GMAT Question of the Day - Daily to your Mailbox; hard ones only

It is currently 12 Dec 2018, 20:06

Close

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
Your Progress

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

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.

Close

Request Expert Reply

Confirm Cancel
Events & Promotions in December
PrevNext
SuMoTuWeThFrSa
2526272829301
2345678
9101112131415
16171819202122
23242526272829
303112345
Open Detailed Calendar
  • The winning strategy for 700+ on the GMAT

     December 13, 2018

     December 13, 2018

     08:00 AM PST

     09:00 AM PST

    What people who reach the high 700's do differently? We're going to share insights, tips and strategies from data we collected on over 50,000 students who used examPAL.
  • GMATbuster's Weekly GMAT Quant Quiz, Tomorrow, Saturday at 9 AM PST

     December 14, 2018

     December 14, 2018

     09:00 AM PST

     10:00 AM PST

    10 Questions will be posted on the forum and we will post a reply in this Topic with a link to each question. There are prizes for the winners.

Is x an integer greater than 1?

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:

Hide Tags

Manager
Manager
avatar
G
Joined: 02 Jun 2015
Posts: 191
Location: Ghana
Premium Member
Is x an integer greater than 1?  [#permalink]

Show Tags

New post Updated on: 30 Jan 2017, 08:20
2
3
00:00
A
B
C
D
E

Difficulty:

  95% (hard)

Question Stats:

19% (01:40) correct 81% (01:20) wrong based on 169 sessions

HideShow timer Statistics

Is x an integer greater than 1?

(1) The cube of x is a positive integer.
(2) The reciprocal of x is less than 1.

_________________

Kindly press kudos if you find my post helpful


Originally posted by duahsolo on 25 Oct 2016, 14:12.
Last edited by Bunuel on 30 Jan 2017, 08:20, edited 3 times in total.
Edited the OA.
Manager
Manager
avatar
Joined: 28 Jun 2016
Posts: 207
Location: Canada
Concentration: Operations, Entrepreneurship
Re: Is x an integer greater than 1?  [#permalink]

Show Tags

New post 25 Oct 2016, 14:45
duahsolo wrote:
Is x an integer greater than 1?

(1) The cube of x is an positive integer.
(2) The reciprocal of x is less than 1.


Statement 1:

x^3 =8, x =2 Yes
x^3=2, x=cuberoot(2) No

Insufficient

Statement 2:

1/x =0.5

Then x=2

Yes

1/x = 0.6667

x=1.5

No

Insufficient

Statement 1&2:

If x= 2, then x^3 = 8 and 1/x=0.5 ---------------Yes

If x= cuberoot(2), then x^3 = 2 and 1/x will always be less than 1. ---------No
Again insufficient

IMO E

duahsolo : Please confirm the answer


Sent from my iPhone using GMAT Club Forum mobile app
VP
VP
User avatar
P
Joined: 05 Mar 2015
Posts: 1004
Re: Is x an integer greater than 1?  [#permalink]

Show Tags

New post 25 Oct 2016, 20:08
duahsolo wrote:
Is x an integer greater than 1?

(1) The cube of x is an positive integer.
(2) The reciprocal of x is less than 1.



Hi duahsolo
Could u confirm your OA

Combining both statements
X could be 2------>YES X is integer>1
or X=2^1/3------> NO X is NOT integer>1
insuff..

Ans E
Manager
Manager
avatar
S
Joined: 29 May 2016
Posts: 103
Re: Is x an integer greater than 1?  [#permalink]

Show Tags

New post 25 Oct 2016, 21:02
1
The cube of x is an positive integer
let x=1 , its cube is still positive integer, which is 1 answer is NO
x=2 answer is YES


The reciprocal of x is less than 1
let x=-2 its reciprocal is less than 1 as it will be negative

combining answer is C because on combining , this rules out the option x<=1
Manager
Manager
avatar
G
Joined: 02 Jun 2015
Posts: 191
Location: Ghana
Premium Member
Re: Is x an integer greater than 1?  [#permalink]

Show Tags

New post 25 Oct 2016, 23:08
rohit8865 wrote:
duahsolo wrote:
Is x an integer greater than 1?

(1) The cube of x is an positive integer.
(2) The reciprocal of x is less than 1.



Hi duahsolo
Could u confirm your OA

Combining both statements
X could be 2------>YES X is integer>1
or X=2^1/3------> NO X is NOT integer>1
insuff..

