Find all School-related info fast with the new School-Specific MBA Forum

 It is currently 27 May 2015, 22:59

### GMAT Club Daily Prep

#### 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

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

# Events & Promotions

###### Events & Promotions in June
Open Detailed Calendar

# If x is an integer greater than 1, is x equal to the 12th

Author Message
TAGS:
Intern
Joined: 14 Nov 2010
Posts: 4
Followers: 0

Kudos [?]: 10 [3] , given: 0

If x is an integer greater than 1, is x equal to the 12th [#permalink]  23 Jun 2012, 09:44
3
KUDOS
11
This post was
BOOKMARKED
00:00

Difficulty:

35% (medium)

Question Stats:

66% (01:58) correct 34% (01:01) wrong based on 270 sessions
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.
[Reveal] Spoiler: OA
Math Expert
Joined: 02 Sep 2009
Posts: 27512
Followers: 4320

Kudos [?]: 42467 [24] , given: 6029

Re: If x is an integer greater than 1, is x equal to the 12th [#permalink]  23 Jun 2012, 10:15
24
KUDOS
Expert's post
6
This post was
BOOKMARKED
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.

Hope it's clear.

_________________
Intern
Joined: 14 Nov 2010
Posts: 4
Followers: 0

Kudos [?]: 10 [0], given: 0

Re: If x is an integer greater than 1, is x equal to the 12th [#permalink]  23 Jun 2012, 22:06
Great help....Thx
Intern
Joined: 04 Jun 2012
Posts: 3
Concentration: General Management, Finance
GMAT Date: 07-23-2012
Followers: 0

Kudos [?]: 2 [0], given: 3

Re: If x is an integer greater than 1, is x equal to the 12th [#permalink]  03 Jul 2012, 07:47
2
This post was
BOOKMARKED
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: 27512
Followers: 4320

Kudos [?]: 42467 [0], given: 6029

Re: If x is an integer greater than 1, is x equal to the 12th [#permalink]  03 Jul 2012, 08:01
Expert's post
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.
_________________
Director
Joined: 05 Sep 2010
Posts: 741
Followers: 42

Kudos [?]: 155 [0], given: 49

Re: If x is an integer greater than 1, is x equal to the 12th [#permalink]  15 Aug 2012, 08:39
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: 926
Followers: 12

Kudos [?]: 456 [0], given: 543

Re: If x is an integer greater than 1, is x equal to the 12th [#permalink]  27 Jan 2013, 20:42
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.

Hope it's clear.

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.
_________________

Click +1 Kudos if my post helped...

Amazing Free video explanation for all Quant questions from OG 13 and much more http://www.gmatquantum.com/og13th/

GMAT Prep software What if scenarios gmat-prep-software-analysis-and-what-if-scenarios-146146.html

Math Expert
Joined: 02 Sep 2009
Posts: 27512
Followers: 4320

Kudos [?]: 42467 [0], given: 6029

Re: If x is an integer greater than 1, is x equal to the 12th [#permalink]  27 Jan 2013, 23:56
Expert's post
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.

Hope it's clear.

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.
_________________
Verbal Forum Moderator
Joined: 10 Oct 2012
Posts: 629
Followers: 54

Kudos [?]: 713 [2] , given: 135

Re: If x is an integer greater than 1, is x equal to the 12th [#permalink]  30 Jan 2013, 23:13
2
KUDOS
Expert's post
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.
_________________
Manager
Joined: 29 Oct 2013
Posts: 173
Concentration: Finance
GMAT 1: 750 Q48 V46
GMAT 2: Q V0
GRE 1: 327 Q161 V166
GPA: 3.7
WE: Corporate Finance (Retail Banking)
Followers: 7

Kudos [?]: 177 [0], given: 116

Re: If x is an integer greater than 1, is x equal to the 12th [#permalink]  21 Nov 2013, 20:12
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 consider giving 'kudos' if you like my post and want to thank

SVP
Joined: 06 Sep 2013
Posts: 2046
Concentration: Finance
GMAT 1: 770 Q0 V
Followers: 26

