• NEW! FREE Beat The GMAT Quizzes
Hundreds of Questions Highly Detailed Reporting Expert Explanations
• 7 CATs FREE!
If you earn 100 Forum Points

Engage in the Beat The GMAT forums to earn
100 points for $49 worth of Veritas practice GMATs FREE VERITAS PRACTICE GMAT EXAMS Earn 10 Points Per Post Earn 10 Points Per Thanks Earn 10 Points Per Upvote ## What is the value of product abc? ##### This topic has 2 expert replies and 0 member replies ### Top Member ## What is the value of product abc? ## Timer 00:00 ## Your Answer A B C D E ## Global Stats Difficult What is the value of product abc? (1) 2^a * 3^b * 5^c = 1728 (2) a, b, and c are nonnegative integers OA C Source: Veritas Prep ### GMAT/MBA Expert GMAT Instructor Joined 09 Oct 2010 Posted: 1273 messages Followed by: 29 members Upvotes: 59 Top Reply BTGmoderatorDC wrote: What is the value of product abc? (1) 2^a * 3^b * 5^c = 1728 (2) a, b, and c are nonnegative integers Source: Veritas Prep $? = abc$ $\left( 1 \right)\,\,\,{2^a} \cdot {3^b} \cdot {5^c} = 1728\,\,\,\,\,\,\left\{ \begin{gathered} \,{\text{Take}}\,\,\left( {a,b,c} \right) = \left( {6,3,0} \right)\,\,\,\,\,\,\,\, \Rightarrow \,\,\,\,\,\,\,? = 0\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\left[ {1728 = {2^6} \cdot {3^3}} \right] \hfill \\ \,{\text{Take}}\,\,\left( {a,b,c} \right) = \left( {{x_{\text{p}}},1,1} \right)\,\,\,\,\,\,\,\mathop \Rightarrow \limits^{\left( * \right)} \,\,\,\,\,\,\,? = {x_{\text{p}}} > 0\,\,\,\,\,\,\,\,\,\, \hfill \\ \end{gathered} \right.$ $\left( * \right)\,\,\,{2^x} = \frac{{1728}}{{15}}\,\,\,\,\, \Rightarrow \,\,\,\,x = {x_p} > 0\,\,\,{\text{unique}}\,\,\,\,\,\,\left( {{\text{see}}\,\,{\text{image}}\,\,{\text{attached}}} \right)$ $\left( 2 \right)\,\,a,b,c\,\,\, \geqslant 0\,\,\,\,{\text{ints}}\,\,\,\,\left\{ \begin{gathered} \,{\text{Take}}\,\,\left( {a,b,c} \right) = \left( {0,0,0} \right)\,\,\,\,\, \Rightarrow \,\,\,\,\,? = 0 \hfill \\ \,\,Take\,\,\left( {a,b,c} \right) = \left( {1,1,1} \right)\,\,\,\,\, \Rightarrow \,\,\,\,\,? = 1 \hfill \\ \end{gathered} \right.$ $\left( {1 + 2} \right)\,\,\,\left\{ \begin{gathered} {2^a} \cdot {3^b} \cdot {5^c} = 1728 = {2^6} \cdot {3^3} \cdot {5^0} \hfill \\ \,a,b,c\,\,\, \geqslant 0\,\,\,\,{\text{ints}} \hfill \\ \end{gathered} \right.\,\,\,\,\,\,\,\,\, \Rightarrow \,\,\,\,\,\,\left( {a,b,c} \right) = \left( {6,3,0} \right)\,\,\,\,\,\,\, \Rightarrow \,\,\,\,? = 0\,\,\,\,\, \Rightarrow \,\,\,\,\,{\text{SUFF}}.\,\,\,\,\,\,\,$ This solution follows the notations and rationale taught in the GMATH method. Regards, Fabio. _________________ Fabio Skilnik :: GMATH method creator ( Math for the GMAT) English-speakers :: https://www.gmath.net Portuguese-speakers :: https://www.gmath.com.br ### GMAT/MBA Expert GMAT Instructor Joined 22 Aug 2016 Posted: 1756 messages Followed by: 28 members Upvotes: 470 Top Reply BTGmoderatorDC wrote: What is the value of product abc? (1) 2^a * 3^b * 5^c = 1728 (2) a, b, and c are nonnegative integers OA C Source: Veritas Prep We have to get the value of abc. Let's take each statement one by one. (1) 2^a * 3^b * 5^c = 1728. Multiple solutions are possible. Note that we do not know that a, b and c are integers. They can be real numbers. For example, at a = b = 0, we have 5^c = 1728 => the value of c is unique, of course it will be a real number; thus abc = 0. In the same way, at a = b = 1, we have 2*3*5^c = 1728 => 5^c = 288 => the value of c is unique; thus abc is some positive value. No unqiue value of abc. Insufficient. (2) a, b, and c are nonnegative integers. Certainly insufficient since the relationship among a, b and c is not known, (1) and (2) together So, we have 2^a * 3^b * 5^c = 1728 2^a * 3^b * 5^c = 2^6 * 3^3 * 5^c Since a, b and c are nonnegative integers, we must have c = 0, a = 6 and b = 3; thus, abc = 6*3*0 = 0. Sufficient. The correct answer: C Hope this helps! -Jay _________________ Manhattan Review GRE Prep Locations: GRE Classes Raleigh NC | GRE Prep Course Singapore | GRE Prep Philadelphia | SAT Prep Classes Toronto | and many more... Schedule your free consultation with an experienced GMAT Prep Advisor! Click here. • Free Trial & Practice Exam BEAT THE GMAT EXCLUSIVE Available with Beat the GMAT members only code • Get 300+ Practice Questions 25 Video lessons and 6 Webinars for FREE Available with Beat the GMAT members only code • Award-winning private GMAT tutoring Register now and save up to$200

Available with Beat the GMAT members only code

• 5-Day Free Trial
5-day free, full-access trial TTP Quant

Available with Beat the GMAT members only code

• 5 Day FREE Trial
Study Smarter, Not Harder

Available with Beat the GMAT members only code

• Free Veritas GMAT Class
Experience Lesson 1 Live Free

Available with Beat the GMAT members only code

• FREE GMAT Exam
Know how you'd score today for \$0

Available with Beat the GMAT members only code

• Free Practice Test & Review
How would you score if you took the GMAT

Available with Beat the GMAT members only code

• Magoosh
Study with Magoosh GMAT prep

Available with Beat the GMAT members only code

• 1 Hour Free
BEAT THE GMAT EXCLUSIVE

Available with Beat the GMAT members only code

### Top First Responders*

1 Brent@GMATPrepNow 65 first replies
2 fskilnik@GMATH 61 first replies
3 GMATGuruNY 46 first replies
4 Jay@ManhattanReview 40 first replies
5 Rich.C@EMPOWERgma... 26 first replies
* Only counts replies to topics started in last 30 days
See More Top Beat The GMAT Members

### Most Active Experts

1 Scott@TargetTestPrep

Target Test Prep

199 posts
2 fskilnik@GMATH

GMATH Teacher

163 posts
3 Brent@GMATPrepNow

GMAT Prep Now Teacher

119 posts
4 Max@Math Revolution

Math Revolution

92 posts
5 GMATGuruNY

The Princeton Review Teacher

72 posts
See More Top Beat The GMAT Experts