|
Author |
Message |
|
TAGS:
|
|
|
Manager
Joined: 02 Dec 2012
Posts: 178
|
For the positive integers a, b, and k, a^k||b means that a^k [#permalink]
Show Tags
 12 Dec 2012, 03:59
9
This post received
KUDOS
26
This post was
BOOKMARKED
D
E
Question Stats:
76% (01:18) correct 24% (01:26) wrong based on 1799 sessions
HideShow timer Statistics
For the positive integers a, b, and k, a^k||b means that a^k is a divisor of b, but a^(k + 1) is not a divisor of b. If k is a positive integer and 2^k||72, then k is equal to (A) 2 (B) 3 (C) 4 (D) 8 (E) 18
Official Answer and Stats are available only to registered users. Register/ Login.
|
|
|
|
|
|
Math Expert
Joined: 02 Sep 2009
Posts: 44573
|
Re: For the positive integers a, b, and k, a^k||b means that a^k [#permalink]
Show Tags
12 Dec 2012, 04:02
4
This post received
KUDOS
Expert's post
8
This post was
BOOKMARKED
Walkabout wrote: For the positive integers a, b, and k, a^k||b means that a^k is a divisor of b, but a^(k + 1) is not a divisor of b. If k is a positive integer and 2^k||72, then k is equal to
(A) 2
(B) 3
(C) 4
(D) 8
(E) 18 \(72=2^3*3^2\), so we have that 2^3 is a divisor of 72 and 2^4 is not. Thus 2^3||72, hence k=3. Answer: B.
_________________
New to the Math Forum?
Please read this: Ultimate GMAT Quantitative Megathread | All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!
Resources:
GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | Tricky questions from previous years.
Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat
DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.
What are GMAT Club Tests?
Extra-hard Quant Tests with Brilliant Analytics
|
|
|
|
|
|
Intern
Joined: 24 Apr 2012
Posts: 48
|
Re: For the positive integers a, b, and k, a^k||b means that a^k [#permalink]
Show Tags
14 Dec 2012, 03:20
Ans: 72= 2^3x3^2, since 2^3 is a divisor of 72 k can be 3. Also 2^4=(2^(k+1)) is not a divisor of 72 , therefore the answer is (B).
_________________
www.mnemoniceducation.com
TURN ON YOUR MINDS!!!
|
|
|
|
|
|
Intern
Joined: 20 Aug 2012
Posts: 3
|
Re: For the positive integers a, b, and k, a^k||b means that a^k [#permalink]
Show Tags
14 Dec 2012, 23:44
4
This post received
KUDOS
1
This post was
BOOKMARKED
Initially looking to the problem one may try to plugin the numbers one by one. Here, 2^2=4 is a divisor of 72 and 2^3=8 is also a divisor of 72. But, we have to choose only one answer.
72=2x2x2x3x3=2^3 *3^2 and it is given that 72/2^k = integer. Here, we can equate 2^3=2^k and hence k=3. But, in fact 2^2 is also a divisor of 72 hence 2 could also be the answer. But, since it is additionally given that k+1 is not a divisor i.e. 2 in this case does not satisfy the condition because 2+1=3 and 2^3 is a divisior of 72. where as 3 satisfies the condition i.e. 3+1= 4 turning into 2^4 which is not a divisor of 72. This is how only one answer choice is left which is equal to 3 = answer choice B.
|
|
|
|
|
|
Intern
Joined: 26 May 2012
Posts: 21
Concentration: Marketing, Technology
GMAT Date: 09-17-2012
|
Re: For the positive integers a, b, and k, a^k||b means that a^k [#permalink]
Show Tags
19 Dec 2012, 07:15
2^k has to be a factor of 72.
Factors of 72: 3^2 x 2^3
Hence, k = 3.
Answer B.
|
|
|
|
|
|
Intern
Joined: 18 May 2013
Posts: 7
Location: Germany
GMAT Date: 09-27-2013
|
Re: For the positive integers a, b, and k, a^k||b means that a^k [#permalink]
Show Tags
25 Jul 2013, 08:30
2
This post received
KUDOS
2
This post was
BOOKMARKED
Prime factorization is also helpful to solve this problem. For ME it´s faster.. Probably it helps someone.
