Last visit was: 23 Apr 2026, 18:00 It is currently 23 Apr 2026, 18:00
Home
Messages
Tests
Schools
Events
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.
Go to My Error Log Learn more
Close
Request Expert Reply
Confirm Cancel
Back to Forum
Create Topic
705-805 (Hard)|   Algebra|   Exponents|      
User avatar
rjkaufman21
User avatar
Joined: 05 May 2011
Last visit: 26 Jun 2014
Posts: 351
Own Kudos:
164
 [14]
Given Kudos: 35
Location: United States (WI)
GMAT 1: 780 Q49 V50
WE:Research (Other)
GMAT 1: 780 Q49 V50
Posts: 351
Kudos: 164
 [14]
If k is an integer and m > 0, is 2^k + 3^k = m ? 04 Oct 2011, 18:52
4
Kudos
Add Kudos
9
Bookmarks
Bookmark this Post
00:00
Start Timer
Pause Timer
Resume Timer
Show Answer
Hide
Show
History
C
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!

Difficulty:

75% (hard)

Question Stats:

55% (02:09) correct 45% (02:12) wrong based on 270 sessions

History

Date
Time
Result
Not Attempted Yet
If k is an integer and m > 0, is 2^k + 3^k = m ?

(1) 4^k + 9 ^k = m^2 - 12
(2) k = 1
ShowHide Answer
Official Answer
C
Most Helpful Reply
avatar
blink005
avatar
Joined: 20 Aug 2011
Last visit: 23 Jun 2016
Posts: 61
Own Kudos:
217
 [6]
Posts: 61
Kudos: 217
 [6]
If k is an integer and m > 0, is 2^k + 3^k = m ? Updated on: 05 Oct 2011, 06:41
Originally posted by blink005 on 05 Oct 2011, 01:19.
Last edited by blink005 on 05 Oct 2011, 06:41, edited 1 time in total.
6
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Well, you need to determine whether 2^k + 3^k =m.

1. 4^k + 9 ^k = m^2 - 12
you can simplify it as

2^2k+3^2k+12=m^2
Can you see that this equation can be of the form (a+b)^2=a^2+b^2+2ab when k=1
Otherwise this form can't be simplified any further.
Insufficient

2. k=1
You don't what's m so you can't compare m with a value.
Insufficient

1+2
(4^1+9^1+12)=m^2
m^2=25
m=5
when k=1
2^1+3^1=5=m
Hence sufficient.

Do you follow?
General Discussion
User avatar
rjkaufman21
User avatar
Joined: 05 May 2011
Last visit: 26 Jun 2014
Posts: 351
Own Kudos:
164
Given Kudos: 35
Location: United States (WI)
GMAT 1: 780 Q49 V50
WE:Research (Other)
GMAT 1: 780 Q49 V50
Posts: 351
Kudos: 164
If k is an integer and m > 0, is 2^k + 3^k = m ? 05 Oct 2011, 06:24
Kudos
Add Kudos
Bookmarks
Bookmark this Post
blink005
Well, you need to determine whether 2^k + 3^k =m.

1. 4^k + 9 ^k = m^2 - 12
you can simplify it as

2^2k+3^2k+12=m^2
Can you see that this equation can be of the form (a+b)^2=a^2+b^2+2ab when k=1
Otherwise this form can't be simplified any further.
Insufficient

2. k=1
You don't what's m so you can't compare m with a value.
Insufficient

1+2
(4^1+9^1+12)=m^2
m^2=5
m=5
when k=1
2^1+3^1=5=m
Hence sufficient.

Do you follow?
Show more

Oh dang, yes ok I see what you mean now. I'm not great at recognizing the quadratic forms.

Thank you for your help!
User avatar
Bunuel
User avatar
Math Expert
Joined: 02 Sep 2009
Last visit: 23 Apr 2026
Posts: 109,785
Own Kudos:
810,870
Given Kudos: 105,853
Products:
GMAT Club Tests Forum Quiz
Expert
Expert reply
Active GMAT Club Expert! Tag them with @ followed by their username for a faster response.
Posts: 109,785
Kudos: 810,870
If k is an integer and m > 0, is 2^k + 3^k = m ? 24 Oct 2013, 14:36
Kudos
Add Kudos
Bookmarks
Bookmark this Post
rjdunn03
If k is an integer and m > 0, is 2^k + 3^k = m ?

(1) 4^k + 9 ^k = m^2 - 12
(2) k = 1
Show more

Similar question to practice: if-k-is-an-integer-is-2-k-3-k-m-158354.html
User avatar
EMPOWERgmatRichC
User avatar
Major Poster
Joined: 19 Dec 2014
Last visit: 31 Dec 2023
Posts: 21,777
Own Kudos:
13,047
Given Kudos: 450
Status:GMAT Assassin/Co-Founder
Affiliations: EMPOWERgmat
Location: United States (CA)
GMAT 1: 800 Q51 V49
GRE 1: Q170 V170
Expert
Expert reply
GMAT 1: 800 Q51 V49
GRE 1: Q170 V170
Posts: 21,777
Kudos: 13,047
If k is an integer and m > 0, is 2^k + 3^k = m ? 08 Feb 2015, 18:40
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Hi All,

While this DS question is a bit "crazy looking", the math behind it is not too difficult. It is perfect for TESTing VALUES.

We're told that K is an integer and that M > 0. We're asked if 2^K + 3^K = M. This is a YES/NO question.

