Author 
Message 
TAGS:

Hide Tags

Intern
Joined: 28 Oct 2013
Posts: 2
Location: United States
GPA: 3.52
WE: General Management (Transportation)

If a is an integer and (a^2)/(12^3) is odd, which of the fol
[#permalink]
Show Tags
Updated on: 31 Dec 2013, 04:23
Question Stats:
52% (01:59) correct 48% (02:10) wrong based on 380 sessions
HideShow timer Statistics
If a is an integer and (a^2)/(12^3) is odd, which of the following must be an odd integer? A. a/4 B. a/12 C. a/27 D. a/36 E. a/72
Official Answer and Stats are available only to registered users. Register/ Login.
_________________
11/5/2013  Economist GMAT test 580 Q28 (20%) / V43 (96%)
Originally posted by teabecca on 30 Dec 2013, 11:22.
Last edited by Bunuel on 31 Dec 2013, 04:23, edited 1 time in total.
Renamed the topic, edited the question and added the OA.




Math Expert
Joined: 02 Sep 2009
Posts: 49208

Re: If a is an integer and (a^2)/(12^3) is odd, which of the fol
[#permalink]
Show Tags
06 Jul 2014, 16:13




Intern
Joined: 11 Nov 2013
Posts: 2
Location: United States

Re: If a is an integer and (a2)/(123) is odd...
[#permalink]
Show Tags
21 Mar 2014, 15:49
My approach:
\(\frac{a^2}{12^3} = \frac{a^2}{2^6*3^3} = \frac{a^2}{2^6}/3^3\) is odd > so \(\frac{a^2}{2^6}\) must be odd > so \(\frac{a}{2^3}=\frac{a}{8}\) must be odd
Therefore, to be odd, the solution must have a multiple of 8 in the denominator.




Intern
Joined: 05 Dec 2013
Posts: 15

Re: If a is an integer and (a2)/(123) is odd...
[#permalink]
Show Tags
30 Dec 2013, 12:21
teabecca wrote: If a is an integer and (a^2)/(12^3) is odd, which of the following must be an odd integer? 1. a/4 2. a/12 3. a/27 4. a/36 5. a/72 Can anybody explain? I'll take a stab at explaining this one, let me know if this helps. In order for the result of the above equation to result in an odd integer, there must be zero even prime integers of the number after canceling out common factors (this is because any even number times an even/odd number will always result in an even number). Therefore, we need to target an answer that will only have odd prime factors. With this said, my first step in tackling this problem was to break down 12 into its prime factors and then distribute the exponent to those prime factors. This left me with a denominator of > 2^6 * 3^3 My next step was to look for an integer in the answer choice that had a prime factor of 2^3 (since the ^2 would distribute to that number making it 2^6 > allowing me to cancel the even numbers and focus on the 3s left over) Beginning with E, a tip that is touted in the Kaplan Advanced GMAT 800 books, I broke 72 down into its primes: 2^3 * 3^2 > distributing this to A^2 resulted in 2^6*3^4 / 2^6 * 3^3. Canceling out common bases leaves me with 3^1 = odd integer Let me know if this helps and/or if you have any follow up questions.



