Jun 29 07:00 AM PDT  09:00 AM PDT Learn reading strategies that can help even nonvoracious reader to master GMAT RC Jun 30 07:00 AM PDT  09:00 AM PDT Get personalized insights on how to achieve your Target Quant Score. Jul 01 08:00 AM PDT  09:00 AM PDT Game of Timers is a teambased competition based on solving GMAT questions to win epic prizes! Starting July 1st, compete to win prep materials while studying for GMAT! Registration is Open! Jul 01 10:00 PM PDT  11:00 PM PDT Join a FREE 1day workshop and learn how to ace the GMAT while keeping your fulltime job. Limited for the first 99 registrants.
Author 
Message 
TAGS:

Hide Tags

Intern
Joined: 14 Nov 2010
Posts: 3

If x is an integer greater than 1, is x equal to the 12th
[#permalink]
Show Tags
23 Jun 2012, 10:44
Question Stats:
61% (01:30) correct 39% (01:38) wrong based on 1036 sessions
HideShow timer Statistics
If x is an integer greater than 1, is x equal to the 12th power of an integer ? (1) x is equal to the 3rd Power of an integer (2) x is equal to the 4th Power of an integer.
Official Answer and Stats are available only to registered users. Register/ Login.




Math Expert
Joined: 02 Sep 2009
Posts: 55804

Re: If x is an integer greater than 1, is x equal to the 12th
[#permalink]
Show Tags
23 Jun 2012, 11:15
If x is an integer greater than 1, is x equal to the 12th power of an integer ?(1) x is equal to the 3rd Power of an integer > \(x=m^3\) for some positive integer \(m\). If \(m\) itself is 4th power of some integer (for example if \(m=2^4\)), then the answer will be YES (since in this case \(x=(2^4)^3=2^{12}\)), but if it's not (for example if \(m=2\)), then the answer will be NO. Not sufficient. (i) Notice that from this statement we have that \(x^4=m^{12}\).(2) x is equal to the 4th Power of an integer > \(x=n^4\) for some positive integer \(n\). If \(n\) itself is 3rd power of some integer (for example if \(n=2^3\)), then the answer will be YES (since in this case \(x=(2^3)^4=2^{12}\)), but if it's not (for example if \(n=2\)), then the answer will be NO. Not sufficient. (ii) Notice that from this statement we have that \(x^3=n^{12}\).(1)+(2) Divide (i) by (ii): \(x=(\frac{m}{n})^{12}=integer\). Now, \(\frac{m}{n}\) can be neither an irrational number (since it's the ratio of two integers) nor some reduced fraction (since no reduced fraction, like 1/2 or 3/2, when raised to some positive integer power can give an integer), therefore \(\frac{m}{n}\) must be an integer, hence \(x=(\frac{m}{n})^{12}=integer^{12}\). Sufficient. Answer: C. Hope it's clear. P.S. Please read and follow: rulesforpostingpleasereadthisbeforeposting133935.html
_________________




Verbal Forum Moderator
Joined: 10 Oct 2012
Posts: 606

Re: If x is an integer greater than 1, is x equal to the 12th
[#permalink]
Show Tags
31 Jan 2013, 00:13
Given that x>1 and an integer. From F.S 1, we have \(x=t^3\),t is a positive integer. Now for t=16, we will have a sufficient condition but not for say t=8. Thus not sufficient. From F.S 2, we have \(x=z^4\). z is a positive integer. Now just as above, for z=8, we will have a sufficient condition but not for say z=16. Thus not sufficient. Combining both of them, we have; \(x=t^3; x=z^4\). Hence, \(t^3 = z^4\). Now this can be written as \(t = z^{\frac{4}{3}}\) \(\to t = z^{\frac{3+1}{3}} \to t = z*z^{\frac{1}{3}}\) Now, as both t and z are integers, we must have \(z^{\frac{1}{3}}\) as an integer.Thus, t = kz , where \(k = z^{\frac{1}{3}}\) Cubing on both sides, we have \(z = k^3.\) Replace this value of z,\(x = z^4 or x = (k^3)^4 = k^{12}\). C.
_________________




Intern
Joined: 04 Jun 2012
Posts: 3
Concentration: General Management, Finance
GMAT Date: 07232012

Re: If x is an integer greater than 1, is x equal to the 12th
[#permalink]
Show Tags
03 Jul 2012, 08:47
By Statement I: x= m^3 not sufficient since m= 16 satisfies but m= 8 does not satisfy By Statement II: x= n^4 not sufficient since n= 8 satisfies but n = 16 does not satisfy By I & II: X= m^3 and x = n^4 => m^3= n^4 which is only true for 1 or 0, in both cases original condition is satisfied



