November 20, 2018 November 20, 2018 09:00 AM PST 10:00 AM PST The reward for signing up with the registration form and attending the chat is: 6 free examPAL quizzes to practice your new skills after the chat. November 20, 2018 November 20, 2018 06:00 PM EST 07:00 PM EST What people who reach the high 700's do differently? We're going to share insights, tips and strategies from data we collected on over 50,000 students who used examPAL.
Author 
Message 
TAGS:

Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 50670

What is the smallest integer k for which 7^k > 14*7^15
[#permalink]
Show Tags
18 Nov 2016, 03:04
Question Stats:
73% (01:01) correct 27% (01:00) wrong based on 269 sessions
HideShow timer Statistics



Senior Manager
Joined: 06 Jun 2016
Posts: 259
Location: India
Concentration: Operations, Strategy
GMAT 1: 600 Q49 V23 GMAT 2: 680 Q49 V34
GPA: 3.9

Re: What is the smallest integer k for which 7^k > 14*7^15
[#permalink]
Show Tags
18 Nov 2016, 03:23
Bunuel wrote: What is the smallest integer k for which 7^k > 14*7^15 ?
A. 14 B. 15 C. 16 D. 17 E. 18 the given can be reduced to 7^k > 2 * 7^16 if 7^k has to be greater then minimum value of k= 17 i.e., 7 * 7^16 > 2 * 7^16 Hence D



Board of Directors
Status: QA & VA Forum Moderator
Joined: 11 Jun 2011
Posts: 4224
Location: India
GPA: 3.5
WE: Business Development (Commercial Banking)

What is the smallest integer k for which 7^k > 14*7^15
[#permalink]
Show Tags
18 Nov 2016, 08:43
Bunuel wrote: What is the smallest integer k for which 7^k > 14*7^15 ?
A. 14 B. 15 C. 16 D. 17 E. 18 \(7^k > 14*7^{15}\) Or, \(7^k > 7*2*7^{15}\) Or, \(7^k > 2*7^{16}\) Now, If k = 16 Or, \(7^{16} > 2*7^{16}\) { Not true since RHS < LHS }To make LHS > RHS lets make LHS > \(7^{16}\) If , \(7^{17} > 2*7^{16}\) Holds good... Hence, answer will be (D)
_________________
Thanks and Regards
Abhishek....
PLEASE FOLLOW THE RULES FOR POSTING IN QA AND VA FORUM AND USE SEARCH FUNCTION BEFORE POSTING NEW QUESTIONS
How to use Search Function in GMAT Club  Rules for Posting in QA forum  Writing Mathematical Formulas Rules for Posting in VA forum  Request Expert's Reply ( VA Forum Only )



Board of Directors
Joined: 17 Jul 2014
Posts: 2645
Location: United States (IL)
Concentration: Finance, Economics
GPA: 3.92
WE: General Management (Transportation)

Re: What is the smallest integer k for which 7^k > 14*7^15
[#permalink]
Show Tags
18 Nov 2016, 09:59
Bunuel wrote: What is the smallest integer k for which 7^k > 14*7^15 ?
A. 14 B. 15 C. 16 D. 17 E. 18 14*7^15 = 2* 7^16 since we have 7^k greater than above expression, smallest possible value for K is 17. answer is D.



Manager
Joined: 03 Oct 2013
Posts: 84

Re: What is the smallest integer k for which 7^k > 14*7^15
[#permalink]
Show Tags
18 Nov 2016, 10:52
7^k>14*(7^15) > 2*(7^16) If k= 16 it does not satisfy. If k=17 that is equal to 7*(7^16) which is greater than 2*(7^16)
_________________
P.S. Don't forget to give Kudos on the left if you like the solution



Target Test Prep Representative
Status: Head GMAT Instructor
Affiliations: Target Test Prep
Joined: 04 Mar 2011
Posts: 2830

Re: What is the smallest integer k for which 7^k > 14*7^15
[#permalink]
Show Tags
29 Nov 2016, 15:36
Bunuel wrote: What is the smallest integer k for which 7^k > 14*7^15 ?
A. 14 B. 15 C. 16 D. 17 E. 18 We are given that 7^k > 14 x 7^15. Let’s first simplify 14 x 7^15: 14 x 7^15 = 2^1 x 7^1 x 7^15 = 2 x 7^16 Thus, 7^k > 2 x 7^16 when k = 17 since 7^17 = 7 x 7^16, which is greater than 2 x 7^16. Answer: D
_________________
Jeffery Miller
Head of GMAT Instruction
GMAT Quant SelfStudy Course
500+ lessons 3000+ practice problems 800+ HD solutions



Manager
Joined: 25 Mar 2013
Posts: 245
Location: United States
Concentration: Entrepreneurship, Marketing
GPA: 3.5

Re: What is the smallest integer k for which 7^k > 14*7^15
[#permalink]
Show Tags
20 Dec 2016, 18:42
K= ? Smallest value \(7^{k} > 14 x 7^{15} 7^{k} > 2 x 7^{1} x 7^{15} 7^{k} > 2 x 7^{16}\) k = 17 D
_________________
I welcome analysis on my posts and kudo +1 if helpful. It helps me to improve my craft.Thank you



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

Re: What is the smallest integer k for which 7^k > 14*7^15
[#permalink]
Show Tags
22 Jun 2017, 14:50
7^k > 14*7^15 ? 7^k > 7*2*7^15 7^k> 2*7^16 7^16>2*7^16 As RHS is greater, in order to make LHS greater we increase the power. 7^17>2*7^16 So, smallest value of k = 17 Hence, Answer is D
_________________
"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



Intern
Joined: 27 Apr 2015
Posts: 41

Re: What is the smallest integer k for which 7^k > 14*7^15
[#permalink]
Show Tags
25 Dec 2017, 06:27
Bunuel wrote: What is the smallest integer k for which 7^k > 14*7^15 ?
A. 14 B. 15 C. 16 D. 17 E. 18 \(7^k>14*7^{15}\)=> \(7^k>2*7*7^{15}\)=> \(7^k>2*7^{16}\)=> Therefore k should be > 16. => Since smallest integer >16 is 17. Therefore k=17 => \(7^k=7^{17}=7*7^{16}\)=> \(7*7^{16}>2*7^{16}\)=> Therefore \(7^{17}>2*7^{16}\)=> Therefore k=17 Hence 'D' Thanks Dinesh



VP
Status: It's near  I can see.
Joined: 13 Apr 2013
Posts: 1304
Location: India
Concentration: International Business, Operations
GPA: 3.01
WE: Engineering (Consulting)

Re: What is the smallest integer k for which 7^k > 14*7^15
[#permalink]
Show Tags
30 Dec 2017, 22:08
Bunuel wrote: What is the smallest integer k for which 7^k > 14*7^15 ?
A. 14 B. 15 C. 16 D. 17 E. 18 Simplifying we get, 7^k > 2^1 x 7^1 x 7^15 7^k > 2^1 x 7^16 As we can see RHS has 7^16, we need LHS at least 7^17 (7^17 = 7^1 x 7^ 16, which is surely greater than 2 x 7^16)Therefore k = 17 (D)
_________________
"Do not watch clock; Do what it does. KEEP GOING."




Re: What is the smallest integer k for which 7^k > 14*7^15 &nbs
[#permalink]
30 Dec 2017, 22:08






