What is the value of x? : GMAT Data Sufficiency (DS)
Check GMAT Club Decision Tracker for the Latest School Decision Releases http://gmatclub.com/AppTrack

 It is currently 24 Jan 2017, 09:42

### 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

# What is the value of x?

Author Message
TAGS:

### Hide Tags

Intern
Joined: 23 Nov 2010
Posts: 7
Location: India
Followers: 0

Kudos [?]: 16 [2] , given: 14

What is the value of x? [#permalink]

### Show Tags

01 Jan 2011, 00:32
2
KUDOS
17
This post was
BOOKMARKED
00:00

Difficulty:

95% (hard)

Question Stats:

31% (01:58) correct 69% (01:00) wrong based on 392 sessions

### HideShow timer Statistics

What is the value of x?

(1) x^3 is a 2-digit positive odd integer.
(2) x^4 is a 2-digit positive odd integer.
[Reveal] Spoiler: OA
Math Expert
Joined: 02 Sep 2009
Posts: 36638
Followers: 7106

Kudos [?]: 93648 [6] , given: 10583

### Show Tags

01 Jan 2011, 03:14
6
KUDOS
Expert's post
6
This post was
BOOKMARKED
shan123 wrote:
What is the value of x?
(1) X3 is a 2-digit positive odd integer. (2) X4 is a 2-digit positive odd integer.

I don't know whether the answer is correct. I got a different one.

What is the value of x?

Note that we are not told that x is an integer

(1) x^3 is a 2-digit positive odd integer --> now, if $$x$$ is an integer then $$x=3$$ as $$x^3=27$$ is the only odd 2-digit positive cube of an integer (1^3=1 and 5^3=125) but if $$x$$ is not an integer then it can be cube root of any 2-digit positive odd integer, for example if $$x=\sqrt[3]{11}$$ then $$x^3=11$$. Not sufficient.

(2) x^4 is a 2-digit positive odd integer --> basically the same here: if $$x$$ is an integer then $$x=3$$ or $$x=-3$$ as $$x^4=81$$ is the only odd 2-digit positive integer which is in fourth power of an integer (1^4=1 and 5^4=625) (so even if $$x$$ is an integer this statement is still insufficient as it gives two values for $$x$$: 3 and -3). $$x$$ also can be non-integer as above: it can be fourth root from any 2-digit positive odd integer, for example if $$x=\sqrt[4]{11}$$ then $$x^4=11$$. Not sufficient.

(1)+(2) $$x$$ cannot be an irrational number (so that both x^3 and x^4 to be integers), so $$x$$ must be 3. Sufficient.

_________________
Intern
Joined: 23 Nov 2010
Posts: 7
Location: India
Followers: 0

Kudos [?]: 16 [0], given: 14

### Show Tags

01 Jan 2011, 03:48
Bunuel wrote:
shan123 wrote:
What is the value of x?
(1) X3 is a 2-digit positive odd integer. (2) X4 is a 2-digit positive odd integer.

I don't know whether the answer is correct. I got a different one.

What is the value of x?

Note that we are not told that x is an integer

(1) x^3 is a 2-digit positive odd integer --> now, if $$x$$ is an integer then $$x=3$$ as $$x^3=27$$ is the only odd 2-digit positive cube of an integer (1^3=1 and 5^3=125) but if $$x$$ is not an integer then it can be cube root of any 2-digit positive odd integer, for example if $$x=\sqrt[3]{11}$$ then $$x^3=11$$. Not sufficient.

(2) x^4 is a 2-digit positive odd integer --> basically the same here: if $$x$$ is an integer then $$x=3$$ or $$x=-3$$ as $$x^4=81$$ is the only odd 2-digit positive integer which is in fourth power of an integer (1^4=1 and 5^4=625) (so even if $$x$$ is an integer this statement is still insufficient as it gives two values for $$x$$: 3 and -3). $$x$$ also can be non-integer as above: it can be fourth root from any 2-digit positive odd integer, for example if $$x=\sqrt[4]{11}$$ then $$x^4=11$$. Not sufficient.