Math Expert
Joined: 02 Sep 2009
Posts: 55804

If x is an integer greater than 1, is x equal to the 12th
[#permalink]
Show Tags
03 Jul 2012, 09:01
shekharverma wrote: By Statement I: x= m^3 not sufficient since m= 16 satisfies but m= 8 does not satisfy By Statement II: x= n^4 not sufficient since n= 8 satisfies but n = 16 does not satisfy By I & II: X= m^3 and x = n^4 => m^3= n^4 which is only true for 1 or 0, in both cases original condition is satisfied Notice that we are told that \(x\) is an integer greater than 1, so \(m=n=0\) or \(m=n=1\) are not possible since in this case \(x\) becomes 0 or 1. Though if we proceed the way you propose, then from \(x=m^3\) and \(x=n^4\) we can conclude that those two conditions also hold true when \(m=a^{4}\) and \(n=a^3\) (for some positive integer \(a\)), so when \(x=m^3=n^4=a^{12}\). Hope it helps.
_________________



Retired Moderator
Joined: 05 Sep 2010
Posts: 647

Re: If x is an integer greater than 1, is x equal to the 12th
[#permalink]
Show Tags
15 Aug 2012, 09:39
i agree that indivisualy we cannot answer this question ...but how abt this approach .if we combine both statement then we can be sure that x =(int ) ^12 becoz under this condition only can both the conditions be met .so we can now be sure that this int can be expressed as some int raised to the power of 12 .expert plz evaluate this !!



Director
Joined: 29 Nov 2012
Posts: 732

Re: If x is an integer greater than 1, is x equal to the 12th
[#permalink]
Show Tags
27 Jan 2013, 21:42
Bunuel wrote: If x is an integer greater than 1, is x equal to the 12th power of an integer ?(1) x is equal to the 3rd Power of an integer > \(x=m^3\) for some positive integer \(m\). If \(m\) itself is 4th power of some integer (for example if \(m=2^4\)), then the answer will be YES (since in this case \(x=(2^4)^3=2^{12}\)), but if it's not (for example if \(m=2\)), then the answer will be NO. Not sufficient. (i) Notice that from this statement we have that \(x^4=m^{12}\).(2) x is equal to the 4th Power of an integer > \(x=n^4\) for some positive integer \(n\). If \(n\) itself is 3rd power of some integer (for example if \(n=2^3\)), then the answer will be YES (since in this case \(x=(2^3)^4=2^{12}\)), but if it's not (for example if \(n=2\)), then the answer will be NO. Not sufficient. (ii) Notice that from this statement we have that \(x^3=n^{12}\).(1)+(2) Divide (i) by (ii): \(x=(\frac{m}{n})^{12}=integer\). Now, \(\frac{m}{n}\) can be neither an irrational number (since it's the ratio of two integers) nor some reduced fraction (since no reduced fraction, like 1/2 or 3/2, when raised to some positive integer power can give an integer), therefore \(\frac{m}{n}\) must be an integer, hence \(x=(\frac{m}{n})^{12}=integer^{12}\). Sufficient.
Answer: C. Hope it's clear. P.S. Please read and follow: rulesforpostingpleasereadthisbeforeposting133935.html Is this true in all cases that it must be an integer ( is there a theorem or something along those lines) , could you please provide an example.



Math Expert
Joined: 02 Sep 2009
Posts: 55804

Re: If x is an integer greater than 1, is x equal to the 12th
[#permalink]
Show Tags
28 Jan 2013, 00:56
fozzzy wrote: Bunuel wrote: If x is an integer greater than 1, is x equal to the 12th power of an integer ?(1) x is equal to the 3rd Power of an integer > \(x=m^3\) for some positive integer \(m\). If \(m\) itself is 4th power of some integer (for example if \(m=2^4\)), then the answer will be YES (since in this case \(x=(2^4)^3=2^{12}\)), but if it's not (for example if \(m=2\)), then the answer will be NO. Not sufficient. (i) Notice that from this statement we have that \(x^4=m^{12}\).(2) x is equal to the 4th Power of an integer > \(x=n^4\) for some positive integer \(n\). If \(n\) itself is 3rd power of some integer (for example if \(n=2^3\)), then the answer will be YES (since in this case \(x=(2^3)^4=2^{12}\)), but if it's not (for example if \(n=2\)), then the answer will be NO. Not sufficient. (ii) Notice that from this statement we have that \(x^3=n^{12}\).(1)+(2) Divide (i) by (ii): \(x=(\frac{m}{n})^{12}=integer\). Now, \(\frac{m}{n}\) can be neither an irrational number (since it's the ratio of two integers) nor some reduced fraction (since no reduced fraction, like 1/2 or 3/2, when raised to some positive integer power can give an integer), therefore \(\frac{m}{n}\) must be an integer, hence \(x=(\frac{m}{n})^{12}=integer^{12}\). Sufficient.
Answer: C. Hope it's clear. P.S. Please read and follow: rulesforpostingpleasereadthisbeforeposting133935.html Is this true in all cases that it must be an integer ( is there a theorem or something along those lines) , could you please provide an example. What you mean by "all cases"? Anyway, if m and n are integers and \(x=(\frac{m}{n})^{12}=integer\), then m/n=integer.
_________________



