November 22, 2018 November 22, 2018 10:00 PM PST 11:00 PM PST Mark your calendars  All GMAT Club Tests are free and open November 22nd to celebrate Thanksgiving Day! Access will be available from 0:01 AM to 11:59 PM, Pacific Time (USA) November 23, 2018 November 23, 2018 10:00 PM PST 11:00 PM PST Practice the one most important Quant section  Integer properties, and rapidly improve your skills.
Author 
Message 
TAGS:

Hide Tags

Manager
Joined: 28 Jul 2013
Posts: 73
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
Updated on: 02 Mar 2015, 02:04
Question Stats:
70% (01:07) correct 30% (01:17) wrong based on 340 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
Official Answer and Stats are available only to registered users. Register/ Login.
Originally posted by sayansarkar on 02 Mar 2015, 01:40.
Last edited by Bunuel on 02 Mar 2015, 02:04, edited 1 time in total.
Renamed the topic, edited the question, added the OA and moved to DS forum.




Math Expert
Joined: 02 Sep 2009
Posts: 50711

Re: For nonnegative integers a, b, and c, what is the value of the product
[#permalink]
Show Tags
02 Mar 2015, 02:10
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? Extrahard Quant Tests with Brilliant Analytics




Manager
Joined: 28 Jul 2013
Posts: 73
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
02 Mar 2015, 02:30
Thank you Bunuel. Now its clear. I missed the point there



Current Student
Joined: 14 Oct 2013
Posts: 45

Re: For nonnegative integers a, b, and c, what is the value of the product
[#permalink]
Show Tags
05 Mar 2015, 11:44
Bunuel you stated that "Either b =0 or a = c." when we get to the point of b(ac)=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 12A9AB=0 factor out the 3A... 3A(43B)=0 So then..only one of these solutions can be true? A=0 OR B=4/3



EMPOWERgmat Instructor
Status: GMAT Assassin/CoFounder
Affiliations: EMPOWERgmat
Joined: 19 Dec 2014
Posts: 12891
Location: United States (CA)

Re: For nonnegative integers a, b, and c, what is the value of the product
[#permalink]
Show Tags
05 Mar 2015, 11:55
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(AC) 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
CoFounder & 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
Joined: 14 Oct 2013
Posts: 45

Re: For nonnegative integers a, b, and c, what is the value of the product
[#permalink]
Show Tags
05 Mar 2015, 13:28
ah that makes sense thank you!



Retired Moderator
Joined: 19 Mar 2014
Posts: 944
Location: India
Concentration: Finance, Entrepreneurship
GPA: 3.5

Re: For nonnegative integers a, b, and c, what is the value of the product
[#permalink]
Show Tags
09 Jul 2017, 05:44
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≠cThis does not give us any values of a or b or c Hence, (2) ===== is NOT SUFFICIENTCombining (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 SUFFICIENTHence, 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/howtoget60awamyguide64327.html#p470475



Math Revolution GMAT Instructor
Joined: 16 Aug 2015
Posts: 6531
GPA: 3.82

Re: For nonnegative integers a, b, and c, what is the value of the product
[#permalink]
Show Tags
10 Jul 2017, 09:59
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 \(b(ac) = 0\). 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 \(b(ac) = 0\). 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 oneandonly 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 Resources30 day online access & Diagnostic Test" "Unlimited Access to over 120 free video lessons  try it yourself"



NonHuman User
Joined: 09 Sep 2013
Posts: 8867

Re: For nonnegative integers a, b, and c, what is the value of the product
[#permalink]
Show Tags
03 Sep 2018, 09:04
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




Re: For nonnegative integers a, b, and c, what is the value of the product &nbs
[#permalink]
03 Sep 2018, 09:04