(1)+(2) $$x$$ can not be an irrational number (so that both x^3 and x^4 to be integers), so $$x$$ must be 3. Sufficient.

Thanks for the answer and detailed explanation.
Current Student
Status: Up again.
Joined: 31 Oct 2010
Posts: 541
Concentration: Strategy, Operations
GMAT 1: 710 Q48 V40
GMAT 2: 740 Q49 V42
Followers: 21

Kudos [?]: 414 [0], given: 75

### Show Tags

17 Feb 2011, 22:29
Carelessly, I overlooked the possibility that x could be negative. Thanks Bunuel!
_________________

My GMAT debrief: http://gmatclub.com/forum/from-620-to-710-my-gmat-journey-114437.html

Manager
Joined: 17 Feb 2011
Posts: 200
Concentration: Real Estate, Finance
Schools: MIT (Sloan) - Class of 2014
GMAT 1: 760 Q50 V44
Followers: 44

Kudos [?]: 708 [0], given: 70

### Show Tags

18 Feb 2011, 09:25
Tricky one, I considered the integer constraint that didn't exist. Must take care with this.

Bunuel wrote:
shan123 wrote:
What is the value of x?
(1) X3 is a 2-digit positive odd integer. (2) X4 is a 2-digit positive odd integer.

I don't know whether the answer is correct. I got a different one.

What is the value of x?

Note that we are not told that x is an integer

(1) x^3 is a 2-digit positive odd integer --> now, if $$x$$ is an integer then $$x=3$$ as $$x^3=27$$ is the only odd 2-digit positive cube of an integer (1^3=1 and 5^3=125) but if $$x$$ is not an integer then it can be cube root of any 2-digit positive odd integer, for example if $$x=\sqrt[3]{11}$$ then $$x^3=11$$. Not sufficient.

(2) x^4 is a 2-digit positive odd integer --> basically the same here: if $$x$$ is an integer then $$x=3$$ or $$x=-3$$ as $$x^4=81$$ is the only odd 2-digit positive integer which is in fourth power of an integer (1^4=1 and 5^4=625) (so even if $$x$$ is an integer this statement is still insufficient as it gives two values for $$x$$: 3 and -3). $$x$$ also can be non-integer as above: it can be fourth root from any 2-digit positive odd integer, for example if $$x=\sqrt[4]{11}$$ then $$x^4=11$$. Not sufficient.

(1)+(2) $$x$$ can not be an irrational number (so that both x^3 and x^4 to be integers), so $$x$$ must be 3. Sufficient.

VP
Status: Current Student
Joined: 24 Aug 2010
Posts: 1345
Location: United States
GMAT 1: 710 Q48 V40
WE: Sales (Consumer Products)
Followers: 107

Kudos [?]: 420 [0], given: 73

### Show Tags

18 Feb 2011, 12:13
_________________

The Brain Dump - From Low GPA to Top MBA (Updated September 1, 2013) - A Few of My Favorite Things--> http://cheetarah1980.blogspot.com

Manager
Joined: 04 Oct 2011
Posts: 224
Location: India
GMAT 1: 440 Q33 V13
GMAT 2: 0 Q0 V0
GPA: 3
Followers: 0

Kudos [?]: 48 [0], given: 44

Re: What is the value of x? [#permalink]

### Show Tags

05 Jan 2013, 21:47
carcass wrote:
What is the value of$$x$$ ?

(1) $$X^3$$ is a 2-digit positive odd integer.

(2)$$X^4$$ is a 2-digit positive odd integer.

Hi carcass,

Stat 1 :

Only 2 digit positive integers for S1 are :
$$x$$-------- 3 ------ 4
$$x^3$$ ----27-----64

Here odd integer is x=3 and x^3 = 27
SUFFICIENT

Stat 2 :

Only 2 digit positive integers for S2 are :
$$x$$----------+/-2-------------+/-3
$$x^3$$----------16----------81

Here odd integer is x=+/-3 and x^3 = 81
INSUFFICIENT (two values for x)

IMO A.

