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

It is currently 12 Nov 2019, 23:38

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

Is X^N an integer? (1) X is an integer (2) N is an integer

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

Hide Tags

Find Similar Topics 
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 58991
Is X^N an integer? (1) X is an integer (2) N is an integer  [#permalink]

Show Tags

New post 09 Sep 2019, 21:04
00:00
A
B
C
D
E

Difficulty:

  55% (hard)

Question Stats:

44% (00:47) correct 56% (00:43) wrong based on 79 sessions

HideShow timer Statistics

Senior Manager
Senior Manager
User avatar
P
Status: Whatever it takes!
Joined: 10 Oct 2018
Posts: 383
GPA: 4
Is X^N an integer? (1) X is an integer (2) N is an integer  [#permalink]

Show Tags

New post Updated on: 10 Sep 2019, 23:19
Is X^N an integer?

(1) X is an integer
(4)^1/2 = 2 (integer), 4^2 = 16 (integer) but (4)^-2 (not integer).................INSUFFICIENT

(2) N is an integer
(1/2)^2 = i/4 (not integer) and 2^2= 4 = integer.............different answers possible......INSUFFICIENT

(1) + (2)
2^1 = integer but 2^-1 = not an integer. INSUFFICIENT

IMO answer is option E
_________________
Kudos OK Please!!

ALL ABOUT GMAT- \(https://exampal.com/gmat/blog/gmat-score-explained\)

Originally posted by EncounterGMAT on 09 Sep 2019, 22:01.
Last edited by EncounterGMAT on 10 Sep 2019, 23:19, edited 1 time in total.
Senior Manager
Senior Manager
avatar
P
Joined: 18 May 2019
Posts: 436
GMAT ToolKit User Premium Member CAT Tests
Re: Is X^N an integer? (1) X is an integer (2) N is an integer  [#permalink]

Show Tags

New post 09 Sep 2019, 22:04
we are to determine if X^N is an integer.
From statement 1, we know that X is an integer. This is however insufficient since we don't know the value of N. If N is an integer, then X^N will be an integer, but if N is not an integer, say 0.5 and N is 3, then 3^0.5 is not an integer.

From statement 2, we know that N is an integer. Since no information is given in relation to X, there are infinite possibilities of X^N, some of which are integers with others not integers. Statement 2 is therefore not sufficient.

1+2 is sufficient because we know X and N are both integers, hence X^N will always be an integer.

The answer is therefore C.
Senior Manager
Senior Manager
avatar
G
Joined: 07 Mar 2019
Posts: 372
Location: India
GMAT 1: 580 Q43 V27
WE: Sales (Energy and Utilities)
CAT Tests
Re: Is X^N an integer? (1) X is an integer (2) N is an integer  [#permalink]

Show Tags

New post 09 Sep 2019, 22:37
(1) X is an integer
N can take any value integer or non - integer.
a. N is an integer → \(X^N\) is an integer. Example X = 2, N = 1, 2, 3 and so on. YES
b. N is non – integer → \(X^N\) is non - integer. Example X = 2, N = 0.1, 0.2, 0.5 and so on. NO
INSUFFICIENT.

(2) N is an integer
X can take any value integer or non - integer.
a. X is an integer → \(X^N\) is an integer. Example N = 2, X = 1, 2, 3 and so on. YES
b. X is non – integer → \(X^N\) is non integer. Example N = 2, X = 0.1, 0.2, 0.5 and so on. NO
INSUFFICIENT.

Together 1) and 2)
Since both are integers Case ‘a’ of both statements suffices YES condition.

SUFFICIENT.
Answer (C).
_________________
Ephemeral Epiphany..!

GMATPREP1 590(Q48,V23) March 6, 2019
GMATPREP2 610(Q44,V29) June 10, 2019
GMATPREPSoft1 680(Q48,V35) June 26, 2019
GMAT Club Legend
GMAT Club Legend
User avatar
D
Joined: 18 Aug 2017
Posts: 5261
Location: India
Concentration: Sustainability, Marketing
GPA: 4
WE: Marketing (Energy and Utilities)
GMAT ToolKit User Premium Member CAT Tests
Re: Is X^N an integer? (1) X is an integer (2) N is an integer  [#permalink]

Show Tags

New post 10 Sep 2019, 01:39
1
#1
value of N not know insufficient as -ve integer value of N will be fraction
insufficient
#2
N is an integer ; value of X not know insufficeint
from 1&2
value of sign of x & n not know
insufficient
IMO E

Is X^N an integer?

(1) X is an integer
(2) N is an integer
Director
Director
avatar
P
Joined: 24 Nov 2016
Posts: 748
Location: United States
Re: Is X^N an integer? (1) X is an integer (2) N is an integer  [#permalink]

Show Tags

New post 10 Sep 2019, 04:01
1
Quote:
Is \(X^N\) an integer?