Kudos [?]: 303 [0], given: 354

Re: If x is an integer greater than 1, is x equal to the 12th [#permalink]  27 Dec 2013, 08:52
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
Manager
Joined: 29 Oct 2013
Posts: 173
Concentration: Finance
GMAT 1: 750 Q48 V46
GMAT 2: Q V0
GRE 1: 327 Q161 V166
GPA: 3.7
WE: Corporate Finance (Retail Banking)
Followers: 7

Kudos [?]: 177 [0], given: 116

Re: If x is an integer greater than 1, is x equal to the 12th [#permalink]  12 May 2014, 23:17
Hi Bunuel, pl could you reply to jlgdr and my query? Thanks!
_________________

Please consider giving 'kudos' if you like my post and want to thank

Math Expert
Joined: 02 Sep 2009
Posts: 27512
Followers: 4320

Kudos [?]: 42467 [0], given: 6029

Re: If x is an integer greater than 1, is x equal to the 12th [#permalink]  12 May 2014, 23:56
Expert's post
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: 29 Oct 2013
Posts: 173
Concentration: Finance
GMAT 1: 750 Q48 V46
GMAT 2: Q V0
GRE 1: 327 Q161 V166
GPA: 3.7
WE: Corporate Finance (Retail Banking)
Followers: 7

Kudos [?]: 177 [0], given: 116

Re: If x is an integer greater than 1, is x equal to the 12th [#permalink]  13 May 2014, 00:00
Thanks, Bunuel, for validating my logic
_________________

Please consider giving 'kudos' if you like my post and want to thank

Intern
Joined: 21 Mar 2013
Posts: 25
Concentration: Operations, Entrepreneurship
GMAT 1: 620 Q47 V28
GMAT 2: 680 Q45 V38
WE: Engineering (Manufacturing)
Followers: 0

Kudos [?]: 10 [0], given: 6

Data Sufficiency problem - exponents [#permalink]  07 Aug 2014, 06:53
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.
Intern
Joined: 05 Jun 2012
Posts: 41
GMAT 1: 480 Q48 V9
Followers: 0

Kudos [?]: 9 [0], given: 46

Re: Data Sufficiency problem - exponents [#permalink]  07 Aug 2014, 12:45
any explanation!!!
Manager
Joined: 22 Feb 2009
Posts: 231
Followers: 5

Kudos [?]: 61 [0], given: 148

Re: Data Sufficiency problem - exponents [#permalink]  07 Aug 2014, 20:26
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

Hope it helps.
_________________

.........................................................................
+1 Kudos please, if you like my post

Intern
Joined: 21 Mar 2013
Posts: 25
Concentration: Operations, Entrepreneurship
GMAT 1: 620 Q47 V28
GMAT 2: 680 Q45 V38
WE: Engineering (Manufacturing)
Followers: 0

Kudos [?]: 10 [1] , given: 6

Re: Data Sufficiency problem - exponents [#permalink]  07 Aug 2014, 21:11
1
KUDOS
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.
Math Expert
Joined: 02 Sep 2009
Posts: 27512
Followers: 4320

Kudos [?]: 42467 [0], given: 6029

Re: If x is an integer greater than 1, is x equal to the 12th [#permalink]  12 Aug 2014, 05:55
Expert's post
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.

Merging topics. Please refer to the solution above.

_________________
Re: If x is an integer greater than 1, is x equal to the 12th   [#permalink] 12 Aug 2014, 05:55
Similar topics Replies Last post
Similar
Topics:
10 If [x] denotes the least integer greater than or equal to x and [x] = 9 29 Aug 2014, 06:09
26 If [x] denotes the least integer greater than or equal to x 8 08 May 2012, 04:34
5 If x is not equal to 1, is x^2/(x-1) greater than x? 4 18 Feb 2011, 10:58
If x is an integer greater than 1, is x equal to 2^k for 2 09 Jan 2011, 00:33
If x and y are integers and are greater than 1, is x a 1 31 Mar 2008, 08:41
Display posts from previous: Sort by