But how come C?
did i missed out anything?
_________________

GMAT - Practice, Patience, Persistence
Kudos if u like

Current Student
Joined: 27 Jun 2012
Posts: 418
Concentration: Strategy, Finance
Followers: 77

Kudos [?]: 782 [0], given: 184

Re: What is the value of x? [#permalink]

### Show Tags

05 Jan 2013, 21:55
Shanmugam, the problem doesnt explicitly state that x is an integer. It can be fraction.

e.g. Choice (A), x can be fraction -> $$x^3 = 35$$ i.e. x = $$\sqrt[3]{35}$$

Similarly Choice (B) alone is not sufficient.

_________________

Thanks,
Prashant Ponde

Tough 700+ Level RCs: Passage1 | Passage2 | Passage3 | Passage4 | Passage5 | Passage6 | Passage7
VOTE GMAT Practice Tests: Vote Here
PowerScore CR Bible - Official Guide 13 Questions Set Mapped: Click here

Current Student
Joined: 27 Jun 2012
Posts: 418
Concentration: Strategy, Finance
Followers: 77

Kudos [?]: 782 [3] , given: 184

Re: What is the value of x? [#permalink]

### Show Tags

05 Jan 2013, 22:42
3
KUDOS

Always watch out for ZIP trap (assuming Zero, Integer, Positive) -> (Make sure to check for 0, factions and negatives)
Especially for inequalities, algebraic, number/fraction problems.
_________________

Thanks,
Prashant Ponde

Tough 700+ Level RCs: Passage1 | Passage2 | Passage3 | Passage4 | Passage5 | Passage6 | Passage7
VOTE GMAT Practice Tests: Vote Here
PowerScore CR Bible - Official Guide 13 Questions Set Mapped: Click here

Moderator
Joined: 01 Sep 2010
Posts: 3097
Followers: 788

Kudos [?]: 6574 [0], given: 1023

Re: What is the value of x? [#permalink]

### Show Tags

06 Jan 2013, 04:47
Sorry Bunuel I do not "visualize" why in C $$x^3$$ and $$x^4$$cannot be rational numbers aka integers

because an irrational can't be at the same time an 2 digits odd number ?' and of course only 3 meets both conditions ?'

Can you explain me please ?'

Thanks
_________________
Math Expert
Joined: 02 Sep 2009
Posts: 36638
Followers: 7106

Kudos [?]: 93648 [0], given: 10583

Re: What is the value of x? [#permalink]

### Show Tags

07 Jan 2013, 03:12
carcass wrote:
Sorry Bunuel I do not "visualize" why in C $$x^3$$ and $$x^4$$cannot be rational numbers aka integers

because an irrational can't be at the same time an 2 digits odd number ?' and of course only 3 meets both conditions ?'

Can you explain me please ?'

Thanks

Not sure I understand what you mean.

Anyway, rational numbers and integers are not the same. Also, irrational numbers are not integers, thus they can be neither odd nor even.

For more check here: math-number-theory-88376.html
_________________
Moderator
Joined: 01 Sep 2010
Posts: 3097
Followers: 788

Kudos [?]: 6574 [0], given: 1023

Re: What is the value of x? [#permalink]

### Show Tags

07 Jan 2013, 04:29
basically 1) is insuff because we have to consider integers and non integers (so irrational numbers). Same for 2)

Bothe statements are suff because we have only 3 that mettes the criteria so we have to consider only the 3 (the integer). So sufficient

But why we C is sufficient ?' why we can not consider the irrational numbers ??

