February 23, 2019 February 23, 2019 07:00 AM PST 09:00 AM PST Learn reading strategies that can help even nonvoracious reader to master GMAT RC. Saturday, February 23rd at 7 AM PT February 24, 2019 February 24, 2019 07:00 AM PST 09:00 AM PST Get personalized insights on how to achieve your Target Quant Score.
Author 
Message 
TAGS:

Hide Tags

Orion Representative
Joined: 26 Jul 2010
Posts: 353

What is the value of product abc?
[#permalink]
Show Tags
Updated on: 09 Jul 2013, 22:16
Question Stats:
39% (01:29) correct 61% (01:34) wrong based on 305 sessions
HideShow timer Statistics
What is the value of product abc? (1) 2^a * 3^b * 5^c = 1728 (2) a, b, and c are nonnegative integers Hello, community: try out this problem that I just wrote up for one of my students.
Official Answer and Stats are available only to registered users. Register/ Login.
_________________
Brian
Curriculum Developer, Instructor, and Host of Veritas Prep On Demand
Save $100 on live Veritas Prep GMAT Courses and Admissions Consulting
Enroll now. Pay later. Take advantage of Veritas Prep's flexible payment plan options.
Veritas Prep Reviews
Originally posted by VeritasPrepBrian on 16 Nov 2010, 17:12.
Last edited by Bunuel on 09 Jul 2013, 22:16, edited 3 times in total.
RENAMED THE TOPIC.




Orion Representative
Joined: 26 Jul 2010
Posts: 353

Re: Data Sufficiency Challenge Problem
[#permalink]
Show Tags
17 Nov 2010, 09:36
Thanks for the responses, everyone! I love this question because of the strategy it brings up, which we call: Why Are You Here? Regarding statement 2, it's nowhere close to being sufficient on its own. So there are two likely reasons that it's there: 1) To trick you into thinking that you need it, and therefore picking C instead of A 2) To add information that IS, in fact, necessary to go with statement 1, so that the correct answer is C and not A The GMAT doesn't use "red herring" statements  those that are simply so far out of scope that they're not even relevant  very often at all; if they provide a statement in a Data Sufficiency problem there has to be a reason...it's either a trap or it's necessary information. The good news for you is that you can use either case the same way: look at that statement to determine whether you really need it. Here, although statement 1 may seem sufficient on its own (c must be 0 in order to make the 5 term equal to 1, since 1728 has no multiples of 5), that only fits if we know that they're all integers. Statement 2, by providing us with that information explicitly (they're nonnegative integers), should make us pause to think about statement 1: Do they have to be integers? We don't need to use logarithms on the GMAT (thankfully!), but we should know enough that there would conceivably exist a set of noninteger exponents that would solve this problem. Even if you just assume that a and b are 1 so that: 5^c = 288 There is some value for c that will get us 288, so we can prove that statement 1 is not on its own sufficient. We need statement 2's help to determine that they're integers, so the correct answer is C. So, strategically, when you see a statement that on its own is clearly not sufficient, ask yourself "why are you here?". Is it providing essential information, or is it there to make you think you need it?
_________________
Brian
Curriculum Developer, Instructor, and Host of Veritas Prep On Demand
Save $100 on live Veritas Prep GMAT Courses and Admissions Consulting
Enroll now. Pay later. Take advantage of Veritas Prep's flexible payment plan options.
Veritas Prep Reviews




Retired Moderator
Joined: 02 Sep 2010
Posts: 762
Location: London

Re: Data Sufficiency Challenge Problem
[#permalink]
Show Tags
16 Nov 2010, 23:55
[quote="VeritasPrepBrian"]Hello, community: Try out this problem that I just wrote up for one of my students: What is the value of product abc? 1) 2^a * 3^b * 5^c = 1728 2) a, b, and c are nonnegative integers[/quote] 1728 = 2^6 * 3^3 * 5^0 (1) If a,b,c are not integers, they can take infinite values Eg (6,3,0) is te integral solution Take c=0, a=1 then b = [m]log_3(864)[/m] Take c=0, a=2 then b = [m]log_3(432)[/m] (2) Not sufficient to know the product (1+2) Since prime factorisation is unique, a=6,b=3,c=0 ()> abc=0
_________________
Math writeups 1) Algebra101 2) Sequences 3) Set combinatorics 4) 3D geometry
My GMAT story
GMAT Club Premium Membership  big benefits and savings