Retired Moderator
Joined: 29 Oct 2013
Posts: 257
Concentration: Finance
GPA: 3.7
WE: Corporate Finance (Retail Banking)

Re: If x is an integer greater than 1, is x equal to the 12th
[#permalink]
Show Tags
21 Nov 2013, 21:12
So the important take away here is: if X = nth power of an integer and x= mth power of an integer simultaneously, x= (LCM of m and n)th power of an integer?
_________________
Please contact me for super inexpensive quality private tutoring
My journey V46 and 750 > http://gmatclub.com/forum/myjourneyto46onverbal750overall171722.html#p1367876



SVP
Joined: 06 Sep 2013
Posts: 1651
Concentration: Finance

Re: If x is an integer greater than 1, is x equal to the 12th
[#permalink]
Show Tags
27 Dec 2013, 09:52
MensaNumber wrote: So the important take away here is: if X = nth power of an integer and x= mth power of an integer simultaneously, x= (LCM of m and n)th power of an integer? Well that's what I'm asking myself but think about it for a sec For perfect cube we need all prime factors to have a multiple of 3 For perfect fourth powers we need all the same prime factors to have a multiple of 4 Hence, for both we need all the prime factors to have multiples of 12 at least So IMHO I think this should be correct under this scenario Bunuel, would you give your blessing on this statement? Cheers! J



Math Expert
Joined: 02 Sep 2009
Posts: 55804

Re: If x is an integer greater than 1, is x equal to the 12th
[#permalink]
Show Tags
13 May 2014, 00:56
jlgdr wrote: MensaNumber wrote: So the important take away here is: if X = nth power of an integer and x= mth power of an integer simultaneously, x= (LCM of m and n)th power of an integer? Well that's what I'm asking myself but think about it for a sec For perfect cube we need all prime factors to have a multiple of 3 For perfect fourth powers we need all the same prime factors to have a multiple of 4 Hence, for both we need all the prime factors to have multiples of 12 at least So IMHO I think this should be correct under this scenario Bunuel, would you give your blessing on this statement? Cheers! J Yes, that's correct.
_________________



Manager
Joined: 22 Feb 2009
Posts: 159

Re: Data Sufficiency problem  exponents
[#permalink]
Show Tags
07 Aug 2014, 21:26
taransambi wrote: Source: Question Pack 1
If X is an integer greater than 1, is X equal to 12th power of an integer?
1. X is equal to 3rd power of an integer. 2. X is equal to 4th power for an integer. Statement 1: x= a^3. For example, x = 2^3 = 8 > cannot equal to 12th power of an integer> INSUFFICIENT Statement 2: x= a^4. For example, x = 2^4 = 16> cannot equal to 12th power of an integer> INSUFFICIENT Combine 2 statements: x= a^3 > x^4= a^12 x= b^4 > x^3=b^12 > x^4/x^3 = x = a^12/b^12 = (a/b)^12 x is an integer, so (a/b)^12 is an integer, so (a/b) has to be an integer also, called c so x= c^12 > SUFFICIENT C is the answer. Hope it helps.
_________________
......................................................................... +1 Kudos please, if you like my post



Intern
Joined: 22 Mar 2013
Posts: 18
Concentration: Operations, Entrepreneurship
GMAT 1: 620 Q47 V28 GMAT 2: 680 Q45 V38
WE: Engineering (Manufacturing)

Re: Data Sufficiency problem  exponents
[#permalink]
Show Tags
07 Aug 2014, 22:11
If X is an integer greater than 1, is X equal to 12th power of an integer?
1. X is equal to 3rd power of an integer. 2. X is equal to 4th power for an integer.
Here is how i solved it. From statements 1 and 2, we know that X=a^3 as well as b^4. Therefore, a^3=b^4.
This is only possible when either 1) a=b=1 OR 2) a=b=0.
The questions says that X>1, so none of the above cases are true.
So, for a^3 to be equal to b^4, a needs to have a 4th power of b in it AND b needs to have a 3rd power of a in it. In either case, X will have a 12th power of an integer in it. Hence, C.



