if 2 is multiple of anything, the result is an even number. Are there any such properties for division too?


I like to write this out whenever I do a number properties problem of this nature:

(e = even & o = odd)

e + e = e
e + o = o
o + o = e

e x e = e
e x o = e
o x o = o

The signs are interchangeable, so for this problem, you could instead write:

e - e = e
e - o = o
o - o = e

e ÷ e = e
e ÷ o = e
o ÷ o = o

This is only a shortcut. Please see the number properties lessons provided above to get a full understanding of the subject. Thanks.
User avatar
GRE Prep Club Legend
GRE Prep Club Legend
Joined: 07 Jan 2021
Posts: 5030
Own Kudos [?]: 74 [0]
Given Kudos: 0
Send PM
Re: If a and b are positive integers [#permalink]
Hello from the GRE Prep Club BumpBot!

Thanks to another GRE Prep 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.
Prep Club for GRE Bot
Re: If a and b are positive integers [#permalink]
Moderators:
GRE Instructor
84 posts
GRE Forum Moderator
37 posts
Moderator
1111 posts
GRE Instructor
234 posts

Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne