Author 
Message 
TAGS:

Hide Tags

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

What is the value of x? [#permalink]
Show Tags
01 Jan 2011, 01:32
2
This post received KUDOS
23
This post was BOOKMARKED
Question Stats:
30% (01:59) correct
70% (00:59) wrong based on 456 sessions
HideShow timer Statistics
What is the value of x? (1) x^3 is a 2digit positive odd integer. (2) x^4 is a 2digit positive odd integer.
Official Answer and Stats are available only to registered users. Register/ Login.



Math Expert
Joined: 02 Sep 2009
Posts: 39662

Re: Value of X [#permalink]
Show Tags
01 Jan 2011, 04:14
7
This post received KUDOS
Expert's post
8
This post was BOOKMARKED
shan123 wrote: What is the value of x? (1) X3 is a 2digit positive odd integer. (2) X4 is a 2digit 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 2digit positive odd integer > now, if \(x\) is an integer then \(x=3\) as \(x^3=27\) is the only odd 2digit 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 2digit positive odd integer, for example if \(x=\sqrt[3]{11}\) then \(x^3=11\). Not sufficient. (2) x^4 is a 2digit 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 2digit 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 noninteger as above: it can be fourth root from any 2digit 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. Answer: C.
_________________
New to the Math Forum? Please read this: All You Need for Quant  PLEASE READ AND FOLLOW: 12 Rules for Posting!!! Resources: GMAT Math Book  Triangles  Polygons  Coordinate Geometry  Factorials  Circles  Number Theory  Remainders; 8. Overlapping Sets  PDF of Math Book; 10. Remainders  GMAT Prep Software Analysis  SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS)  Tricky questions from previous years.
Collection of Questions: PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.
What are GMAT Club Tests? Extrahard Quant Tests with Brilliant Analytics



Current Student
Joined: 27 Jun 2012
Posts: 411
Concentration: Strategy, Finance

Re: What is the value of x? [#permalink]
Show Tags
05 Jan 2013, 23:42
3
This post received KUDOS
Glad that helped. 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 Reading Comprehension notes: Click here VOTE GMAT Practice Tests: Vote Here PowerScore CR Bible  Official Guide 13 Questions Set Mapped: Click here Looking to finance your tuition: Click here



Math Expert
Joined: 02 Sep 2009
Posts: 39662

Re: Value of X [#permalink]
Show Tags
23 May 2014, 10:41
1
This post received 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.
Answer: C.
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 2digit 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?
_________________
New to the Math Forum? Please read this: All You Need for Quant  PLEASE READ AND FOLLOW: 12 Rules for Posting!!! Resources: GMAT Math Book  Triangles  Polygons  Coordinate Geometry  Factorials  Circles  Number Theory  Remainders; 8. Overlapping Sets  PDF of Math Book; 10. Remainders  GMAT Prep Software Analysis  SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS)  Tricky questions from previous years.
Collection of Questions: PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.
What are GMAT Club Tests? Extrahard Quant Tests with Brilliant Analytics



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

Re: Value of X [#permalink]
Show Tags
01 Jan 2011, 04:48
Bunuel wrote: shan123 wrote: What is the value of x? (1) X3 is a 2digit positive odd integer. (2) X4 is a 2digit 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 2digit positive odd integer > now, if \(x\) is an integer then \(x=3\) as \(x^3=27\) is the only odd 2digit 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 2digit positive odd integer, for example if \(x=\sqrt[3]{11}\) then \(x^3=11\). Not sufficient. (2) x^4 is a 2digit 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 2digit 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 noninteger as above: it can be fourth root from any 2digit 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. Answer: C. Thanks for the answer and detailed explanation.



Current Student
Status: Up again.
Joined: 31 Oct 2010
Posts: 533
Concentration: Strategy, Operations
GMAT 1: 710 Q48 V40 GMAT 2: 740 Q49 V42

Re: Value of X [#permalink]
Show Tags
17 Feb 2011, 23:29
Carelessly, I overlooked the possibility that x could be negative. Thanks Bunuel!
_________________
My GMAT debrief: http://gmatclub.com/forum/from620to710mygmatjourney114437.html



Manager
Joined: 17 Feb 2011
Posts: 193
Concentration: Real Estate, Finance
Schools: MIT (Sloan)  Class of 2014

Re: Value of X [#permalink]
Show Tags
18 Feb 2011, 10:25
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 2digit positive odd integer. (2) X4 is a 2digit 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 2digit positive odd integer > now, if \(x\) is an integer then \(x=3\) as \(x^3=27\) is the only odd 2digit 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 2digit positive odd integer, for example if \(x=\sqrt[3]{11}\) then \(x^3=11\). Not sufficient. (2) x^4 is a 2digit 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 2digit 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 noninteger as above: it can be fourth root from any 2digit 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. Answer: C.



