It is currently 16 Oct 2017, 17:51

Close

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
Your Progress

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

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

Close

Request Expert Reply

Confirm Cancel

Events & Promotions

Events & Promotions in June
Open Detailed Calendar

If a, b, and c are integers and ab^2/c is a positive even in

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:

Hide Tags

2 KUDOS received
Intern
Intern
avatar
Joined: 16 Jan 2013
Posts: 33

Kudos [?]: 33 [2], given: 8

Concentration: Finance, Entrepreneurship
GMAT Date: 08-25-2013
If a, b, and c are integers and ab^2/c is a positive even in [#permalink]

Show Tags

New post 20 Jun 2013, 00:04
2
This post received
KUDOS
2
This post was
BOOKMARKED
00:00
A
B
C
D
E

Difficulty:

  55% (hard)

Question Stats:

59% (01:16) correct 41% (01:24) wrong based on 195 sessions

HideShow timer Statistics

If a, b, and c are integers and ab^2/c is a positive even integer, which of the following must be true?

I. ab is even
II. ab > 0
III. c is even

A. I only
B. II only
C. I and II
D. I and III
E. I, II, and III
[Reveal] Spoiler: OA

Last edited by Bunuel on 20 Jun 2013, 00:50, edited 1 time in total.
Renamed the topic, edited the question and the tags.

Kudos [?]: 33 [2], given: 8

1 KUDOS received
Intern
Intern
avatar
Joined: 26 May 2010
Posts: 10

Kudos [?]: 39 [1], given: 4

Re: Odd or even [#permalink]

Show Tags

New post 20 Jun 2013, 00:14
1
This post received
KUDOS
Countdown wrote:
Please help regarding the below question wid explanation.



If a , b, and c are integers and ab2 / c is a positive even integer, which of the following must be true?
I. ab is even II. ab > 0 III. c is even
I only
II only
I and II
I and III
I, II, and III


ab2/c is positive which means a and C >0 or a and c<0 since b2 is positive
Case 1 - a=3 b=2 c=3 or c=6 where ab2 /2 would be even when c= 3 or c=6
lets see III option where C is even as per our assumption C can be even and odd, hence it is out.
lets see option II ab>0 a and b can positive or negative hence sign of ab cannot be determined hence it is out

So options B,C,D,E are gone and ans is A

Kudos would be appreciated

Kudos [?]: 39 [1], given: 4

2 KUDOS received
Current Student
User avatar
Joined: 28 Apr 2012
Posts: 306

Kudos [?]: 474 [2], given: 142

Location: India
Concentration: Finance, Technology
GMAT 1: 650 Q48 V31
GMAT 2: 770 Q50 V47
WE: Information Technology (Computer Software)
Re: Odd or even [#permalink]

Show Tags

New post 20 Jun 2013, 00:26
2
This post received
KUDOS
Countdown wrote:
Please help regarding the below question wid explanation.



If a , b, and c are integers and ab2 / c is a positive even integer, which of the following must be true?
I. ab is even II. ab > 0 III. c is even
I only
II only
I and II
I and III
I, II, and III


I believe the expression is \(ab^2/c\) is a positive integer.
Now we know,

1. even * even = even (2*4 = 8)
2. even * odd = even (2*3 = 6)
3. even / even = even or odd (8/2 = 4 , 6/2 = 3)
4. even / odd = even (6/3 = 2)
5. odd * odd = odd
6. odd / odd = odd (if the are divisible)
7. odd / even = <not divisible> as the denominator will always have an extra 2.

Coming back to my question, my result is even. Hence my numerator must be even, as odd numerator can never give even result. (we are considering divisible integers only)

\(ab^2\) is even, hence either a is even or \(b^2\) is even. If \(b^2\) is even then b is even. Hence ab = even. (I) is true.
now \(\sqrt{b^2}\) = +/- b, so ab can be > 0 or < 0, (II) is false
From rule 3 and 4, c can be even or odd. so (III) is false.

Answer A.
_________________

"Appreciation is a wonderful thing. It makes what is excellent in others belong to us as well."
― Voltaire


Press Kudos, if I have helped.
Thanks!