(1) X is an integer
(2) N is an integer


rule: "integer" = {positive, negative or zero}

(1) X is an integer: \(X,N=(2,1):X^N=2^1=2=integer…X,N=(2,-1):X^N=2^{(-1)}=0.5=not.integer\)
(2) N is an integer: \(X,N=(2,1):X^N=2^1=2=integer…X,N=(2,-1):X^N=2^{(-1)}=0.5=not.integer\)

Answer (E)
GMAT Tutor
User avatar
S
Joined: 17 Sep 2014
Posts: 217
Location: United States
GMAT 1: 780 Q51 V45
GRE 1: Q170 V167
Is X^N an integer? (1) X is an integer (2) N is an integer  [#permalink]

Show Tags

New post Updated on: 11 Sep 2019, 08:58
1
Analyzing the question:
Note that x does not have to be an integer for this to be sufficient. For example, we may have x = sqrt(2) and N be any even number, and this would be sufficient. Also, N = 0 is automatically sufficient if x cannot be 0.

Statement 1:
Without knowing N this is insufficient. N can be 1/2, which is square of x. There's also the possibility that N is a negative integer.

Statement 2:
x can be sqrt(2) and N=1. Insufficient.

Combined:
Still insufficient as we can let N = -1 and x be any integer greater than 1 to create a fractional result. Answer is E.
_________________
Source: We are an NYC based, in-person and online GMAT tutoring and prep company. We are the only GMAT provider in the world to guarantee specific GMAT scores with our flat-fee tutoring packages, or to publish student score increase rates. Our typical new-to-GMAT student score increase rate is 3-9 points per tutoring hour, the fastest in the world. Feel free to reach out!

Originally posted by TestPrepUnlimited on 10 Sep 2019, 13:31.
Last edited by TestPrepUnlimited on 11 Sep 2019, 08:58, edited 1 time in total.
Intern
Intern
avatar
Joined: 26 Jun 2017
Posts: 1
Re: Is X^N an integer? (1) X is an integer (2) N is an integer  [#permalink]

Show Tags

New post 10 Sep 2019, 13:41
Both statements are not sufficient as for X to the power of N to be an integer, we need X to be an integer and N to be a positive integer. From the given information, N can be either positive or negative and statement 1 is anyway not sufficient.

Posted from my mobile device
Senior Manager
Senior Manager
avatar
G
Joined: 01 Mar 2019
Posts: 258
Location: India
Concentration: Strategy, Social Entrepreneurship
Schools: Ross '22, ISB '20, NUS '20
GPA: 4
Reviews Badge
Re: Is X^N an integer? (1) X is an integer (2) N is an integer  [#permalink]

Show Tags

New post 10 Sep 2019, 21:21
Clearly statement 1,2 are not sufficient exclusively
If we consider both, for x=2, n=3 .....x^n is integer but if n=-2 then x^n is not integer
SO OA:E
SVP
SVP
User avatar
P
Joined: 03 Jun 2019
Posts: 1837
Location: India
Premium Member Reviews Badge CAT Tests
Is X^N an integer? (1) X is an integer (2) N is an integer  [#permalink]

Show Tags

New post 10 Sep 2019, 22:31
Bunuel wrote:

Competition Mode Question



Is X^N an integer?

(1) X is an integer
(2) N is an integer


Is X^N an integer?

(1) X is an integer
\(2^2\) is an integer
\(2^{-2}\) is not an integer
NOT SUFFICIENT

(2) N is an integer
\(2^2\) is an integer
\(2^{-2}\) is not an integer
NOT SUFFICIENT

Combining (1) & (2)
\(2^2\) is an integer
\(2^{-2}\) is not an integer
NOT SUFFICIENT

IMO E
_________________
"Success is not final; failure is not fatal: It is the courage to continue that counts."

Please provide kudos if you like my post. Kudos encourage active discussions.

My GMAT Resources: -

Efficient Learning
All you need to know about GMAT quant

Tele: +91-11-40396815
Mobile : +91-9910661622
E-mail : kinshook.chaturvedi@gmail.com
Intern
Intern
avatar
B
Joined: 29 Aug 2019
Posts: 15
Re: Is X^N an integer? (1) X is an integer (2) N is an integer  [#permalink]

Show Tags

New post 30 Sep 2019, 19:13
Is X^N an integer?

(1) X is an integer
N could be negative - which leads to a fraction.
(2) N is an integer
N could still be negative - which leads to a fraction.
GMAT Club Bot
Re: Is X^N an integer? (1) X is an integer (2) N is an integer   [#permalink] 30 Sep 2019, 19:13
Display posts from previous: Sort by

Is X^N an integer? (1) X is an integer (2) N is an integer

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





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