Ans E


Hi rohit8865,

I can confirm that the OA is (C)
_________________

Kindly press kudos if you find my post helpful

Manager
Manager
avatar
G
Joined: 02 Jun 2015
Posts: 191
Location: Ghana
Premium Member
Re: Is x an integer greater than 1?  [#permalink]

Show Tags

New post 25 Oct 2016, 23:09
acegmat123 wrote:
duahsolo wrote:
Is x an integer greater than 1?

(1) The cube of x is an positive integer.
(2) The reciprocal of x is less than 1.


Statement 1:

x^3 =8, x =2 Yes
x^3=2, x=cuberoot(2) No

Insufficient

Statement 2:

1/x =0.5

Then x=2

Yes

1/x = 0.6667

x=1.5

No

Insufficient

Statement 1&2:

If x= 2, then x^3 = 8 and 1/x=0.5 ---------------Yes

If x= cuberoot(2), then x^3 = 2 and 1/x will always be less than 1. ---------No
Again insufficient

IMO E

duahsolo : Please confirm the answer


Sent from my iPhone using GMAT Club Forum mobile app


Hi acegmat123,

I can confirm that the OA is (C)
_________________

Kindly press kudos if you find my post helpful

Senior Manager
Senior Manager
avatar
B
Joined: 13 Oct 2016
Posts: 367
GPA: 3.98
Re: Is x an integer greater than 1?  [#permalink]

Show Tags

New post 09 Jan 2017, 08:50
Bunuel wrote:
Is x an integer greater than 1?

(1) The cube of x is an positive integer.
(2) The reciprocal of x is less than 1.


(1) x=2 ---> \(x^3=8\), x=\(\sqrt[3]{2}\) --> \(x^3 = 2\) or x=1, \(x^3 = 1\) Insufficient.

(2) x=-4, 1/x=-1/4 < 1
x=-1/2, 1/x = -2 < 1
x=\(\sqrt[3]{2}\), 1/x = 1/\(\sqrt[3]{2}\) < 1
x=2, 1/x = 1/2 < 1
Insufficient

(1) & (2) We can discard negative values and 1 but still have positive irrationals and integers >1.

E.
Intern
Intern
avatar
B
Joined: 20 Jun 2016
Posts: 5
Location: India
Concentration: Entrepreneurship, Strategy
GPA: 3.1
WE: Marketing (Manufacturing)
Re: Is x an integer greater than 1?  [#permalink]

Show Tags

New post 10 Jan 2017, 07:59
ANS (E)
Q) X>1 ?

(1) X^3 IS AN INTEGER X=2, 2^3= 8 X=1, 1^3=1 NOT SUF.

(2) RECP >1
1/2 <1 SUF.
-2 <1 , RECIPROCAL = -1/2< 1 HENCE NOT SUFF

1 AND 2 COMBINED NO UNIQUE ANSWER.








-
_________________

I'm just a happy camper! Rockin' and a-rollin'!

Intern
Intern
avatar
B
Joined: 25 Mar 2016
Posts: 40
Location: India
Concentration: Finance, General Management
WE: Other (Other)
Re: Is x an integer greater than 1?  [#permalink]

Show Tags

New post 11 Jan 2017, 08:49
Bunuel wrote:
Is x an integer greater than 1?

(1) The cube of x is an positive integer.
(2) The reciprocal of x is less than 1.



From option 1 we can identify that x is positive and from option 2 we can reach the conclusion that x >1 (if x is positive) x<1 (x is negative)

So combining 1 & 2 we can say that x>1

so Answer is C
VP
VP
User avatar
P
Joined: 05 Mar 2015
Posts: 1004
Re: Is x an integer greater than 1?  [#permalink]

Show Tags

New post 11 Jan 2017, 10:09
Bunuel wrote:
Is x an integer greater than 1?

(1) The cube of x is an positive integer.
(2) The reciprocal of x is less than 1.



(1) if x=1 then NO
if x=2 then YES
insuff

(2) 1/x<1
(1-x)/x<0

thus x<0 or x>1
if x= -2 then NO
if x= 2 then YES

not suff

Combining we know 3 √x is positive integer(from (1) )
and x>1 from (2) thus x>1
but if x= cube rt 3
then NO

insuff


Ans E
Senior Manager
Senior Manager
avatar
G
Status: Countdown Begins...
Joined: 03 Jul 2016
Posts: 293
Location: India
Concentration: Technology, Strategy
Schools: IIMB
GMAT 1: 580 Q48 V22
GPA: 3.7
WE: Information Technology (Consulting)
GMAT ToolKit User Reviews Badge
Re: Is x an integer greater than 1?  [#permalink]

Show Tags

New post 11 Jan 2017, 10:53
Bunuel wrote:
Is x an integer greater than 1?

(1) The cube of x is an positive integer.
(2) The reciprocal of x is less than 1.