Manager
Status: Starting Work
Affiliations: Chartered Engineer
Joined: 20 Jun 2010
Posts: 194
Location: United Arab Emirates
Concentration: General Management, Leadership
Schools: INSEAD  Class of 2013
WE: Business Development (Energy and Utilities)

Re: Data Sufficiency Challenge Problem
[#permalink]
Show Tags
Updated on: 17 Nov 2010, 03:50
1728=(2^6)X(3^3)X(5^0) => c=0 by equating the powers of like terms on both sides.
So what ever the value of a & b, the product with c will be zero.
The statement that neither of the nos a,b,c are non negative doesnt give any solution.
So i feel the answer is A
Please correct me if I am wrong.
Originally posted by mattapraveen on 17 Nov 2010, 02:04.
Last edited by mattapraveen on 17 Nov 2010, 03:50, edited 1 time in total.



Intern
Joined: 25 Nov 2009
Posts: 39
Location: India

Re: Data Sufficiency Challenge Problem
[#permalink]
Show Tags
17 Nov 2010, 02:30
I chose A, as 1728 is 2^6*3^3 . Please explain the OA.
_________________
When going gets tough, tough gets going.........



Manager
Joined: 19 Aug 2010
Posts: 66

Re: Data Sufficiency Challenge Problem
[#permalink]
Show Tags
17 Nov 2010, 13:51
It should be C. (1) does not give me enough information. There are different variations of a,b,c (integers, nonintegers, lagorithmus, positive and negative values) that will satisfy the equations. insufficient
(2) alone insufficient.
Combining (1) and (2) we have now the information that supplement statement (1). If we know that a,b,c are nonnegative integers, we could then say that the only possible values are 6,3 and 0 (1728=2^6*3^3*5^0) and the value of a*b*c=0 Hence C



Intern
Joined: 02 Jul 2009
Posts: 40

Re: Data Sufficiency Challenge Problem
[#permalink]
Show Tags
17 Nov 2010, 16:36
1) 2^a * 3^b * 5^c = 1728 => 2^6 * 3^3 * 5^0 . Therefore, abc = 6*3*0 =0 . So, 1) should be sufficient. 2) a, b, c are non negative . i.e they can be positive or 0. However, this could lead to multiple values for abc. So, 2) is not sufficient. Answer is A, 1) ALONE is sufficient
_________________
Please provide kudos if you like my post. Thank you.



Manager
Joined: 30 Jun 2006
Posts: 82

Re: Data Sufficiency Challenge Problem
[#permalink]
Show Tags
17 Nov 2010, 23:47
A for me. 2^a * 3^b * 5^c = 1728 would mean that the factor of 5 does not contribute to the multiplication (mutiples of 5 end with 5 or 0). Hence the value of c = 0. By knowing this, I can say that the value of abc = 0.



Intern
Joined: 02 Sep 2010
Posts: 42
WE 1: Business Development Manger
WE 2: Assistant ManagerCarbon Trading
WE 3: ManagerCarbon Trading

Re: Data Sufficiency Challenge Problem
[#permalink]
Show Tags
18 Nov 2010, 08:48
From statement 1 we can factor out 1728=2^6 *3^3 *5^1