Attachments
PS 110 - prime factorization.jpg [ 20.75 KiB | Viewed 21410 times ]
|
|
|
|
|
|
Manager
Joined: 07 Apr 2014
Posts: 120
|
Re: For the positive integers a, b, and k, a^k||b means that a^k [#permalink]
Show Tags
11 Sep 2014, 11:29
1
This post received
KUDOS
Walkabout wrote: For the positive integers a, b, and k, a^k||b means that a^k is a divisor of b, but a^(k + 1) is not a divisor of b. If k is a positive integer and 2^k||72, then k is equal to
(A) 2
(B) 3
(C) 4
(D) 8
(E) 18 72 = 2*2*2*3*3 72/ 2^k = int ; 72/2^k+1 not integer if k= 2 then divisible ,k=3 then also .. if K=3 then divisible , k=4 then not.. Answer =B
|
|
|
|
|
|
Senior Manager
Status: Math is psycho-logical
Joined: 07 Apr 2014
Posts: 425
Location: Netherlands
GMAT Date: 02-11-2015
WE: Psychology and Counseling (Other)
|
Re: For the positive integers a, b, and k, a^k||b means that a^k [#permalink]
Show Tags
02 Mar 2015, 02:35
If we say that 2^k is a divisor of 72 could we also do this to solve the problem?
Do the prime factorization of 72: 2^3 * 3^3, and then create the following equation:
2^k * 3^3 = 2^3 * 3^3, so k = 3?
Then we are assuming that k is 72, but 72 is still a divisor of 72. So, could we also do that?
As I see it, it is just a more visual way to say what everyone said above. Right...?
|
|
|
|
|
|
Intern
Joined: 12 Nov 2013
Posts: 43
|
Re: For the positive integers a, b, and k, a^k||b means that a^k [#permalink]
Show Tags
28 Aug 2015, 21:28
Bunuel wrote: Walkabout wrote: For the positive integers a, b, and k, a^k||b means that a^k is a divisor of b, but a^(k + 1) is not a divisor of b. If k is a positive integer and 2^k||72, then k is equal to
(A) 2
(B) 3
(C) 4
(D) 8
(E) 18 \(72=2^3*3^2\), so we have that 2^3 is a divisor of 72 and 2^4 is not. Thus 2^3||72, hence k=3. Answer: B. Why is the answer not A? if k= 2 it is still a divisor of 72
_________________
Kindly support by giving Kudos, if my post helped you!
|
|
|
|
|
|
Math Expert
Joined: 02 Sep 2009
Posts: 44573
|
Re: For the positive integers a, b, and k, a^k||b means that a^k [#permalink]
Show Tags
29 Aug 2015, 02:16
harishbiyani8888 wrote: Bunuel wrote: Walkabout wrote: For the positive integers a, b, and k, a^k||b means that a^k is a divisor of b, but a^(k + 1) is not a divisor of b. If k is a positive integer and 2^k||72, then k is equal to
(A) 2
(B) 3
(C) 4
(D) 8
(E) 18 \(72=2^3*3^2\), so we have that 2^3 is a divisor of 72 and 2^4 is not. Thus 2^3||72, hence k=3. Answer: B. Why is the answer not A? if k= 2 it is still a divisor of 72 We need such k that 2^k IS a divisor of 72 but 2^(k+1) is NOT. k cannot be 2 because 2^(2+1) IS a divisor of 72.
_________________
New to the Math Forum?
Please read this: Ultimate GMAT Quantitative Megathread | All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!
Resources:
GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | Tricky questions from previous years.
Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat
DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.
What are GMAT Club Tests?
Extra-hard Quant Tests with Brilliant Analytics
|
|
|
|
|
|
Intern
Joined: 12 Nov 2013
Posts: 43
|
Re: For the positive integers a, b, and k, a^k||b means that a^k [#permalink]
Show Tags
29 Aug 2015, 02:52
Thanks Bunuel for your prompt reply.
