NEW HERE? LEARN MORE
closeclose
Last visit was: 26 Apr 2024, 17:28 It is currently 26 Apr 2024, 17:28
Decision Tracker
My Rewards
New posts
New comers' posts

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

If k is an integer, is 2^k + 3^k = m ?

SORT BY:
Date
Kudos
Tags:
Find Similar Topics 
Show Tags
Hide Tags
User avatar
danzig
Manager
Manager
Joined: 11 Aug 2012
Posts: 103
Own Kudos [?]: 328 [2]
Given Kudos: 16
Schools: HBS '16 Stanford '16
Send PM
If k is an integer, is 2^k + 3^k = m ? [#permalink] New post   Updated on: 21 Aug 2013, 12:26
2
Bookmarks
00:00
A
B
C
D
E

Difficulty:

75% (hard)

Question Stats:

47% (02:02) correct 53% (02:09) wrong based on 139 sessions
Hide Show timer Statistics
If k is an integer, is 2^k + 3^k = m ?

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

(2) k = 1

I don't agree with the OA. If we use statements 1 and 2 together, we get this:

We replace the value of \(k\) in the original question, so the question now is:\(is k = 5 ?\)

Now we replace the value of \(k\) in statement (1), so:

\(m^2 = 25\)

So,\(m = +/- 25\)

There is not indication whether m is possitive.

IMO, the answer: E
ShowHide Answer
Official Answer
E

Originally posted by danzig on 21 Aug 2013, 12:05.
Last edited by Bunuel on 21 Aug 2013, 12:26, edited 1 time in total.
Edited the OA.
User avatar
L
Bunuel
Math Expert
Joined: 02 Sep 2009
Posts: 92948
Own Kudos [?]: 619244 [0]
Given Kudos: 81609
Send PM
CAT Tests Forum Quiz Mode
Re: If k is an integer, is 2^k + 3^k = m ? [#permalink] New post   21 Aug 2013, 12:16
Expert Reply
danzig wrote:
If k is an integer, is 2^k + 3^k = m ?

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

(2) k = 1

I don't agree with the OA. If we use statements 1 and 2 together, we get this:

We replace the value of \(k\) in the original question, so the question now is: is m = 5 ?

Now we replace the value of \(k\) in statement (1), so:

\(m^2 = 25\)

So, m = +/- 5

There is not indication whether m is possitive.

IMO, the answer: E


Yes, you are right. When we combine we get that m is either 5 or -5. If m=5 then the answer is YES but if m=-5, then the answer is No.

Answer: E.
User avatar
L
stne
SVP
SVP
Joined: 27 May 2012
Posts: 1680
Own Kudos [?]: 1424 [0]
Given Kudos: 632
Send PM
Re: If k is an integer, is 2^k + 3^k = m ? [#permalink] New post   30 Aug 2013, 01:26
danzig wrote:
If k is an integer, is 2^k + 3^k = m ?

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

(2) k = 1

I don't agree with the OA. If we use statements 1 and 2 together, we get this:

We replace the value of \(k\) in the original question, so the question now is:\(is k = 5 ?\)

Now we replace the value of \(k\) in statement (1), so:

\(m^2 = 25\)

So,\(m = +/- 25\)

There is not indication whether m is possitive.

IMO, the answer: E


I don't know what was the original OA but I am assuming it was C, here's how I think the answer should be C, please do correct if there is a flaw in my reasoning.

Given If k is an integer, is \(2^k + 3^k = m\)?
Squaring both sides original equation now becomes \(2^{2k} +3^{2k}+2.6^k=m^2\)

statement 1:\(4^k + 9^k = m^2 - 12\)this can be written as \(2^{2k} +3^{2k}+12 =m^2\)..

Comparing this with original equation we see that this will be equal to original equation only if K=1 since we do not have the value of K, hence insufficient

statement 2 : K=1 , by itself it is insufficient as we do not know the value of M

1+ 2

K=1 then \(m^2\) = 25

this is also what we get from the original equation,doesn't matter what m is, \(m^2\) is 25
Please share your views
User avatar
L
Bunuel
Math Expert
Joined: 02 Sep 2009
Posts: 92948
Own Kudos [?]: 619244 [1]
Given Kudos: 81609
Send PM
CAT Tests Forum Quiz Mode
Re: If k is an integer, is 2^k + 3^k = m ? [#permalink] New post   30 Aug 2013, 04:41
1
Kudos
Expert Reply
stne wrote:
danzig wrote:
If k is an integer, is 2^k + 3^k = m ?