Orion Representative
Joined: 26 Jul 2010
Posts: 353

Yesterday's DS Challenge Question  solution here!
[#permalink]
Show Tags
18 Nov 2010, 14:37
Hey everyone  sorry...yesterday's question was formatted as "competition mode" and I can't figure out how to undo it, so I don't think anyone has seen my response yet. Here it is: _______________________________________________________________________________________________________________ Thanks for the responses, everyone! I love this question because of the strategy it brings up, which we call: Why Are You Here? Regarding statement 2, it's nowhere close to being sufficient on its own. So there are two likely reasons that it's there: 1) To trick you into thinking that you need it, and therefore picking C instead of A 2) To add information that IS, in fact, necessary to go with statement 1, so that the correct answer is C and not A The GMAT doesn't use "red herring" statements  those that are simply so far out of scope that they're not even relevant  very often at all; if they provide a statement in a Data Sufficiency problem there has to be a reason...it's either a trap or it's necessary information. The good news for you is that you can use either case the same way: look at that statement to determine whether you really need it. Here, although statement 1 may seem sufficient on its own (c must be 0 in order to make the 5 term equal to 1, since 1728 has no multiples of 5), that only fits if we know that they're all integers. Statement 2, by providing us with that information explicitly (they're nonnegative integers), should make us pause to think about statement 1: Do they have to be integers? We don't need to use logarithms on the GMAT (thankfully!), but we should know enough that there would conceivably exist a set of noninteger exponents that would solve this problem. Even if you just assume that a and b are 1 so that: 5^c = 288 There is some value for c that will get us 288, so we can prove that statement 1 is not on its own sufficient. We need statement 2's help to determine that they're integers, so the correct answer is C. So, strategically, when you see a statement that on its own is clearly not sufficient, ask yourself "why are you here?". Is it providing essential information, or is it there to make you think you need it?
_________________
Brian
Curriculum Developer, Instructor, and Host of Veritas Prep On Demand
Save $100 on live Veritas Prep GMAT Courses and Admissions Consulting
Enroll now. Pay later. Take advantage of Veritas Prep's flexible payment plan options.
Veritas Prep Reviews



Manager
Status: Starting Work
Affiliations: Chartered Engineer
Joined: 20 Jun 2010
Posts: 194
Location: United Arab Emirates
Concentration: General Management, Leadership
Schools: INSEAD  Class of 2013
WE: Business Development (Energy and Utilities)

Re: Yesterday's DS Challenge Question  solution here!
[#permalink]
Show Tags
19 Nov 2010, 07:28
I picked the answer as A and now I figure out what was my mistake.
But still, its very difficult to think that in the expression 2^a * 3^b * 5^c = 1728, even with a,b and c taking non integer value we can get the product,1728.



Manager
Joined: 20 Oct 2013
Posts: 54

Re: What is the value of product abc?
[#permalink]
Show Tags
04 May 2014, 08:26
hi brian so basically we should never assume that the numbers r integers if it is not given... also i need some explanation for statement one.... how is a,b,c being integers matter?... if they were fractions... how would they give us that number 1728?
_________________
Hope to clear it this time!! GMAT 1: 540 Preparing again



Intern
Joined: 16 May 2014
Posts: 39

Re: What is the value of product abc?
[#permalink]
Show Tags
20 May 2014, 06:25
NGGMAT wrote: hi brian
so basically we should never assume that the numbers r integers if it is not given... also i need some explanation for statement one.... how is a,b,c being integers matter?... if they were fractions... how would they give us that number 1728? When a, b, c are integers, and we have first statement as well, we need to put c=0 because 1728 has no 5 in it, and we have to make 5^c as 1. Even if they are fractions there can be two cases, Case 1: They can be rational numbers/fractions, in which case the information coupled with statement 1 will be sufficient. Case 2: They can be irrational numbers/fractions. In this case it won't suffice. Hope it makes sense!!!



