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

It is currently 24 Sep 2018, 06:40

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

For nonnegative integers a, b, and c, what is the value of the product

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

Hide Tags

Manager
Manager
avatar
Joined: 28 Jul 2013
Posts: 78
Location: India
Concentration: Marketing, Strategy
GPA: 3.62
WE: Engineering (Manufacturing)
For nonnegative integers a, b, and c, what is the value of the product  [#permalink]

Show Tags

New post Updated on: 02 Mar 2015, 03:04
1
13
00:00
A
B
C
D
E

Difficulty:

  25% (medium)

Question Stats:

66% (00:38) correct 34% (00:37) wrong based on 330 sessions

HideShow timer Statistics

For nonnegative integers a, b, and c, what is the value of the product abc?

(1) ab=bc
(2) a≠c

I cannot understand the explanation given by veritas prep. Need help on this one. will post the explanation

Originally posted by sayansarkar on 02 Mar 2015, 02:40.
Last edited by Bunuel on 02 Mar 2015, 03:04, edited 1 time in total.
Renamed the topic, edited the question, added the OA and moved to DS forum.
Veritas Prep GMAT Discount CodesMath Revolution Discount CodesJamboree Discount Codes
Most Helpful Expert Reply
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 49417
Re: For nonnegative integers a, b, and c, what is the value of the product  [#permalink]

Show Tags

New post 02 Mar 2015, 03:10
10
11
For nonnegative integers a, b, and c, what is the value of the product abc?

(1) ab=bc;
ab - bc = 0;
b(a - c) = 0;
Either b =0 or a = c.
If b = 0, then abc = 0 but if b ≠ 0, then the value of abc will depend on the individual values of the variables. Not sufficient.

(2) a≠c. Not sufficient.

(1)+(2) Since from (2) a≠c, then from (1) we'd have that b = 0, making abc equal to 0, irrespective of the values of a and c. Sufficient.

Answer: C.

Hope it's clear.
_________________

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
Manager
Manager
avatar
Joined: 28 Jul 2013
Posts: 78
Location: India
Concentration: Marketing, Strategy
GPA: 3.62
WE: Engineering (Manufacturing)
Re: For nonnegative integers a, b, and c, what is the value of the product  [#permalink]

Show Tags

New post 02 Mar 2015, 03:30
Thank you Bunuel. Now its clear. I missed the point there
Current Student
avatar
Joined: 14 Oct 2013
Posts: 45
GMAT ToolKit User
Re: For nonnegative integers a, b, and c, what is the value of the product  [#permalink]

Show Tags

New post 05 Mar 2015, 12:44
Bunuel- you stated that "Either b =0 or a = c." when we get to the point of b(a-c)=0 is that always the case, where only one is true, when we have an equation that looks like that? So for example (just making this up)...

12A=9AB
12A-9AB=0
factor out the 3A...
3A(4-3B)=0
So then..only one of these solutions can be true?
A=0 OR B=4/3
EMPOWERgmat Instructor
User avatar
V
Status: GMAT Assassin/Co-Founder
Affiliations: EMPOWERgmat
Joined: 19 Dec 2014
Posts: 12443
Location: United States (CA)
GMAT 1: 800 Q51 V49
GRE 1: Q170 V170
Re: For nonnegative integers a, b, and c, what is the value of the product  [#permalink]

Show Tags

New post 05 Mar 2015, 12:55
1
Hi soniasawhney,

Both possibilities COULD be true, but it's not grammatically correct (nor mathematically correct) to state:

B=0 AND A=C (as both DO NOT need to be true for the product of B(A-C) to equal 0 - only one of them needs to be true).

If you were taking the notes, then you might find it useful to write....

B=0 or A=C OR BOTH

In your example:
12A = 9AB
12A - 9AB = 0
3A(4 - 3B) = 0

A=0 or B=4/3 OR BOTH

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!***********************

Current Student
avatar
Joined: 14 Oct 2013
Posts: 45
GMAT ToolKit User
Re: For nonnegative integers a, b, and c, what is the value of the product  [#permalink]

Show Tags

New post 05 Mar 2015, 14:28
ah that makes sense- thank you!
Retired Moderator
User avatar
P
Joined: 19 Mar 2014
Posts: 961
Location: India
Concentration: Finance, Entrepreneurship
GPA: 3.5
GMAT ToolKit User Premium Member
Re: For nonnegative integers a, b, and c, what is the value of the product  [#permalink]

Show Tags

New post 09 Jul 2017, 06:44
1
sayansarkar wrote:
For nonnegative integers a, b, and c, what is the value of the product abc?