Kudos [?]: 474 [2], given: 142

Expert Post
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 41875

Kudos [?]: 128459 [0], given: 12173

Re: If a, b, and c are integers and ab^2/c is a positive even in [#permalink]

Show Tags

New post 20 Jun 2013, 01:11
Countdown wrote:
If a, b, and c are integers and ab^2/c is a positive even integer, which of the following must be true?

I. ab is even
II. ab > 0
III. c is even

A. I only
B. II only
C. I and II
D. I and III
E. I, II, and III


Given: a, b, and c are integers and ab^2/c is a positive even integer.

Evaluate each option:

I. ab is even.

ab^2/c to be positive even integer ab^2 must be even, from which it follows that either a or b must be even, thus ab has to be even.

II. ab > 0

Since b is squared in our expression, then we can say nothing about its sign, thus we cannot say whether ab is positive.

III. c is even

The easiest one: ab^2/c = integer/c = even --> c could be even as well as odd.

Answer: A.

P.S. Please read carefully and follow: 11-rules-for-posting-133935.html Pay attention to the rules #3 and 10. Thank you.
_________________

New to the Math Forum?
Please read this: Ultimate GMAT Quantitative Megathread | All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:
GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | Tricky questions from previous years.

Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


What are GMAT Club Tests?
Extra-hard Quant Tests with Brilliant Analytics

Kudos [?]: 128459 [0], given: 12173

GMAT Club Legend
GMAT Club Legend
User avatar
Joined: 09 Sep 2013
Posts: 16794

Kudos [?]: 273 [0], given: 0

Premium Member
Re: If a, b, and c are integers and ab^2/c is a positive even in [#permalink]

Show Tags

New post 21 Oct 2014, 09:12
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.
_________________

GMAT Books | GMAT Club Tests | Best Prices on GMAT Courses | GMAT Mobile App | Math Resources | Verbal Resources

Kudos [?]: 273 [0], given: 0

GMAT Club Legend
GMAT Club Legend
User avatar
Joined: 09 Sep 2013
Posts: 16794

Kudos [?]: 273 [0], given: 0

Premium Member
Re: If a, b, and c are integers and ab^2/c is a positive even in [#permalink]

Show Tags

New post 14 Mar 2017, 10:16
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.
_________________

GMAT Books | GMAT Club Tests | Best Prices on GMAT Courses | GMAT Mobile App | Math Resources | Verbal Resources

Kudos [?]: 273 [0], given: 0

Director
Director
avatar
G
Joined: 02 Sep 2016
Posts: 778

Kudos [?]: 41 [0], given: 267

Premium Member CAT Tests
If a, b, and c are integers and ab^2/c is a positive even in [#permalink]

Show Tags

New post 03 Apr 2017, 04:39
ab^2/c is an even integer.
When is that possible:
When b^2 or b is even (If b is even then b^2 would be even i.e. even*even is even. For example, 2*2=4)

a and c can either be even or odd. Why? Because an odd number can have an even multiple (e.g. 12 is multiple of 3). Also in 12, the first digit is odd and then also the number is even because it ends with an even digit.

Check the options:
(1) ab is even. YES!! Because we know b is even. So odd*even=even (e.g. 3*2=6) or even*even=even (e.g. 2*2=4)
(2) ab>0. Well!! It can be or can't be. Because ab^2/c is a positive integer. That tells us a few things:
- If b is negative, then b^2 is positive. And a and c are positive. In this case, ab will be less than 0.
- If a is negative and b is also negative, then ab>0 (negative*negative= positive). In this case ab>0. (Can eliminate this choice here only as we know that we are not getting a unique answer).
- If b is not negative and c and a are negative, then ab will be less than zero.

So no unique answer.

(3) c is even.
We already know that c can be odd or even.
And in mUST BE TRUE questions, there SHOULD be ONLY one answer.

The answer is statement 1.
_________________

Help me make my explanation better by providing a logical feedback.

If you liked the post, HIT KUDOS !!

Don't quit.............Do it.

Kudos [?]: 41 [0], given: 267

If a, b, and c are integers and ab^2/c is a positive even in   [#permalink] 03 Apr 2017, 04:39
Display posts from previous: Sort by

If a, b, and c are integers and ab^2/c is a positive even in

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  


GMAT Club MBA Forum Home| About| Terms and Conditions| GMAT Club Rules| Contact| Sitemap

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®.