SVP
Joined: 06 Sep 2013
Posts: 1821
Concentration: Finance

Re: If a is an integer and (a2)/(123) is odd...
[#permalink]
Show Tags
06 Jan 2014, 11:08
bparrish89 wrote: teabecca wrote: If a is an integer and (a^2)/(12^3) is odd, which of the following must be an odd integer? 1. a/4 2. a/12 3. a/27 4. a/36 5. a/72 Can anybody explain? I'll take a stab at explaining this one, let me know if this helps. In order for the result of the above equation to result in an odd integer, there must be zero even prime integers of the number after canceling out common factors (this is because any even number times an even/odd number will always result in an even number). Therefore, we need to target an answer that will only have odd prime factors. With this said, my first step in tackling this problem was to break down 12 into its prime factors and then distribute the exponent to those prime factors. This left me with a denominator of > 2^6 * 3^3 My next step was to look for an integer in the answer choice that had a prime factor of 2^3 (since the ^2 would distribute to that number making it 2^6 > allowing me to cancel the even numbers and focus on the 3s left over) Beginning with E, a tip that is touted in the Kaplan Advanced GMAT 800 books, I broke 72 down into its primes: 2^3 * 3^2 > distributing this to A^2 resulted in 2^6*3^4 / 2^6 * 3^3. Canceling out common bases leaves me with 3^1 = odd integer Let me know if this helps and/or if you have any follow up questions. Do you recommend that book? Was it helpful in terms of tips? or basic? Cheers! J



Director
Joined: 03 Feb 2013
Posts: 894
Location: India
Concentration: Operations, Strategy
GPA: 3.88
WE: Engineering (Computer Software)

Re: If a is an integer and (a^2)/(12^3) is odd, which of the fol
[#permalink]
Show Tags
06 Jan 2014, 11:54
teabecca wrote: If a is an integer and (a^2)/(12^3) is odd, which of the following must be an odd integer?
A. a/4 B. a/12 C. a/27 D. a/36 E. a/72 I think "If a is an integer and (a^2)/(12^3) is odd," should be odd integer. If not, all of the options can be odd. Consider a = 1. First and foremost, simplify. a^2/ (2^6 * 3^3) so if we need a^2 to be 2^6 to eliminate any 2s and also we need to eliminate 3^3. so a^2 can be 2^6 * 3^6. Now just test the options Option E) 2^6 * 3^6 / (2^3 * 3^2) leaves one 3 in numerator. Hence the right option.
_________________
Thanks, Kinjal My Debrief : http://gmatclub.com/forum/hardworknevergetsunrewardedforever189267.html#p1449379 My Application Experience : http://gmatclub.com/forum/hardworknevergetsunrewardedforever18926740.html#p1516961 Linkedin : https://www.linkedin.com/in/kinjaldas/
Please click on Kudos, if you think the post is helpful



Intern
Joined: 05 Dec 2013
Posts: 15

Re: If a is an integer and (a2)/(123) is odd...
[#permalink]
Show Tags
06 Jan 2014, 16:22
jlgdr wrote: bparrish89 wrote: teabecca wrote: If a is an integer and (a^2)/(12^3) is odd, which of the following must be an odd integer? 1. a/4 2. a/12 3. a/27 4. a/36 5. a/72 Can anybody explain? I'll take a stab at explaining this one, let me know if this helps. In order for the result of the above equation to result in an odd integer, there must be zero even prime integers of the number after canceling out common factors (this is because any even number times an even/odd number will always result in an even number). Therefore, we need to target an answer that will only have odd prime factors. With this said, my first step in tackling this problem was to break down 12 into its prime factors and then distribute the exponent to those prime factors. This left me with a denominator of > 2^6 * 3^3 My next step was to look for an integer in the answer choice that had a prime factor of 2^3 (since the ^2 would distribute to that number making it 2^6 > allowing me to cancel the even numbers and focus on the 3s left over) Beginning with E, a tip that is touted in the Kaplan Advanced GMAT 800 books, I broke 72 down into its primes: 2^3 * 3^2 > distributing this to A^2 resulted in 2^6*3^4 / 2^6 * 3^3. Canceling out common bases leaves me with 3^1 = odd integer Let me know if this helps and/or if you have any follow up questions. Do you recommend that book? Was it helpful in terms of tips? or basic? Cheers! J Hey J, I would recommend the Manhattan Advanced GMAT Quant books over the Kaplan GMAT 800 book. Felt as if the Kaplan book just provided additional set of questions and explanations of 700 level question, of which you can get just as much out of reviewing on this website. Let me know if this helps. Or feel free to PM if you have any followup questions.