Statement1: x^3 can be equal to 1 or greater than 1. Not Sufficient.
Statement2: 1/2 =0.5 1/-2 =-0.5 Not Sufficient.

E.
Director
Director
avatar
P
Joined: 14 Nov 2014
Posts: 635
Location: India
GMAT 1: 700 Q50 V34
GPA: 3.76
Re: Is x an integer greater than 1?  [#permalink]

Show Tags

New post 29 Jan 2017, 09:50
Bunuel wrote:
Is x an integer greater than 1?

(1) The cube of x is an positive integer.
(2) The reciprocal of x is less than 1.


1. It means X is positive but we don't know it is grater than 1 or 1 itself.So insuff
2.From this we can conclude that x can't be 1.
Now we have X is positive,X can't be 1,X is a integer
we can get X>1
C .suff.
Manager
Manager
avatar
S
Joined: 22 Mar 2014
Posts: 132
Location: United States
Concentration: Finance, Operations
GMAT 1: 530 Q45 V20
GPA: 3.91
WE: Information Technology (Computer Software)
Re: Is x an integer greater than 1?  [#permalink]

Show Tags

New post 29 Jan 2017, 11:13
Hi, as per me ans should be E.

From Statement 1: x can be = 4, x can be = Cube root(2), or x= -5, so insuff
From Statement 2: again x can be = 4, x can be = Cube root(2), or x= -5, so insuff

From 1 + 2: x can be = 4, x can be = Cube root(2), so insuff. So ans: E
Director
Director
avatar
P
Joined: 14 Nov 2014
Posts: 635
Location: India
GMAT 1: 700 Q50 V34
GPA: 3.76
Re: Is x an integer greater than 1?  [#permalink]

Show Tags

New post 29 Jan 2017, 11:49
pandeyamit07 wrote:
Hey sobby, I didn't get your answer as in statement 2, it's not given X is integer or not.

Can you please explain this.

Sent from my Redmi Note 3 using GMAT Club Forum mobile app

Ok..It is given reciprocal of x is less then 1 ...So any value above 1 will have its reciprocal less then 1...
Now ,1 have reciprocal equal to 1 ..So we can discard 1 here...And reciprocal between 0 to 1 will be greater than 1...Discard that too..
We have negative values too in the set..So from statement 2 we can't conclude anything..It is in suff.

Combining...

From statement 1 we have x is positive integer only,and statement 2 tells it is not 1 atleast...So it is obvious that value of x will be all positive value greater than 1..



Sent from my HM NOTE 1LTE using GMAT Club Forum mobile app
Current Student
avatar
B
Joined: 22 Jan 2017
Posts: 7
Concentration: Marketing, Leadership
GMAT 1: 730 Q50 V37
WE: Engineering (Computer Hardware)
Re: Is x an integer greater than 1?  [#permalink]

Show Tags

New post 29 Jan 2017, 20:24
sobby wrote:
Bunuel wrote:
Is x an integer greater than 1?

(1) The cube of x is an positive integer.
(2) The reciprocal of x is less than 1.


1. It means X is positive but we don't know it is grater than 1 or 1 itself.So insuff
2.From this we can conclude that x can't be 1.
Now we have X is positive,X can't be 1,X is a integer
we can get X>1
C .suff.


How do we get X as an Integer.
Let's take X= Cube root of 4
Cube root of 4 has it's Cube as 4 (Satisfies 1)
Reciprocal of Cube root of 4 is < 1 (Satisfies 2)

X is Positive and greater than 1 but not Integer

If we take X=3
Then Cube of 3 is Integer (Satisfies 1)
Reciprocal if 3 is < 1 (Satisfies 2)
X is Positive Integer greater than 1.

Depending on how what we chose as X it can be Integer or not. So Why isn't the answer C. What am I missing here.
Manager
Manager
avatar
B
Joined: 08 Feb 2016
Posts: 71
Location: India
Concentration: Technology
Schools: AGSM '20 (A)
GMAT 1: 650 Q49 V30
GPA: 4
Is x an integer greater than 1?  [#permalink]

Show Tags

New post 30 Jan 2017, 10:53
Bunuel wrote:
duahsolo wrote:
Is x an integer greater than 1?

(1) The cube of x is a positive integer.
(2) The reciprocal of x is less than 1.


Edited the OA. It should be E.


Hi Bunuel, if OA is E, can you please share where I am going wrong below ?

Given x is an integer,

St.1 - (x^3) is >0. Put x=2. Yes. Put x=1. No. So, insufficient.

St 2 - (1/x) is < 1. If x is positive, x >1. If x is negative, x <1. So, insufficient.