Senior Manager
Status: Verbal Forum Moderator
Joined: 17 Apr 2013
Posts: 463
Location: India
GMAT 1: 710 Q50 V36 GMAT 2: 750 Q51 V41 GMAT 3: 790 Q51 V49
GPA: 3.3

Re: If x is an integer greater than 1, is x equal to the 12th
[#permalink]
Show Tags
04 Jun 2015, 09:16
Bunuel wrote: If x is an integer greater than 1, is x equal to the 12th power of an integer ?(1) x is equal to the 3rd Power of an integer > \(x=m^3\) for some positive integer \(m\). If \(m\) itself is 4th power of some integer (for example if \(m=2^4\)), then the answer will be YES (since in this case \(x=(2^4)^3=2^{12}\)), but if it's not (for example if \(m=2\)), then the answer will be NO. Not sufficient. (i) Notice that from this statement we have that \(x^4=m^{12}\).(2) x is equal to the 4th Power of an integer > \(x=n^4\) for some positive integer \(n\). If \(n\) itself is 3rd power of some integer (for example if \(n=2^3\)), then the answer will be YES (since in this case \(x=(2^3)^4=2^{12}\)), but if it's not (for example if \(n=2\)), then the answer will be NO. Not sufficient. (ii) Notice that from this statement we have that \(x^3=n^{12}\).(1)+(2) Divide (i) by (ii): \(x=(\frac{m}{n})^{12}=integer\). Now, \(\frac{m}{n}\) can be neither an irrational number (since it's the ratio of two integers) nor some reduced fraction (since no reduced fraction, like 1/2 or 3/2, when raised to some positive integer power can give an integer), therefore \(\frac{m}{n}\) must be an integer, hence \(x=(\frac{m}{n})^{12}=integer^{12}\). Sufficient. Answer: C. Hope it's clear. P.S. Please read and follow: rulesforpostingpleasereadthisbeforeposting133935.html What if m/n = √2 type that is quite possible.
_________________
Like my post Send me a Kudos It is a Good manner.My Debrief: http://gmatclub.com/forum/howtoscore750and750imovedfrom710to189016.html



Math Expert
Joined: 02 Sep 2009
Posts: 55804

Re: If x is an integer greater than 1, is x equal to the 12th
[#permalink]
Show Tags
04 Jun 2015, 09:21
honchos wrote: Bunuel wrote: If x is an integer greater than 1, is x equal to the 12th power of an integer ?(1) x is equal to the 3rd Power of an integer > \(x=m^3\) for some positive integer \(m\). If \(m\) itself is 4th power of some integer (for example if \(m=2^4\)), then the answer will be YES (since in this case \(x=(2^4)^3=2^{12}\)), but if it's not (for example if \(m=2\)), then the answer will be NO. Not sufficient. (i) Notice that from this statement we have that \(x^4=m^{12}\).(2) x is equal to the 4th Power of an integer > \(x=n^4\) for some positive integer \(n\). If \(n\) itself is 3rd power of some integer (for example if \(n=2^3\)), then the answer will be YES (since in this case \(x=(2^3)^4=2^{12}\)), but if it's not (for example if \(n=2\)), then the answer will be NO. Not sufficient. (ii) Notice that from this statement we have that \(x^3=n^{12}\).(1)+(2) Divide (i) by (ii): \(x=(\frac{m}{n})^{12}=integer\). Now, \(\frac{m}{n}\) can be neither an irrational number (since it's the ratio of two integers) nor some reduced fraction (since no reduced fraction, like 1/2 or 3/2, when raised to some positive integer power can give an integer), therefore \(\frac{m}{n}\) must be an integer, hence \(x=(\frac{m}{n})^{12}=integer^{12}\). Sufficient. Answer: C. Hope it's clear. P.S. Please read and follow: rulesforpostingpleasereadthisbeforeposting133935.html What if m/n = √2 type that is quite possible. Have you read the highlighted part?
_________________



Senior Manager
Status: Verbal Forum Moderator
Joined: 17 Apr 2013
Posts: 463
Location: India
GMAT 1: 710 Q50 V36 GMAT 2: 750 Q51 V41 GMAT 3: 790 Q51 V49
GPA: 3.3