Intern
Joined: 20 May 2014
Posts: 35
Location: India

Re: What is the value of product abc?
[#permalink]
Show Tags
23 May 2014, 02:04
Hi, Find value of abc Statement 1: \(2^a * 3^b * 5^c = 1728\) \(1728 = 2^6 * 3^3 * 5^0\) Therefore, \(2^a * 3^b * 5^c = 2^6 * 3^3 * 5^0\) a, b and c can have values: 6, 3 and 0 respectively. or if we take values for a and b to be 5, 3, we get: \(5^c = 2\) =>\(c=\frac{log 2}{log5}\) if we take values for a and b to be 6, 2, we get: \(5^c = 3\) =>\(c= \frac{log 3}{log5}\) Multiple solutions exist. So not sufficientStatement 2: a, b, and c are nonnegative integers Not sufficientCombining both Statements,we get, a = 6, b= 3 and c= 0 Hence, Answer is C
_________________
If you liked the post, please press the'Kudos' button on the left



GMATH Teacher
Status: GMATH founder
Joined: 12 Oct 2010
Posts: 768

Re: What is the value of product abc?
[#permalink]
Show Tags
12 Sep 2018, 10:14
VeritasPrepBrian wrote: What is the value of product abc?
(1) 2^a * 3^b * 5^c = 1728 (2) a, b, and c are nonnegative integers
\(? = abc\) \(\left( 1 \right)\,\,\,{2^a} \cdot {3^b} \cdot {5^c} = 1728\,\,\,\,\,\,\left\{ \begin{gathered} \,{\text{Take}}\,\,\left( {a,b,c} \right) = \left( {6,3,0} \right)\,\,\,\,\,\,\,\, \Rightarrow \,\,\,\,\,\,\,? = 0\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\left[ {1728 = {2^6} \cdot {3^3}} \right] \hfill \\ \,{\text{Take}}\,\,\left( {a,b,c} \right) = \left( {{x_{\text{p}}},1,1} \right)\,\,\,\,\,\,\,\mathop \Rightarrow \limits^{\left( * \right)} \,\,\,\,\,\,\,? = {x_{\text{p}}} > 0\,\,\,\,\,\,\,\,\,\, \hfill \\ \end{gathered} \right.\) \(\left( * \right)\,\,\,{2^x} = \frac{{1728}}{{15}}\,\,\,\,\, \Rightarrow \,\,\,\,x = {x_p} > 0\,\,\,{\text{unique}}\,\,\,\,\,\,\left( {{\text{see}}\,\,{\text{image}}\,\,{\text{attached}}} \right)\) \(\left( 2 \right)\,\,a,b,c\,\,\, \geqslant 0\,\,\,\,{\text{ints}}\,\,\,\,\left\{ \begin{gathered} \,{\text{Take}}\,\,\left( {a,b,c} \right) = \left( {0,0,0} \right)\,\,\,\,\, \Rightarrow \,\,\,\,\,? = 0 \hfill \\ \,\,Take\,\,\left( {a,b,c} \right) = \left( {1,1,1} \right)\,\,\,\,\, \Rightarrow \,\,\,\,\,? = 1 \hfill \\ \end{gathered} \right.\) \(\left( {1 + 2} \right)\,\,\,\left\{ \begin{gathered} {2^a} \cdot {3^b} \cdot {5^c} = 1728 = {2^6} \cdot {3^3} \cdot {5^0} \hfill \\ \,a,b,c\,\,\, \geqslant 0\,\,\,\,{\text{ints}} \hfill \\ \end{gathered} \right.\,\,\,\,\,\,\,\,\, \Rightarrow \,\,\,\,\,\,\left( {a,b,c} \right) = \left( {6,3,0} \right)\,\,\,\,\,\,\, \Rightarrow \,\,\,\,? = 0\,\,\,\,\, \Rightarrow \,\,\,\,\,{\text{SUFF}}.\,\,\,\,\,\,\,\) This solution follows the notations and rationale taught in the GMATH method. Regards, Fabio.
Attachments
12Set18_2q.gif [ 11.82 KiB  Viewed 455 times ]
_________________
Fabio Skilnik :: GMATH method creator (Math for the GMAT) Our highlevel "quant" preparation starts here: https://gmath.net




Re: What is the value of product abc?
[#permalink]
12 Sep 2018, 10:14