(1) ab=bc
(2) a≠c

I cannot understand the explanation given by veritas prep. Need help on this one. will post the explanation


(1) ab=bc

\(ab = bc\)

\(ab - bc = 0\)

\(b(a - c) = 0\)

Either \(b = 0\) or \(a = c\)

We will get multiple answers based on values of b and a or c.

If b = 0 then we will the value of equation as ZERO, however if the a = c then we will get value, based on a or c.

Hence, (1) ===== is NOT SUFFICIENT

(2) a≠c

This does not give us any values of a or b or c

Hence, (2) ===== is NOT SUFFICIENT

Combining (1) & (2)

We get that a≠c which means \(b = 0\) as per (1) and this gives us the value of ZERO foe abc.

Hence, (1) & (2) ===== is SUFFICIENT

Hence, Answer is C
_________________

"Nothing in this world can take the place of persistence. Talent will not: nothing is more common than unsuccessful men with talent. Genius will not; unrewarded genius is almost a proverb. Education will not: the world is full of educated derelicts. Persistence and determination alone are omnipotent."

Best AWA Template: https://gmatclub.com/forum/how-to-get-6-0-awa-my-guide-64327.html#p470475

Math Revolution GMAT Instructor
User avatar
V
Joined: 16 Aug 2015
Posts: 6239
GMAT 1: 760 Q51 V42
GPA: 3.82
Premium Member
Re: For nonnegative integers a, b, and c, what is the value of the product  [#permalink]

Show Tags

New post 10 Jul 2017, 10:59
sayansarkar wrote:
For nonnegative integers a, b, and c, what is the value of the product abc?

(1) ab=bc
(2) a≠c

I cannot understand the explanation given by veritas prep. Need help on this one. will post the explanation


Forget conventional ways of solving math questions. In DS, Variable approach is the easiest and quickest way to find the answer without actually solving the problem. Remember equal number of variables and independent equations ensures a solution.

There are 3 variables and 0 equation. Thus the answer E is most likely.

Condition 1)
\(ab = bc\) is equivalent to \(ab - bc = 0\) or \(b(a-c) = 0\).
Thus \(b = 0\) or \(a = c\).
If \(b = 0\), then we have \(abc = 0\).
However, if \(b \ne 0\) and \(a = c\), we have the case \(a = b = c = 1\) with \(abc = 1\).
Since the answer is not unique, this is not sufficient.

Condition 2)
If \(a = 1\), \(b = 1\), \(c = 2\), then \(abc = 2\).
If \(a = 1\), \(b = 2\), \(c = 3\), then \(abc = 6\).

Since the answer is not unique, this is not sufficient either.

Conditions 1) & 2)
From the condition 1), \(ab = bc\) is equivalent to \(ab - bc = 0\) or \(b(a-c) = 0\).
Thus \(b = 0\) or \(a = c\).
However, \(b = 0\), since \(a \ne c\) by the condition 2)
Thus \(abc = 0\).

Therefore, C is the answer.


For cases where we need 3 more equations, such as original conditions with “3 variables”, or “4 variables and 1 equation”, or “5 variables and 2 equations”, we have 1 equation each in both 1) and 2). Therefore, there is 80 % chance that E is the answer, while C has 15% chance and A, B or D has 5% chance. Since E is most likely to be the answer using 1) and 2) together according to DS definition. Obviously there may be cases where the answer is A, B, C or D.
_________________

MathRevolution: Finish GMAT Quant Section with 10 minutes to spare
The one-and-only World’s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy.
"Only $99 for 3 month Online Course"
"Free Resources-30 day online access & Diagnostic Test"
"Unlimited Access to over 120 free video lessons - try it yourself"

Non-Human User
User avatar
Joined: 09 Sep 2013
Posts: 8161
Premium Member
Re: For nonnegative integers a, b, and c, what is the value of the product  [#permalink]

Show Tags

New post 03 Sep 2018, 10:04
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

GMAT Club Bot
Re: For nonnegative integers a, b, and c, what is the value of the product &nbs [#permalink] 03 Sep 2018, 10:04
Display posts from previous: Sort by

For nonnegative integers a, b, and c, what is the value of the product

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

Events & Promotions

PREV
NEXT


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®.