Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.
Customized for You
we will pick new questions that match your level based on your Timer History
Track Your Progress
every week, we’ll send you an estimated GMAT score based on your performance
Practice Pays
we will pick new questions that match your level based on your Timer History
Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.
Thank you for using the timer!
We noticed you are actually not timing your practice. Click the START button first next time you use the timer.
There are many benefits to timing your practice, including:
For the positive integers a, b, and k, a^k||b means that a^k
[#permalink]
Show Tags
12 Dec 2012, 03:59
10
35
00:00
A
B
C
D
E
Difficulty:
25% (medium)
Question Stats:
76% (01:45) correct 24% (02:00) wrong based on 2266 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
Re: For the positive integers a, b, and k, a^k||b means that a^k
[#permalink]
Show Tags
12 Dec 2012, 04:02
7
7
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.
Re: For the positive integers a, b, and k, a^k||b means that a^k
[#permalink]
Show Tags
14 Dec 2012, 23:44
6
2
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.
Re: For the positive integers a, b, and k, a^k||b means that a^k
[#permalink]
Show Tags
11 Sep 2014, 11:29
2
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..
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!
Re: For the positive integers a, b, and k, a^k||b means that a^k
[#permalink]
Show Tags
29 Aug 2015, 02:16
1
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.
_________________
Re: For the positive integers a, b, and k, a^k||b means that a^k
[#permalink]
Show Tags
18 May 2016, 12:30
1
1
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
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
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.
_________________
close
76% (01:45) correct 
