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

It is currently 20 Oct 2018, 02:08

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

If a, b and c are integers, is abc divisible by 4?

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

Hide Tags

Intern
Intern
avatar
Joined: 29 Sep 2013
Posts: 6
If a, b and c are integers, is abc divisible by 4?  [#permalink]

Show Tags

New post Updated on: 29 Sep 2013, 23:58
2
3
00:00
A
B
C
D
E

Difficulty:

  65% (hard)

Question Stats:

67% (01:42) correct 33% (01:39) wrong based on 211 sessions

HideShow timer Statistics

If a, b and c are integers, is abc divisible by 4?

(1) a + b + 2c is even.
(2) a + 2b + c is odd.

Hi Everyone,

Not sure if this has been posted before, but here is my question: I'm using the manhattan gmat advanced quant book (just because I tried doing a GMAT practice test and found that I wasn't doing as well as I hoped on the quant - 70th percentile) and I found the suggestion to use scenario charts very interesting. However, when I try using them, I can't get my time to go below 3:30s to 4 mins which I know is too long to be working on any one problem.
I'm sure people have had success with the tool, which is why MGMAT recommends it; however, does anyone have any idea on how to use the chart more efficiently?

As an example:
I'm using the chart for try-it problem 4-7 in the MGMAT advanced quant book:
If a,b and c are integers, is abc divisible by 4?

(1) a + b + 2c is even.
(2) a + 2b + c is odd.


I have 5 columns: a, b, c, 4th column: to ensure a+b+2c is even and 5th column to check if abc is divisible by 4. I try different values for a, b and c and etc till I find whether abc is always divisible by 4 or not.

MGMAT suggests to look at a, b and c as O/E numbers. I find this would not have been intuitive for me (since the question asks "is it divisible by 4," I would automatically start by trying out numbers.)

Anyways, if anyone has some tips or something that you think I should do different, please feel free to share. Any help will be appreciated!

Thanks!!

Originally posted by dukenukem on 29 Sep 2013, 19:14.
Last edited by Bunuel on 29 Sep 2013, 23:58, edited 1 time in total.
Renamed the topic, edited the question and added the OA.
Manhattan GMAT Discount CodesMath Revolution Discount CodesVeritas Prep GMAT Discount Codes
Most Helpful Expert Reply
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 50003
Re: If a, b and c are integers, is abc divisible by 4?  [#permalink]

Show Tags

New post 30 Sep 2013, 00:12
3
3
dukenukem wrote:
If a, b and c are integers, is abc divisible by 4?

(1) a + b + 2c is even.
(2) a + 2b + c is odd.

Hi Everyone,

Not sure if this has been posted before, but here is my question: I'm using the manhattan gmat advanced quant book (just because I tried doing a GMAT practice test and found that I wasn't doing as well as I hoped on the quant - 70th percentile) and I found the suggestion to use scenario charts very interesting. However, when I try using them, I can't get my time to go below 3:30s to 4 mins which I know is too long to be working on any one problem.
I'm sure people have had success with the tool, which is why MGMAT recommends it; however, does anyone have any idea on how to use the chart more efficiently?

As an example:
I'm using the chart for try-it problem 4-7 in the MGMAT advanced quant book:
If a,b and c are integers, is abc divisible by 4?

(1) a + b + 2c is even.
(2) a + 2b + c is odd.


I have 5 columns: a, b, c, 4th column: to ensure a+b+2c is even and 5th column to check if abc is divisible by 4. I try different values for a, b and c and etc till I find whether abc is always divisible by 4 or not.

MGMAT suggests to look at a, b and c as O/E numbers. I find this would not have been intuitive for me (since the question asks "is it divisible by 4," I would automatically start by trying out numbers.)

Anyways, if anyone has some tips or something that you think I should do different, please feel free to share. Any help will be appreciated!

Thanks!!


If a, b and c are integers, is abc divisible by 4?

(1) a + b + 2c is even --> \(a+b+2c=even\) --> \(a+b+even=even\) --> \(a+b=even-even=even\) --> a and b are either both odd or both even. Not sufficient.

(2) a + 2b + c is odd --> \(a+2b+c=odd\) --> \(a+even+c=odd\) --> \(a+c=odd-even=odd\) --> a is odd and c is even or vise-versa. Not sufficient.

(1)+(2) If a and b are both odd (satisfies the first statement) and c is even but not a multiple of 4, then abc is NOT divisible by 4 but if a and b are both odd and c is a multiple of 4 (so even), then abc IS divisible by 4. We already have two different answers, thus no need to consider the case when a and b are both even. Not sufficient.

Answer: E.

