Author 
Message 
TAGS:

Hide Tags

EMPOWERgmat Instructor
Status: GMAT Assassin/CoFounder
Affiliations: EMPOWERgmat
Joined: 19 Dec 2014
Posts: 11957
Location: United States (CA)
GRE 1: 340 Q170 V170

Problem Solving Pack 4, Question 3) If a, b and c are consecutive... [#permalink]
Show Tags
19 Nov 2015, 17:43
Question Stats:
70% (01:23) correct 30% (01:09) wrong based on 115 sessions
HideShow timer Statistics
QUANT 4PACK SERIES Problem Solving Pack 4 Question 3 If a, b and c are consecutive...If a, b and c are consecutive positive integers and a < b < c, then what is the minimum possible value of \(\frac{3^{2bc}}{3^{2ab}}\) A) 81 B) 2,187 C) 3,300 D) 6,561 E) 19,683 48 Hour Window Answer & Explanation WindowEarn KUDOS! Post your answer and explanation. OA, and explanation will be posted after the 48 hour window closes. This question is part of the Quant 4Pack seriesScroll Down For Official Explanation
Official Answer and Stats are available only to registered users. Register/ Login.
_________________
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!***********************





Senior Manager
Joined: 28 Feb 2014
Posts: 295
Location: United States
Concentration: Strategy, General Management

Re: Problem Solving Pack 4, Question 3) If a, b and c are consecutive... [#permalink]
Show Tags
19 Nov 2015, 18:28
If a, b and c are consecutive positive integers and a < b < c, then what is the minimum possible value of
\(3^{2bc}\) / \(3^{2ab}\)
A) 81 B) 2,187 C) 3,300 D) 6,561 E) 19,683
assume a=1, b=2, c=3 for minimum possible value
the equation then becomes \(3^{12}\) / \(3^{4}\) =\(3^{8}\) calculating only for the units digit to save time, we can then see that 1 is the last units digit of \(3^{8}\)
Answer: D



Current Student
Joined: 20 Mar 2014
Posts: 2642
Concentration: Finance, Strategy
GPA: 3.7
WE: Engineering (Aerospace and Defense)

Re: Problem Solving Pack 4, Question 3) If a, b and c are consecutive... [#permalink]
Show Tags
23 Nov 2015, 09:26
EMPOWERgmatRichC wrote: QUANT 4PACK SERIES Problem Solving Pack 4 Question 3 If a, b and c are consecutive...If a, b and c are consecutive positive integers and a < b < c, then what is the minimum possible value of \(3^{2bc}\) / \(3^{2ab}\) A) 81 B) 2,187 C) 3,300 D) 6,561 E) 19,683 48 Hour Window Answer & Explanation WindowEarn KUDOS! Post your answer and explanation. OA, and explanation will be posted after the 48 hour window closes. This question is part of the Quant 4Pack seriesScroll Down For Official Explanation \(\frac {3^{2bc}}{3^{2ab}} = ?\) > \(\frac {3^{2bc}}{3^{2ab}} = 3^{2bc2ab} = 3^{2b(ca)}\)and as a,b,c are consecutive integers, ca will always be = 2. Thus, \(3^{2b(ca)} = 3^{4b}\) and as all 3 a,b,c are POSITIVE integers, minimum value of a=1, making b =2 > \(3^{4b} = 3^8 = 65\)61. D is the correct answer.



EMPOWERgmat Instructor
Status: GMAT Assassin/CoFounder
Affiliations: EMPOWERgmat
Joined: 19 Dec 2014
Posts: 11957
Location: United States (CA)
GRE 1: 340 Q170 V170

Re: Problem Solving Pack 4, Question 3) If a, b and c are consecutive... [#permalink]
Show Tags
24 Nov 2015, 01:07
EMPOWERgmatRichC wrote: QUANT 4PACK SERIES Problem Solving Pack 4 Question 3 If a, b and c are consecutive...
If a, b and c are consecutive positive integers and a < b < c, then what is the minimum possible value of
\(3^{2bc}\) / \(3^{2ab}\)
A) 81 B) 2,187 C) 3,300 D) 6,561 E) 19,683
Hi All, To start, the answer choices to this question are rather 'spread out', so we might be able to use that spread to our advantage (and avoid some calculations). We're told that a, b and c are consecutive positive integers and a < b < c. We're asked for the MINIMUM value of \(3^{2bc}\) / \(3^{2ab}\)... Since the prompt asks for the MINIMUM value, it's likely that we'll have to make the 3 variables as small as possible, but we'll have to check to make sure that that's what is required to get to the correct answer. The smallest 3 numbers that 'fit' are... a = 1 b = 2 c = 3 This makes the calculation... \(3^{12}\) / \(3^{4}\) = \(3^{8}\) \(3^{8}\)= \(9^{4}\) = \(81^{2}\) = ABOUT \(80^{2}\) = ABOUT 6400, so the answer appears to be D. We just need to confirm that that's the case.... IF.... a = 2 b = 3 c = 4 This makes the calculation... \(3^{24}\) / \(3^{12}\) = \(3^{12}\) \(3^{12}\) is clearly bigger than \(3^{8}\), meaning that increasing the values of a, b and c will lead to a LARGER end result. This proves that D is actually the smallest possible result. Final Answer: 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!***********************



Board of Directors
Joined: 17 Jul 2014
Posts: 2726
Location: United States (IL)
Concentration: Finance, Economics
GPA: 3.92
WE: General Management (Transportation)

Re: Problem Solving Pack 4, Question 3) If a, b and c are consecutive... [#permalink]
Show Tags
28 Nov 2015, 10:57
since a, b, and c are consecutive integers, and positive: we can rewrite the fraction as
3^[2bc2ab] or 3^[2(bcab)] or 3^[2(b(ca))]
since a,b,c are consecutive integers, ca is always = 2 regardless of the values they take.
now, we are left with 3^4b to minimize the value, we need to take the minimal value of b, while taking into consideration that a,b,c  must be positive and numbers are consecutive numbers. minimal value of b is 2.
now, 3^8 = 9^4 or 81^2. don't need to solve for the exact value. the correct answer choice must have 1 at the end, and since A cannot be the answer, the only correct answer that it can be is D.



NonHuman User
Joined: 09 Sep 2013
Posts: 7241

Re: Problem Solving Pack 4, Question 3) If a, b and c are consecutive... [#permalink]
Show Tags
26 Nov 2017, 11:20
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: Problem Solving Pack 4, Question 3) If a, b and c are consecutive...
[#permalink]
26 Nov 2017, 11:20