Re: If x is an integer greater than 1, is x equal to the 12th
[#permalink]
Show Tags
04 Jun 2015, 09:26
Bunuel wrote: honchos wrote: Bunuel wrote: If x is an integer greater than 1, is x equal to the 12th power of an integer ?(1) x is equal to the 3rd Power of an integer > \(x=m^3\) for some positive integer \(m\). If \(m\) itself is 4th power of some integer (for example if \(m=2^4\)), then the answer will be YES (since in this case \(x=(2^4)^3=2^{12}\)), but if it's not (for example if \(m=2\)), then the answer will be NO. Not sufficient. (i) Notice that from this statement we have that \(x^4=m^{12}\).(2) x is equal to the 4th Power of an integer > \(x=n^4\) for some positive integer \(n\). If \(n\) itself is 3rd power of some integer (for example if \(n=2^3\)), then the answer will be YES (since in this case \(x=(2^3)^4=2^{12}\)), but if it's not (for example if \(n=2\)), then the answer will be NO. Not sufficient. (ii) Notice that from this statement we have that \(x^3=n^{12}\).(1)+(2) Divide (i) by (ii): \(x=(\frac{m}{n})^{12}=integer\). Now, \(\frac{m}{n}\) can be neither an irrational number (since it's the ratio of two integers) nor some reduced fraction (since no reduced fraction, like 1/2 or 3/2, when raised to some positive integer power can give an integer), therefore \(\frac{m}{n}\) must be an integer, hence \(x=(\frac{m}{n})^{12}=integer^{12}\). Sufficient. Answer: C. Hope it's clear. P.S. Please read and follow: rulesforpostingpleasereadthisbeforeposting133935.html What if m/n = √2 type that is quite possible. Have you read the highlighted part? Ratio of two Integers is never an Irrational number, right?
_________________
Like my post Send me a Kudos It is a Good manner.My Debrief: http://gmatclub.com/forum/howtoscore750and750imovedfrom710to189016.html



Math Expert
Joined: 02 Sep 2009
Posts: 55804

Re: If x is an integer greater than 1, is x equal to the 12th
[#permalink]
Show Tags
04 Jun 2015, 09:29
honchos wrote: Ratio of two Integers is never an Irrational number, right?
Yes. In mathematics, an irrational number is any real number that cannot be expressed as a ratio of integers. Irrational numbers cannot be represented as terminating or repeating decimals.
_________________



Current Student
Status: DONE!
Joined: 05 Sep 2016
Posts: 368

Re: If x is an integer greater than 1, is x equal to the 12th
[#permalink]
Show Tags
23 Sep 2016, 09:53
C is correct. Here's why:
(1) x = n^3 > Try plugging in arbitrary value for n.
x = 2^3 > x = 8 > now ask yourself what integer raised to the 12th power could give you 8. Answer = none
INSUFFICIENT
(2) x = n^4 > repeat the same process as in (1)
x = 2^4 > x= 16 > There is no integer that could give us this value using main equation
INSUFFICIENT
(1) + (2) Together  SUFFICIENT



Manager
Joined: 28 Sep 2013
Posts: 81

Re: If x is an integer greater than 1, is x equal to the 12th
[#permalink]
Show Tags
08 Dec 2016, 15:23
Bunuel wrote: [b] Now, \(\frac{m}{n}\) can be neither an irrational number (since it's the ratio of two integers) I am unable to understand this part can you please explain or perhaps provide me a link where I can understand my knowledge gap. Thanks!
_________________
Richa Champion  My GMAT Journey  470 → 720 → 740Target → 760+ Not Improving after Multiple attempts. I can guide You. Contact me → richacrunch2@gmail.com



Math Expert
Joined: 02 Sep 2009
Posts: 55804

Re: If x is an integer greater than 1, is x equal to the 12th
[#permalink]
Show Tags
09 Dec 2016, 02:55
RichaChampion wrote: Bunuel wrote: [b] Now, \(\frac{m}{n}\) can be neither an irrational number (since it's the ratio of two integers) I am unable to understand this part can you please explain or perhaps provide me a link where I can understand my knowledge gap. Thanks! Check here: ifnpqpandqarenonzerointegersisaninteger101475.html and here: isaeven133175.html
_________________




Re: If x is an integer greater than 1, is x equal to the 12th
[#permalink]
09 Dec 2016, 02:55



Go to page
1 2
Next
[ 27 posts ]