As for improving your score and speeding up, check under the spoiler:
ALL YOU NEED FOR QUANT: new-to-the-math-forum-please-read-this-first-140445.html

HOW TO IMPROVE YOUR QUANT SCORE


Improving from 30-35 to 40-44
Improving from 44 to 50

Other discussions dedicated to this issue:
quant-strategy-to-go-from-q47-to-q50-q51-137078.html
i-m-getting-a-consistent-q-48-49-i-m-an-engg-student-and-134999.html
3-weeks-to-increase-quant-score-134473.html
improving-q-from-a-50-to-a-145212.html
the-final-climb-quest-for-q-50-from-q47-129441.html
help-need-for-quant-150311.html
hitting-the-wall-please-share-your-prep-experience-150112.html
how-to-improve-quant-score-137975.html
need-pointers-to-move-q42-43-q50-148568.html
a-way-to-increase-from-q35-40-to-q-138750.html
do-i-need-to-change-the-way-i-study-110611.html
several-people-has-asked-me-if-it-is-possible-to-improve-40820.html
gmat-in-less-than-4-weeks-desperately-need-quant-advice-127092.html
stuck-at-47-test-in-a-month-137521.html
improve-gmat-score-from-620-to-700-need-urgent-help-144530.html
calling-quant-experts-need-a-strategy-to-improve-146045.html
final-weeks-calculation-silly-errors-and-speed-129408.html
knocked-down-by-the-gmat-for-the-second-time-150350.html
several-people-has-asked-me-if-it-is-possible-to-improve-40820.html
how-to-improve-your-quant-from-q44-to-q50-141670.html
help-gmat-in-3-days-134350.html

HOW TO SPEED UP


Want to speed up? Check this: Timing Strategies on the GMAT
Other discussions dedicated to this issue:
for-non-quant-beasts-128188.html
how-to-speed-up-answering-math-questions-19365.html
having-trouble-finishing-quant-section-any-ideas-110613.html
ds-and-timing-help-108310.html
final-weeks-calculation-silly-errors-and-speed-129408.html

Hope it helps.

P.S. Please read carefully and follow: rules-for-posting-please-read-this-before-posting-133935.html Pay arrention to the rules 3 and 7. 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

General Discussion
VP
VP
User avatar
B
Joined: 24 Aug 2011
Posts: 1408
Location: India
Concentration: Technology, Strategy
GMAT 1: 760 Q50 V42
GPA: 3.35
WE: Consulting (Computer Software)
GMAT ToolKit User Premium Member Reviews Badge
Re: Working with scenario charts  [#permalink]

Show Tags

New post 29 Sep 2013, 23:59
2
dukenukem wrote:
Hi Everyone,

Not sure if this has been posted before, but here is my question: I'm using the manhattan gmat advanced quant book (just because I tried doing a GMAT practice test and found that I wasn't doing as well as I hoped on the quant - 70th percentile) and I found the suggestion to use scenario charts very interesting. However, when I try using them, I can't get my time to go below 3:30s to 4 mins which I know is too long to be working on any one problem.
I'm sure people have had success with the tool, which is why MGMAT recommends it; however, does anyone have any idea on how to use the chart more efficiently?

As an example:
I'm using the chart for try-it problem 4-7 in the MGMAT advanced quant book:
If a,b and c are integers, is abc divisible by 4?
1. a + b + 2c is even.
2. a + 2b + c is odd.

I have 5 columns: a, b, c, 4th column: to ensure a+b+2c is even and 5th column to check if abc is divisible by 4. I try different values for a, b and c and etc till I find whether abc is always divisible by 4 or not.

MGMAT suggests to look at a, b and c as O/E numbers. I find this would not have been intuitive for me (since the question asks "is it divisible by 4," I would automatically start by trying out numbers.)

Anyways, if anyone has some tips or something that you think I should do different, please feel free to share. Any help will be appreciated!

Thanks!!


Hi,

i you try to put numbers and then find out the answer you will have to make too many sets, which will be very cumbersome and time consuming.

I would directly approach the problem by looking for odd or even numbers.
I would suggest that whenever you find such problems, try to do in terms of odd or even only.
If it is asked that the number is divided by 6, then try for 2 and 3 both.

Hope it helps!!

Regards,
Ankur
_________________

ISB Preparation Kit | GMAT Debrief

VP
VP
User avatar
Status: Been a long time guys...
Joined: 03 Feb 2011
Posts: 1169
Location: United States (NY)
Concentration: Finance, Marketing
GPA: 3.75
GMAT ToolKit User Premium Member
Re: If a, b and c are integers, is abc divisible by 4?  [#permalink]

Show Tags

New post 30 Sep 2013, 00:11
dukenukem wrote:
If a, b and c are integers, is abc divisible by 4?

(1) a + b + 2c is even.
(2) a + 2b + c is odd.



I shall say, be flexible.

statement 1 says: either a & b are both even OR a & b are both odd.
a=3, b=3 c=2 Answer is NO
a=3, b=3, c=4 Answer is YES

Not sufficient

statement 2 says: a+c is odd.
so either of a or c is even
Still insufficient.