Thanks. Now I hope is more clear what I mean. I'm sorry if I have explained myself badly
_________________
Math Expert
Joined: 02 Sep 2009
Posts: 36638
Followers: 7106

Kudos [?]: 93648 [0], given: 10583

Re: What is the value of x? [#permalink]

### Show Tags

07 Jan 2013, 05:11
Expert's post
1
This post was
BOOKMARKED
carcass wrote:
basically 1) is insuff because we have to consider integers and non integers (so irrational numbers). Same for 2)

Bothe statements are suff because we have only 3 that mettes the criteria so we have to consider only the 3 (the integer). So sufficient

But why we C is sufficient ?' why we can not consider the irrational numbers ??

Thanks. Now I hope is more clear what I mean. I'm sorry if I have explained myself badly

If x is an irrational number then x^3 and x^4 cannot both be integers as given in the statements, so x can only be 3.
_________________
Manager
Joined: 14 Nov 2011
Posts: 149
Location: United States
Concentration: General Management, Entrepreneurship
GPA: 3.61
WE: Consulting (Manufacturing)
Followers: 0

Kudos [?]: 16 [0], given: 103

Re: What is the value of x? [#permalink]

### Show Tags

16 Jun 2013, 02:59
Bunuel wrote:
carcass wrote:
basically 1) is insuff because we have to consider integers and non integers (so irrational numbers). Same for 2)

Bothe statements are suff because we have only 3 that mettes the criteria so we have to consider only the 3 (the integer). So sufficient

But why we C is sufficient ?' why we can not consider the irrational numbers ??

Thanks. Now I hope is more clear what I mean. I'm sorry if I have explained myself badly

If x is an irrational number then x^3 and x^4 cannot both be integers as given in the statements, so x can only be 3.

Hi Bunnel,

Still did not get this part:
If x is an irrational number then x^3 and x^4 cannot both be integers as given in the statements, so x can only be 3

Irrational no cannot be expressed as p/q, where p and q are integers.

I made my understand it like this:
Their is only 1 number possible whose cube is 27 and only one number has fourth power equal to 81.
Which is integer 3.

Please explain why have you mentioned it here.
Math Expert
Joined: 02 Sep 2009
Posts: 36638
Followers: 7106

Kudos [?]: 93648 [0], given: 10583

Re: What is the value of x? [#permalink]

### Show Tags

16 Jun 2013, 03:15
cumulonimbus wrote:
Bunuel wrote:
carcass wrote:
basically 1) is insuff because we have to consider integers and non integers (so irrational numbers). Same for 2)

Bothe statements are suff because we have only 3 that mettes the criteria so we have to consider only the 3 (the integer). So sufficient

But why we C is sufficient ?' why we can not consider the irrational numbers ??

Thanks. Now I hope is more clear what I mean. I'm sorry if I have explained myself badly

If x is an irrational number then x^3 and x^4 cannot both be integers as given in the statements, so x can only be 3.

Hi Bunnel,

Still did not get this part:
If x is an irrational number then x^3 and x^4 cannot both be integers as given in the statements, so x can only be 3

Irrational no cannot be expressed as p/q, where p and q are integers.

I made my understand it like this:
Their is only 1 number possible whose cube is 27 and only one number has fourth power equal to 81.
Which is integer 3.

Please explain why have you mentioned it here.

_________________
Senior Manager
Joined: 29 Oct 2013
Posts: 297
Concentration: Finance
GMAT 1: 750 Q V46
GPA: 3.7
WE: Corporate Finance (Retail Banking)
Followers: 14

Kudos [?]: 378 [0], given: 197

### Show Tags

23 May 2014, 06:25
Bunuel wrote:
shan123 wrote:

(1)+(2) $$x$$ cannot be an irrational number (so that both x^3 and x^4 to be integers), so $$x$$ must be 3. Sufficient.