Fact 1: 4^K + 9^K = M^2 - 12

IF....
K = 0
4^0 + 9^0 = M^2 - 12
2 = M^2 - 12
14 = M^2
Normally, M would have 2 values, but we were told that M is POSITIVE....
M = root14
The answer to the question (is 2^0 + 3^0 = root14?) is NO.

IF.....
K = 1
4^1 + 9^1 = M^2 - 12
13 = M^2 - 12
25 = M^2
M = 5
The answer to the question (is 2^1 + 3^1 = 5?) is YES.
Fact 1 is INSUFFICIENT

Fact 1: K = 1

This tells us NOTHING about the value of M, so we have no way to know if the answer to the question is YES or NO.
Fact 2 is INSUFFICIENT

Combined, we know that there's just one permissible value for K (1) and the resulting calculation (from Fact 1) yields just one answer: ALWAYS YES.
Combined, SUFFICIENT

Final Answer:
Show Spoiler
C

GMAT assassins aren't born, they're made,
Rich
User avatar
Madhavi1990
User avatar
Joined: 15 Jan 2017
Last visit: 15 Jul 2021
Posts: 250
Own Kudos:
93
Given Kudos: 931
Posts: 250
Kudos: 93
If k is an integer and m > 0, is 2^k + 3^k = m ? 09 Oct 2017, 13:25
Kudos
Add Kudos
Bookmarks
Bookmark this Post
EMPOWERgmatRichC
Hi All,

While this DS question is a bit "crazy looking", the math behind it is not too difficult. It is perfect for TESTing VALUES.

We're told that K is an integer and that M > 0. We're asked if 2^K + 3^K = M. This is a YES/NO question.

Fact 1: 4^K + 9^K = M^2 - 12

IF....
K = 0
4^0 + 9^0 = M^2 - 12
2 = M^2 - 12
14 = M^2
Normally, M would have 2 values, but we were told that M is POSITIVE....
M = root14
The answer to the question (is 2^0 + 3^0 = root14?) is NO.

IF.....
K = 1
4^1 + 9^1 = M^2 - 12
13 = M^2 - 12
25 = M^2
M = 5
The answer to the question (is 2^1 + 3^1 = 5?) is YES.
Fact 1 is INSUFFICIENT

Fact 1: K = 1

This tells us NOTHING about the value of M, so we have no way to know if the answer to the question is YES or NO.
Fact 2 is INSUFFICIENT

Combined, we know that there's just one permissible value for K (1) and the resulting calculation (from Fact 1) yields just one answer: ALWAYS YES.
Combined, SUFFICIENT

Final Answer:
Show Spoiler
C

GMAT assassins aren't born, they're made,
Rich
Show more


Hi!I had a query here: if st 2 says k =1; then we get 2^1+3^1 = m; so m = 5. Why does M have nothing as a value? Why can't we assume LHS = RHS? Would be glad to know my error here.
User avatar
EMPOWERgmatRichC
User avatar
Major Poster
Joined: 19 Dec 2014
Last visit: 31 Dec 2023
Posts: 21,777
Own Kudos:
13,047
 [1]
Given Kudos: 450
Status:GMAT Assassin/Co-Founder
Affiliations: EMPOWERgmat
Location: United States (CA)
GMAT 1: 800 Q51 V49
GRE 1: Q170 V170
Expert
Expert reply
GMAT 1: 800 Q51 V49
GRE 1: Q170 V170
Posts: 21,777
Kudos: 13,047
 [1]
If k is an integer and m > 0, is 2^k + 3^k = m ? 09 Oct 2017, 18:02
1
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Hi Madhavi1990,

When dealing with DS prompts, you have to be careful to differentiate between information that is given and the question that is ASKED. Here, we're asked IF 2^K + 3^K = M.

Fact 2 tells us that K=1, but it tells us NOTHING about M.
IF.... M = 5, then the answer to the question is YES.
IF.... M = anything other than 5, then the answer to the question is NO.
Thus, since there's more than one possible answer to the given question, Fact 2 is INSUFFICIENT.

GMAT assassins aren't born, they're made,
Rich
User avatar
Madhavi1990
User avatar
Joined: 15 Jan 2017
Last visit: 15 Jul 2021
Posts: 250
Own Kudos:
93
Given Kudos: 931
Posts: 250
Kudos: 93
If k is an integer and m > 0, is 2^k + 3^k = m ? 10 Oct 2017, 09:35
Kudos
Add Kudos
Bookmarks
Bookmark this Post
EMPOWERgmatRichC
Hi Madhavi1990,

When dealing with DS prompts, you have to be careful to differentiate between information that is given and the question that is ASKED. Here, we're asked IF 2^K + 3^K = M.

Fact 2 tells us that K=1, but it tells us NOTHING about M.
IF.... M = 5, then the answer to the question is YES.
IF.... M = anything other than 5, then the answer to the question is NO.
Thus, since there's more than one possible answer to the given question, Fact 2 is INSUFFICIENT.

GMAT assassins aren't born, they're made,
Rich
Show more


Thank you, Rich, it was really helpful :)
User avatar
bumpbot
User avatar
Non-Human User
Joined: 09 Sep 2013
Last visit: 04 Jan 2021
Posts: 38,964
Own Kudos:
1,117
Posts: 38,964
Kudos: 1,117
If k is an integer and m > 0, is 2^k + 3^k = m ? 06 Dec 2025, 23:08
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Automated notice from GMAT Club BumpBot:

A member just gave Kudos to this thread, showing it’s still useful. I’ve bumped it to the top so more people can benefit. Feel free to add your own questions or solutions.

This post was generated automatically.
Moderators:
Bunuel
Math Expert
109785 posts
kingbucky
498 posts
Gmat860sanskar
212 posts