If m and n are integers and x>0, what is value of x^m + x^n? : GMAT Data Sufficiency (DS)
Check GMAT Club App Tracker for the Latest School Decision Releases http://gmatclub.com/AppTrack

It is currently 04 Dec 2016, 17:53
GMAT Club Tests

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

Events & Promotions

Events & Promotions in June
Open Detailed Calendar

If m and n are integers and x>0, what is value of x^m + x^n?

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

Hide Tags

Intern
Intern
avatar
Joined: 21 Sep 2013
Posts: 9
Followers: 0

Kudos [?]: 4 [0], given: 54

GMAT ToolKit User Premium Member
If m and n are integers and x>0, what is value of x^m + x^n? [#permalink]

Show Tags

New post 20 Jun 2014, 04:23
1
This post was
BOOKMARKED
00:00
A
B
C
D
E

Difficulty:

  15% (low)

Question Stats:

77% (02:02) correct 23% (01:30) wrong based on 141 sessions

HideShow timer Statistics

If m and n are integers and x > 0, what is the value of \(x^m + x^n\)?

(1) \(x^m = 81\)

(2) \(1 + x^{n-m} = 10\)
[Reveal] Spoiler: OA
Expert Post
Math Expert
User avatar
Joined: 02 Sep 2009
Posts: 35843
Followers: 6837

Kudos [?]: 89859 [0], given: 10381

Re: If m and n are integers and x>0, what is value of x^m + x^n? [#permalink]

Show Tags

New post 20 Jun 2014, 04:36
Expert's post
3
This post was
BOOKMARKED
If m and n are integers and x > 0, what is the value of \(x^m + x^n\)?

(1) \(x^m = 81\). No info about n. Not sufficient.

(2) \(1 + x^{n-m} = 10\) --> \(x^{n-m} = 9\) --> \(\frac{x^n}{x^m}=9\) --> \(x^n =9x^m\) --> \(x^m + x^n=10x^m\). Not sufficient.

(1)+(2) \(x^m + x^n=10x^m=10*81\). 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?
Extra-hard Quant Tests with Brilliant Analytics

Senior Manager
Senior Manager
User avatar
Joined: 13 Jun 2013
Posts: 279
Followers: 13

Kudos [?]: 334 [0], given: 13

Premium Member
Re: If m and n are integers and x>0, what is value of x^m + x^n? [#permalink]

Show Tags

New post 20 Jun 2014, 04:52
newbornmuse wrote:
If m and n are integers and x > 0, what is the value of \(x^m + x^n\)?

(1) \(x^m = 81\)

(2) \(1 + x^{n-m} = 10\)


x^m + x^n= x^m(1+x^n-m)---------------------------A)

st1 x^m=81 insufficient as no information about n is provided

st2 (1 + x^n-m) =10

as seen from 'A' we still need the value of x^m to calculate the value of x^m+x^n hence insufficient


combining 1 and 2 we can substitute the value of 1 + x^n-m and x^m in 'A' to calculate the total value which is 81*10=810 hence C
Manager
Manager
avatar
Joined: 24 May 2016
Posts: 173
Followers: 1

Kudos [?]: 74 [0], given: 33

If m and n are integers and x>0, what is value of x^m + x^n? [#permalink]

Show Tags

New post 09 Oct 2016, 12:47
I concluded that statement 2 was sufficient.

This is what I did.

X^m + X^n = 1 + (X^n)/(X^m)

Statement 2: 1 + (X^n)*(X^-m) = 10 ---> 1 + (X^n)/(X^m) = 10

Hence: X^m + X^n = 1 + (X^n)/(X^m) = 10 ---> Sufficient.

Can anyone please explain me what am I doing wrong?

Thank you.
Expert Post
Math Expert
User avatar
Joined: 02 Sep 2009
Posts: 35843
Followers: 6837

Kudos [?]: 89859 [0], given: 10381

Re: If m and n are integers and x>0, what is value of x^m + x^n? [#permalink]

Show Tags

New post 09 Oct 2016, 23:04
EBITDA wrote:
I concluded that statement 2 was sufficient.

This is what I did.

X^m + X^n = 1 + (X^n)/(X^m)

Statement 2: 1 + (X^n)*(X^-m) = 10 ---> 1 + (X^n)/(X^m) = 10

Hence: X^m + X^n = 1 + (X^n)/(X^m) = 10 ---> Sufficient.

Can anyone please explain me what am I doing wrong?

Thank you.


How did you get the highlighted part?
_________________

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?
Extra-hard Quant Tests with Brilliant Analytics

Manager
Manager
avatar
Joined: 24 May 2016
Posts: 173
Followers: 1

Kudos [?]: 74 [0], given: 33

If m and n are integers and x>0, what is value of x^m + x^n? [#permalink]

Show Tags

New post 10 Oct 2016, 00:02
The question asks us for the value of: X^m + X^n

If we divide this expression by X^m, we get: 1 + (X^n)/(X^m)

Per statement 2: 1 + (X^n)/(X^m) = 10.

Hence, statement 2 allows us to know what is the value of the initial expression.

Where am I making the error?
Expert Post
1 KUDOS received
Math Expert
User avatar
Joined: 02 Sep 2009
Posts: 35843
Followers: 6837

Kudos [?]: 89859 [1] , given: 10381

Re: If m and n are integers and x>0, what is value of x^m + x^n? [#permalink]

Show Tags

New post 10 Oct 2016, 00:07
1
This post received
KUDOS
Expert's post
EBITDA wrote:
The question asks us for the value of: X^m + X^n

If we divide this expression by X^m, we get: 1 + (X^n)/(X^m)

Per statement 2: 1 + (X^n)/(X^m) = 10.

Hence, statement 2 allows us to know what is the value of the initial expression.

Where am I making the error?


I see what you are doing there but it's wrong. We need the value of x^m + x^n. When you divide this by x^m, you get the value of (x^m + x^n)/x^m, not x^m + x^n.
_________________

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?
Extra-hard Quant Tests with Brilliant Analytics

Intern
Intern
avatar
Joined: 10 Mar 2015
Posts: 5
Followers: 0

Kudos [?]: 0 [0], given: 8

Re: If m and n are integers and x>0, what is value of x^m + x^n? [#permalink]

Show Tags

New post 13 Oct 2016, 11:36
I choose C but I was wondering if my approach was correct?
Here is what I did :
1) insuff.
2) insuff.

C) Given 1+x^n−m=10 I rewrote as 1+ x^n/x^m = 10 then substitute x^m from 1)
I got 1+ x^n/81 = 10
81+x^n=810
x^n=729
So If I got x^n and x^m to answer the question.

But is it a correct way to arrive at solution?
thank you
Re: If m and n are integers and x>0, what is value of x^m + x^n?   [#permalink] 13 Oct 2016, 11:36
    Similar topics Author Replies Last post
Similar
Topics:
1 If N is a single digit integer and M>0, what is the value of M? stonecold 1 18 Nov 2016, 22:36
1 Experts publish their posts in the topic If x^{n+1} - 2x^n=3x^n, then what is the value of x^n? Bunuel 7 17 Jul 2016, 10:25
19 Experts publish their posts in the topic x^n = x^(n+2) for any integer n. Is it true that x > 0? Bunuel 6 21 Jan 2015, 01:59
5 Experts publish their posts in the topic If n is an integer and x^n – x^-n = 0, what is the value of DeeptiM 4 05 Sep 2011, 11:17
Is X^N an integer? banksy 2 15 Mar 2011, 15:41
Display posts from previous: Sort by

If m and n are integers and x>0, what is value of x^m + x^n?

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


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

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®.