Hi Bunuel: Just like others, I also have a hard time visualizing that there does not exist an irrational number whose 3rd and 4th power both result in an odd digit integer. I mean integer is a smaller set compared to irrational numbers and we still have 3 (an integer) whose 3rd and 4th power both result in an odd 2-digit integer. On the other hand in terms of irrational numbers we have tremendous possibilities even between two integers we have infinite irrational numbers and we cannot have such a number. It some how feels odd to me. I have no doubt what you are saying is right but I have hard time imagining it. Maybe my understanding of irrational numbers and their powers is still primordial.
_________________

My journey V46 and 750 -> http://gmatclub.com/forum/my-journey-to-46-on-verbal-750overall-171722.html#p1367876

Math Expert
Joined: 02 Sep 2009
Posts: 36638
Followers: 7106

Kudos [?]: 93648 [1] , given: 10583

### Show Tags

23 May 2014, 09:41
1
KUDOS
Expert's post
1
This post was
BOOKMARKED
MensaNumber wrote:
Bunuel wrote:
shan123 wrote:

(1)+(2) $$x$$ cannot be an irrational number (so that both x^3 and x^4 to be integers), so $$x$$ must be 3. Sufficient.

Hi Bunuel: Just like others, I also have a hard time visualizing that there does not exist an irrational number whose 3rd and 4th power both result in an odd digit integer. I mean integer is a smaller set compared to irrational numbers and we still have 3 (an integer) whose 3rd and 4th power both result in an odd 2-digit integer. On the other hand in terms of irrational numbers we have tremendous possibilities even between two integers we have infinite irrational numbers and we cannot have such a number. It some how feels odd to me. I have no doubt what you are saying is right but I have hard time imagining it. Maybe my understanding of irrational numbers and their powers is still primordial.

Say x IS an irrational number and x*x*x=x^3=integer. In this case x*x*x*x=x^3*x=integer*irrational=irrational.

If x is an irrational number and x*x*x*x=x^4=integer, then x^3=x^4/x=integer/irrational=irrational.

So, as you can see if x is an irrational number, then both x^3 and x^4 cannot be rational.

Does this make sense?
_________________
Senior Manager
Joined: 29 Oct 2013
Posts: 297
Concentration: Finance
GMAT 1: 750 Q V46
GPA: 3.7
WE: Corporate Finance (Retail Banking)
Followers: 14

Kudos [?]: 378 [0], given: 197

### Show Tags

23 May 2014, 11:38
1
This post was
BOOKMARKED
Bunuel wrote:
Say x IS an irrational number and x*x*x=x^3=integer. In this case x*x*x*x=x^3*x=integer*irrational=irrational.

If x is an irrational number and x*x*x*x=x^4=integer, then x^3=x^4/x=integer/irrational=irrational.

So, as you can see if x is an irrational number, then both x^3 and x^4 cannot be rational.

Does this make sense?

Wow! Makes complete sense. This explanation is superb. Thanks!
_________________

My journey V46 and 750 -> http://gmatclub.com/forum/my-journey-to-46-on-verbal-750overall-171722.html#p1367876

GMAT Club Legend
Joined: 09 Sep 2013
Posts: 13543
Followers: 578

Kudos [?]: 163 [0], given: 0

Re: What is the value of x? [#permalink]

### Show Tags

19 Jun 2015, 02:12
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 Club Legend
Joined: 09 Sep 2013
Posts: 13543
Followers: 578

Kudos [?]: 163 [0], given: 0

Re: What is the value of x? [#permalink]

### Show Tags

26 Jun 2016, 04:14
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.
_________________
Re: What is the value of x?   [#permalink] 26 Jun 2016, 04:14
Similar topics Replies Last post
Similar
Topics:
19 What is the value of |x| ? 8 24 May 2012, 20:24
1 What is the value of x? 7 01 Jan 2012, 21:31
1 What is the value of x^2 ? 4 13 Oct 2011, 01:36
4 What is the value of |x| ? 25 07 Oct 2011, 22:39
30 What is the value of integer x ? 11 20 Apr 2010, 06:04
Display posts from previous: Sort by

# What is the value of x?

 Powered by phpBB © phpBB Group and phpBB SEO Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.