Manager
Joined: 25 Apr 2014
Posts: 126

Re: If a is an integer and (a^2)/(12^3) is odd, which of the fol
[#permalink]
Show Tags
06 Jul 2014, 15:24
Hi Bunuel,
Can you provide clear insight on this question?



Intern
Joined: 29 Mar 2015
Posts: 22

If a is an integer and (a^2)/(12^3) is odd, which of the fol
[#permalink]
Show Tags
08 Oct 2015, 18:16
Here's my approach.
\(\frac{a^2}{3^3 * 4^3}=\frac{a^2}{3^3 * 2^6}=odd\)
We know that \(a^2\) needs to be a multiple of \(2^6\) otherwise \(\frac{a^2}{12}\) wouldn't be an odd integer. Thus, \(a\) must be at least a multiple of \(2^3\). In order to get an odd number when dividing \(a\) by some integer, we need to get rid of \(2^3\). The only answer choice that got three 2s as factors is E) 72.



Board of Directors
Joined: 17 Jul 2014
Posts: 2697
Location: United States (IL)
Concentration: Finance, Economics
GPA: 3.92
WE: General Management (Transportation)

Re: If a is an integer and (a^2)/(12^3) is odd, which of the fol
[#permalink]
Show Tags
18 Mar 2016, 20:39
teabecca wrote: If a is an integer and (a^2)/(12^3) is odd, which of the following must be an odd integer?
A. a/4 B. a/12 C. a/27 D. a/36 E. a/72 we can rewrite: a^2 / 2^6 x 3^3 so a^2 must be at least 2^6*3^4 or a is at least 2^3 * 3^2 A. if we divide by 4, or 2^2, we still have a factor of 2 left out, which will make an even integer..so no B. if we divide by 12 (3x2^2), we are still left with a factor of 2 so no C. 27=3^3. it might be even a noninteger, so no. moreover, we are left with 2^3 ..which will make the number even. D. 36 = 2^2 * 3^2. still we have at least one factor of 2, so no. E. by poe, E is left..72=2^3 * 3^2. since we know that a is at least this number (other variations would include another odd factor)..then dividing it by this will always yield an odd integer.



Target Test Prep Representative
Status: Founder & CEO
Affiliations: Target Test Prep
Joined: 14 Oct 2015
Posts: 3497
Location: United States (CA)

Re: If a is an integer and (a^2)/(12^3) is odd, which of the fol
[#permalink]
Show Tags
12 Jul 2017, 17:00
teabecca wrote: If a is an integer and (a^2)/(12^3) is odd, which of the following must be an odd integer?
A. a/4 B. a/12 C. a/27 D. a/36 E. a/72 If (a^2)/(12^3) is odd and 12^3 is even, we see that a^2 must cancel out all even factors of 12^3. Let’s break down 12^3: 12^3 = (2^2 x 3^1)^3 = 2^6 x 3^3 Thus, a^2 must cancel out 2^6 and also be divisible by 3^3 = 27. The smallest value a could be is 2^3 x 3^2, since then a^2 = 2^6 x 3^4 and (a^2)/(12^3) = 3. Moreover, a cannot have more than 3 factors of 2, because otherwise a^2/12^3 would have been even. The only answer choice in which the denominator has 3 factors of 2 is E, and when a is divided by 72, all the factors of 2 are cancelled out; therefore, the result must be an odd integer. Answer: E
_________________
Scott WoodburyStewart
Founder and CEO
GMAT Quant SelfStudy Course
500+ lessons 3000+ practice problems 800+ HD solutions



NonHuman User
Joined: 09 Sep 2013
Posts: 8069

Re: If a is an integer and (a^2)/(12^3) is odd, which of the fol
[#permalink]
Show Tags
17 Jul 2018, 10:02
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: If a is an integer and (a^2)/(12^3) is odd, which of the fol &nbs
[#permalink]
17 Jul 2018, 10:02






