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• ### $450 Tuition Credit & Official CAT Packs FREE November 15, 2018 November 15, 2018 10:00 PM MST 11:00 PM MST EMPOWERgmat is giving away the complete Official GMAT Exam Pack collection worth$100 with the 3 Month Pack ($299) • ### Free GMAT Strategy Webinar November 17, 2018 November 17, 2018 07:00 AM PST 09:00 AM PST Nov. 17, 7 AM PST. Aiming to score 760+? Attend this FREE session to learn how to Define your GMAT Strategy, Create your Study Plan and Master the Core Skills to excel on the GMAT. # What is the value of product abc?  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics Author Message TAGS: ### Hide Tags Veritas Prep and Orion Instructor Joined: 26 Jul 2010 Posts: 306 What is the value of product abc? [#permalink] ### Show Tags Updated on: 09 Jul 2013, 22:16 5 11 00:00 Difficulty: 85% (hard) Question Stats: 39% (01:29) correct 61% (01:33) wrong based on 299 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. _________________ Brian Save$100 on live Veritas Prep GMAT Courses and Admissions Consulting

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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.
Veritas Prep and Orion Instructor
Joined: 26 Jul 2010
Posts: 306
Re: Data Sufficiency Challenge Problem  [#permalink]

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17 Nov 2010, 09:36
4
2
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

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. GMAT self-study has never been more personalized or more fun. Try ORION Free! Veritas Prep Reviews ##### General Discussion Retired Moderator Joined: 02 Sep 2010 Posts: 769 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 _________________ 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: 41 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: 68 Re: Data Sufficiency Challenge Problem [#permalink] ### Show Tags 17 Nov 2010, 13:51 1 It should be C. (1) does not give me enough information. There are different variations of a,b,c (integers, non-integers, 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 non-negative 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: 45 Re: Data Sufficiency Challenge Problem [#permalink] ### Show Tags 17 Nov 2010, 16:36 1 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: 84 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 Manager-Carbon Trading WE 3: Manager-Carbon 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 Veritas Prep and Orion Instructor Joined: 26 Jul 2010 Posts: 306 Yesterday's DS Challenge Question - solution here! [#permalink] ### Show Tags 18 Nov 2010, 14:37 2 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 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.

GMAT self-study has never been more personalized or more fun. Try ORION Free!

Veritas Prep Reviews

Manager
Status: Starting Work
Affiliations: Chartered Engineer
Joined: 20 Jun 2010
Posts: 194
Location: United Arab Emirates
Schools: INSEAD - Class of 2013
WE: Business Development (Energy and Utilities)
Re: Yesterday's DS Challenge Question - solution here!  [#permalink]

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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.
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Re: What is the value of product abc?  [#permalink]

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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?
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Re: What is the value of product abc?  [#permalink]

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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!!!
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Re: What is the value of product abc?  [#permalink]

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23 May 2014, 02:04
1
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 sufficient

Statement 2: a, b, and c are nonnegative integers

Not sufficient

Combining both Statements,

we get, a = 6, b= 3 and c= 0

Hence,
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Re: What is the value of product abc?  [#permalink]

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