St.1 + St.2 - Suppose x=2. (2^3) is +ve integer & (1/2) is less than 1. So, x is an integer >1.
Suppose x=1. (1^3) is +ve integer. Reciprocal of x is not less than one. Can't take x=1.

Combining st1 & 2, we have to take integer values of x>1 to satisfy both the statements. So, C.
VP
VP
User avatar
P
Joined: 05 Mar 2015
Posts: 1004
Is x an integer greater than 1?  [#permalink]

Show Tags

New post 30 Jan 2017, 11:40
ajay2121988 wrote:
Bunuel wrote:
duahsolo wrote:
Is x an integer greater than 1?

(1) The cube of x is a positive integer.
(2) The reciprocal of x is less than 1.


Edited the OA. It should be E.


Hi Bunuel, if OA is E, can you please share where I am going wrong below ?

Given x is an integer,

St.1 - (x^3) is >0. Put x=2. Yes. Put x=1. No. So, insufficient.

St 2 - (1/x) is < 1. If x is positive, x >1. If x is negative, x <1. So, insufficient.

St.1 + St.2 - Suppose x=2. (2^3) is +ve integer & (1/2) is less than 1. So, x is an integer >1.
Suppose x=1. (1^3) is +ve integer. Reciprocal of x is not less than one. Can't take x=1.

Combining st1 & 2, we have to take integer values of x>1 to satisfy both the statements. So, C.


had the question asked that "Is integer x greater than 1?"
then your solution is a valid one..

Hope this helps !!
Manager
Manager
avatar
D
Joined: 17 May 2015
Posts: 249
Re: Is x an integer greater than 1?  [#permalink]

Show Tags

New post 31 Jan 2017, 00:01
deepayanc wrote:
sobby wrote:
Bunuel wrote:
Is x an integer greater than 1?

(1) The cube of x is an positive integer.
(2) The reciprocal of x is less than 1.


1. It means X is positive but we don't know it is grater than 1 or 1 itself.So insuff
2.From this we can conclude that x can't be 1.
Now we have X is positive,X can't be 1,X is a integer
we can get X>1
C .suff.


How do we get X as an Integer.
Let's take X= Cube root of 4
Cube root of 4 has it's Cube as 4 (Satisfies 1)
Reciprocal of Cube root of 4 is < 1 (Satisfies 2)

X is Positive and greater than 1 but not Integer

If we take X=3
Then Cube of 3 is Integer (Satisfies 1)
Reciprocal if 3 is < 1 (Satisfies 2)
X is Positive Integer greater than 1.

Depending on how what we chose as X it can be Integer or not. So Why isn't the answer C. What am I missing here.


Hi deepayanc,

Please refer the highlighted part. Since there is no unique answer, so the correct answer should be E.
Intern
Intern
avatar
B
Joined: 16 Dec 2017
Posts: 5
Re: Is x an integer greater than 1?  [#permalink]

Show Tags

New post 25 Feb 2018, 17:43
Bunuel, what is the official solution of this problem?
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 51121
Re: Is x an integer greater than 1?  [#permalink]

Show Tags

New post 25 Feb 2018, 22:59
1
1
futurephilantropist wrote:
Bunuel, what is the official solution of this problem?


Is x an integer greater than 1?

Notice that we are not told that x is an integer. We should determine exactly that plus whether it's more than 1.

(1) The cube of x is a positive integer --> \(x^3 = positive \ integer\). This is true for any positive integer so x certainly could be an integer greater than 1 but not necessarily. For example:

If x = 1 --> the answer is NO.
If \(x = \sqrt[3]{2}\) --> the answer is NO.

Not sufficient.

(2) The reciprocal of x is less than 1 --> 1/x < 1. This holds true for any value greater than 1 (not necessarily an integer) as well as any negative value. Not sufficient.

(1)+(2) From (1) it follows that x is positive, so from (2) that x must be greater than 1 but x still could be an integer greater than 1 (for example 2) as well as some irrational number, which gives an integer when cubed (for example \(\sqrt[3]{2}\)). Not sufficient.

Answer: E.

Hope it's clear.
_________________

New to the Math Forum?
Please read this: Ultimate GMAT Quantitative Megathread | 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?
Extra-hard Quant Tests with Brilliant Analytics

GMAT Club Bot
Re: Is x an integer greater than 1? &nbs [#permalink] 25 Feb 2018, 22:59

Go to page    1   2    Next  [ 21 posts ] 

Display posts from previous: Sort by

Is x an integer greater than 1?

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  


Copyright

GMAT Club MBA Forum Home| About| Terms and Conditions and Privacy Policy| GMAT Club Rules| Contact| Sitemap

Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne

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®.