VP
Status: Current Student
Joined: 24 Aug 2010
Posts: 1345
Location: United States
WE: Sales (Consumer Products)

Re: Value of X [#permalink]
Show Tags
18 Feb 2011, 13:13
I always forget about radical roots. Thanks for the explanation Bunnel.
_________________
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: 218
Location: India
Concentration: Entrepreneurship, International Business
GPA: 3

Re: What is the value of x? [#permalink]
Show Tags
05 Jan 2013, 22:47
carcass wrote: What is the value of\(x\) ?
(1) \(X^3\) is a 2digit positive odd integer.
(2)\(X^4\) is a 2digit positive odd integer. Hi carcass, Stat 1 : Only 2 digit positive integers for S1 are : \(x\) 3  4 \(x^3\) 2764 Here odd integer is x=3 and x^3 = 27 SUFFICIENT Stat 2 : Only 2 digit positive integers for S2 are : \(x\)+/2+/3 \(x^3\)1681 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: 411
Concentration: Strategy, Finance

Re: What is the value of x? [#permalink]
Show Tags
05 Jan 2013, 22:55
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. Hence (C) is the answer.
_________________
Thanks, Prashant Ponde
Tough 700+ Level RCs: Passage1  Passage2  Passage3  Passage4  Passage5  Passage6  Passage7 Reading Comprehension notes: Click here VOTE GMAT Practice Tests: Vote Here PowerScore CR Bible  Official Guide 13 Questions Set Mapped: Click here Looking to finance your tuition: Click here



Moderator
Joined: 01 Sep 2010
Posts: 3211

Re: What is the value of x? [#permalink]
Show Tags
06 Jan 2013, 05:47



Math Expert
Joined: 02 Sep 2009
Posts: 39662

Re: What is the value of x? [#permalink]
Show Tags
07 Jan 2013, 04:12



Moderator
Joined: 01 Sep 2010
Posts: 3211

Re: What is the value of x? [#permalink]
Show Tags
07 Jan 2013, 05:29
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
_________________
COLLECTION OF QUESTIONS AND RESOURCES Quant: 1. ALL GMATPrep questions Quant/Verbal 2. Bunuel Signature Collection  The Next Generation 3. Bunuel Signature Collection ALLINONE WITH SOLUTIONS 4. Veritas Prep Blog PDF Version 5. MGMAT Study Hall Thursdays with Ron Quant Videos Verbal:1. Verbal question bank and directories by Carcass 2. MGMAT Study Hall Thursdays with Ron Verbal Videos 3. Critical Reasoning_Oldy but goldy question banks 4. Sentence Correction_Oldy but goldy question banks 5. Readingcomprehension_Oldy but goldy question banks



Math Expert
Joined: 02 Sep 2009
Posts: 39662

Re: What is the value of x? [#permalink]
Show Tags
07 Jan 2013, 06:11



Manager
Joined: 14 Nov 2011
Posts: 149
Location: United States
Concentration: General Management, Entrepreneurship
GPA: 3.61
WE: Consulting (Manufacturing)

Re: What is the value of x? [#permalink]
Show Tags
16 Jun 2013, 03:59
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 3Irrational 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: 39662

Re: What is the value of x? [#permalink]
Show Tags
16 Jun 2013, 04:15
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 3Irrational 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. I don't understand your question. Please elaborate.
_________________
New to the Math Forum? Please read this: All You Need for Quant  PLEASE READ AND FOLLOW: 12 Rules for Posting!!! Resources: GMAT Math Book  Triangles  Polygons  Coordinate Geometry  Factorials  Circles  Number Theory  Remainders; 8. Overlapping Sets  PDF of Math Book; 10. Remainders  GMAT Prep Software Analysis  SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS)  Tricky questions from previous years.
Collection of Questions: PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.
What are GMAT Club Tests? Extrahard Quant Tests with Brilliant Analytics



Senior Manager
Joined: 29 Oct 2013
Posts: 296
Concentration: Finance
GPA: 3.7
WE: Corporate Finance (Retail Banking)

Re: Value of X [#permalink]
Show Tags
23 May 2014, 07:25
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.
Answer: C.
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 2digit 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.
_________________
Please contact me for super inexpensive quality private tutoring
My journey V46 and 750 > http://gmatclub.com/forum/myjourneyto46onverbal750overall171722.html#p1367876



Senior Manager
Joined: 29 Oct 2013
Posts: 296
Concentration: Finance
GPA: 3.7
WE: Corporate Finance (Retail Banking)

Re: Value of X [#permalink]
Show Tags
23 May 2014, 12:38
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!
_________________
Please contact me for super inexpensive quality private tutoring
My journey V46 and 750 > http://gmatclub.com/forum/myjourneyto46onverbal750overall171722.html#p1367876



GMAT Club Legend
Joined: 09 Sep 2013
Posts: 15963

Re: What is the value of x? [#permalink]
Show Tags
19 Jun 2015, 03:12
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 Books  GMAT Club Tests  Best Prices on GMAT Courses  GMAT Mobile App  Math Resources  Verbal Resources



GMAT Club Legend
Joined: 09 Sep 2013
Posts: 15963

Re: What is the value of x? [#permalink]
Show Tags
26 Jun 2016, 05:14
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.
_________________
GMAT Books  GMAT Club Tests  Best Prices on GMAT Courses  GMAT Mobile App  Math Resources  Verbal Resources




Re: What is the value of x?
[#permalink]
26 Jun 2016, 05:14



Go to page
1 2
Next
[ 21 posts ]