On combining both of these info, we are still not sure if any of these is an even multiple of 2.
Not sufficient.
+1 E
_________________

Prepositional Phrases Clarified|Elimination of BEING| Absolute Phrases Clarified
Rules For Posting
www.Univ-Scholarships.com

Intern
Intern
avatar
Joined: 29 Sep 2013
Posts: 6
Re: If a, b and c are integers, is abc divisible by 4?  [#permalink]

Show Tags

New post 02 Oct 2013, 17:00
Thank you! And also thanks for those links Bunuel!

Posted from my mobile device
Intern
Intern
avatar
Joined: 29 Sep 2013
Posts: 6
Re: If a, b and c are integers, is abc divisible by 4?  [#permalink]

Show Tags

New post 02 Oct 2013, 17:05
And apologies, spoiler: You guys are right! E is the right answer. wow so many ways to get there :( (sad face only cause I didn't realize there were so many methods when solving myself!)

Posted from my mobile device
Intern
Intern
avatar
B
Joined: 23 Mar 2014
Posts: 2
Re: If a, b and c are integers, is abc divisible by 4?  [#permalink]

Show Tags

New post 19 Dec 2014, 16:33
Can't we solve this problem by knowing that a, b, or c could be zero? Zero is an integer and it is even.
EMPOWERgmat Instructor
User avatar
V
Status: GMAT Assassin/Co-Founder
Affiliations: EMPOWERgmat
Joined: 19 Dec 2014
Posts: 12685
Location: United States (CA)
GMAT 1: 800 Q51 V49
GRE 1: Q170 V170
Re: If a, b and c are integers, is abc divisible by 4?  [#permalink]

Show Tags

New post 24 Dec 2014, 10:02
Hi FWU,

YES, you COULD use 0 in any of your TESTs and come up with a quick "YES" answer. You still have to be thorough enough with your work to find one of the various "NO" answers that also exists though, so that you can get to the correct answer.

GMAT assassins aren't born, they're made,
Rich
_________________

760+: Learn What GMAT Assassins Do to Score at the Highest Levels
Contact Rich at: Rich.C@empowergmat.com

Rich Cohen

Co-Founder & GMAT Assassin

Special Offer: Save $75 + GMAT Club Tests Free
  Official GMAT Exam Packs + 70 Pt. Improvement Guarantee
www.empowergmat.com/

*****Select EMPOWERgmat Courses now include ALL 6 Official GMAC CATs!*****

GMATH Teacher
User avatar
S
Status: GMATH founder
Joined: 12 Oct 2010
Posts: 379
Re: If a, b and c are integers, is abc divisible by 4?  [#permalink]

Show Tags

New post 07 Oct 2018, 13:05
dukenukem wrote:
If a, b and c are integers, is abc divisible by 4?

(1) a + b + 2c is even.
(2) a + 2b + c is odd.

\(a,b,c\,\,{\rm{ints}}\,\,\,\,\left( * \right)\)

\({{abc} \over 4}\,\,\mathop = \limits^? \,\,{\mathop{\rm int}}\)

\(\left( {1 + 2} \right)\,\,\,\,\)

\(\left( 1 \right)\,\,\,{{a + b + 2c} \over 2} = {\mathop{\rm int}} \,\,\,\,\,\mathop \Leftrightarrow \limits^{\left( * \right)} \,\,\,\,\,\,{{a + b} \over 2} = {\mathop{\rm int}} \,\,\,\,\)

\(\left( 2 \right)\,\,\,{{a + 2b + c} \over 2} \ne {\mathop{\rm int}} \,\,\,\,\,\mathop \Leftrightarrow \limits^{\left( * \right)} \,\,\,\,\,\,{{a + c} \over 2} \ne {\mathop{\rm int}}\)


\(\left\{ \matrix{
\,{\rm{Take}}\,\,\left( {a,b,c} \right) = \left( {0,0,1} \right)\,\,\,\,\,\,\, \Rightarrow \,\,\,\,\,\,\left\langle {{\rm{YES}}} \right\rangle \,\, \hfill \cr
\,{\rm{Take}}\,\,\left( {a,b,c} \right) = \left( {1,1,2} \right)\,\,\,\,\,\, \Rightarrow \,\,\,\,\,\left\langle {{\rm{NO}}} \right\rangle \hfill \cr} \right.\,\,\,\)


This solution follows the notations and rationale taught in the GMATH method.

Regards,
Fabio.
_________________

Fabio Skilnik :: http://www.GMATH.net (Math for the GMAT)
Course release PROMO : finish our test drive till 31/Oct with (at least) 60 correct answers out of 92 (12-questions Mock included) to gain a 60% discount!

GMAT Club Bot
Re: If a, b and c are integers, is abc divisible by 4? &nbs [#permalink] 07 Oct 2018, 13:05
Display posts from previous: Sort by

If a, b and c are integers, is abc divisible by 4?

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


Copyright

GMAT Club MBA Forum Home| About| Terms and Conditions and Privacy Policy| 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®.