_________________
Kindly support by giving Kudos, if my post helped you!
|
|
|
|
|
|
BSchool Forum Moderator
Joined: 12 Aug 2015
Posts: 2576
GRE 1: 323 Q169 V154
|
Re: For the positive integers a, b, and k, a^k||b means that a^k [#permalink]
Show Tags
14 Mar 2016, 08:18
|
|
|
|
|
|
Target Test Prep Representative
Status: Head GMAT Instructor
Affiliations: Target Test Prep
Joined: 04 Mar 2011
Posts: 2273
|
Re: For the positive integers a, b, and k, a^k||b means that a^k [#permalink]
Show Tags
18 May 2016, 12:30
Walkabout wrote: For the positive integers a, b, and k, a^k||b means that a^k is a divisor of b, but a^(k + 1) is not a divisor of b. If k is a positive integer and 2^k||72, then k is equal to
(A) 2
(B) 3
(C) 4
(D) 8
(E) 18 Solution: This is called a "defined function" problem. The parallel lines mean intrinsically nothing, except to establish a relationship between a^k and b.We are given that a^k || b means: 1) b/a^k = integer 2) b/a^(k+1) ≠ integer Next we are given specific numbers 2^k || 72, and we must use the pattern to determine k, using a = 2 and b = 72; thus, we know: 72/2^k = integer AND 72/2^(k+1) ≠ integer In order for 72/2^k = integer AND 72/2^(k+1) ≠ integer to be true, k must equal 3. If have trouble seeing how this works, we can plug 3 back in to prove it. When k = 3, we know: 1) 72/2^3 = 72/8 = 9, which IS an integer. AND 2) 72/2^(3+1) = 72/2^4 = 72/16 = 4 1/2, which is NOT an integer. The answer is B.
_________________
Jeffery Miller
Head of GMAT Instruction
 
GMAT Quant Self-Study Course
500+ lessons 3000+ practice problems 800+ HD solutions
|
|
|
|
|
|
SVP
Joined: 06 Nov 2014
Posts: 1891
|
Re: For the positive integers a, b, and k, a^k||b means that a^k [#permalink]
Show Tags
06 Jun 2016, 08:42
Walkabout wrote: For the positive integers a, b, and k, a^k||b means that a^k is a divisor of b, but a^(k + 1) is not a divisor of b. If k is a positive integer and 2^k||72, then k is equal to
(A) 2
(B) 3
(C) 4
(D) 8
(E) 18 2^k ||72 means 2^k is a divisor of 72, but 2^(k+1) is not a divisor of 72 72 = 2^3*3^2 The maximum powers of 2 in 72 = 3 Hence 2^3 is a divisor of 72 and 2^4 is not a divisor of 72 k = 3 Correct Option: B
|
|
|
|
|
|
Manager
Joined: 03 Jan 2017
Posts: 184
|
Re: For the positive integers a, b, and k, a^k||b means that a^k [#permalink]
Show Tags
25 Mar 2017, 06:28
the formula says that 72 is devisible by 2^k, but not by 2^(k+1)
so, let's factor 72, 2^3 * 3^2, k is 3
Answer is B
|
|
|
|
|
|
Director
Joined: 02 Sep 2016
Posts: 754
|
Re: For the positive integers a, b, and k, a^k||b means that a^k [#permalink]
Show Tags
01 Apr 2017, 07:05
The main point is what if the power of 2 in the integer 72? Factorize 72 72=2^3*3^2 Just concerned with 2. The answer (thus) is 3.
_________________
Help me make my explanation better by providing a logical feedback.
If you liked the post, HIT KUDOS !!
Don't quit.............Do it.
|
|
|
|
|
|
Non-Human User
Joined: 09 Sep 2013
Posts: 6645
|
Re: For the positive integers a, b, and k, a^k||b means that a^k [#permalink]
Show Tags
06 Apr 2018, 12:35
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: For the positive integers a, b, and k, a^k||b means that a^k
[#permalink]
06 Apr 2018, 12:35
|
|
|
|
|
|
|
|
|
|
|