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

(2) k = 1

I don't agree with the OA. If we use statements 1 and 2 together, we get this:

We replace the value of \(k\) in the original question, so the question now is:\(is k = 5 ?\)

Now we replace the value of \(k\) in statement (1), so:

\(m^2 = 25\)

So,\(m = +/- 25\)

There is not indication whether m is possitive.

IMO, the answer: E


I don't know what was the original OA but I am assuming it was C, here's how I think the answer should be C, please do correct if there is a flaw in my reasoning.

Given If k is an integer, is \(2^k + 3^k = m\)?
Squaring both sides original equation now becomes \(2^{2k} +3^{2k}+2.6^k=m^2\)

statement 1:\(4^k + 9^k = m^2 - 12\)this can be written as \(2^{2k} +3^{2k}+12 =m^2\)..

Comparing this with original equation we see that this will be equal to original equation only if K=1 since we do not have the value of K, hence insufficient

statement 2 : K=1 , by itself it is insufficient as we do not know the value of M

1+ 2

K=1 then \(m^2\) = 25

this is also what we get from the original equation,doesn't matter what m is, \(m^2\) is 25
Please share your views


It does matter. If m=-5, then the question is: does \(2^k + 3^k = -5\)? And you cannot square this.
User avatar
L
stne
SVP
SVP
Joined: 27 May 2012
Posts: 1680
Own Kudos [?]: 1424 [0]
Given Kudos: 632
Send PM
Re: If k is an integer, is 2^k + 3^k = m ? [#permalink] New post   30 Aug 2013, 07:00
Bunuel wrote:
stne wrote:
danzig wrote:
If k is an integer, is 2^k + 3^k = m ?

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

(2) k = 1

I don't agree with the OA. If we use statements 1 and 2 together, we get this:

We replace the value of \(k\) in the original question, so the question now is:\(is k = 5 ?\)

Now we replace the value of \(k\) in statement (1), so:

\(m^2 = 25\)

So,\(m = +/- 25\)

There is not indication whether m is possitive.

IMO, the answer: E


I don't know what was the original OA but I am assuming it was C, here's how I think the answer should be C, please do correct if there is a flaw in my reasoning.

Given If k is an integer, is \(2^k + 3^k = m\)?
Squaring both sides original equation now becomes \(2^{2k} +3^{2k}+2.6^k=m^2\)

statement 1:\(4^k + 9^k = m^2 - 12\)this can be written as \(2^{2k} +3^{2k}+12 =m^2\)..

Comparing this with original equation we see that this will be equal to original equation only if K=1 since we do not have the value of K, hence insufficient

statement 2 : K=1 , by itself it is insufficient as we do not know the value of M

1+ 2

K=1 then \(m^2\) = 25

this is also what we get from the original equation,doesn't matter what m is, \(m^2\) is 25
Please share your views


It does matter. If m=-5, then the question is: does \(2^k + 3^k = -5\)? And you cannot square this.


Well if you say so, there are many ways algebraic equations can be manipulated and I thought they could be squared .Thank you +1
User avatar
L
EMPOWERgmatRichC
GMAT Club Legend
GMAT Club Legend
Joined: 19 Dec 2014
Status:GMAT Assassin/Co-Founder
Affiliations: EMPOWERgmat
Posts: 21846
Own Kudos [?]: 11669 [1]
Given Kudos: 450
Location: United States (CA)
GMAT 1: 800 Q51 V49
GRE 1: Q170 V170
Send PM
Re: If k is an integer, is 2^k + 3^k = m ? [#permalink] New post   25 Dec 2014, 10:58
1
Kudos
Expert Reply
Hi All,

This question can be solved with a combination of TESTing VALUES and some basic algebra/arithmetic skills.

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

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

At first glance, I would want to TEST something simple...
K = 1
4^1 + 9^1 = M^2 - 12
4 + 9 = M^2 - 12
25 = M^2
M = +5 or -5

In the question, we have to track BOTH options...
Is 2^1 + 3^1 = 5? The answer is YES
Is 2^1 + 3^1 = -5 The answer is NO
Fact 1 is INSUFFICIENT

Fact 2: K = 1

This tells us NOTHING about M, so the answer COULD be YES or it COULD be NO.
Fact 2 is INSUFFICIENT

Combined, we have the same options that we had in Fact 1 - a YES and a NO.
Combined, INSUFFICIENT

Final Answer:
Show Spoiler
E


GMAT assassins aren't born, they're made,
Rich
User avatar
bumpbot
Non-Human User
Joined: 09 Sep 2013
Posts: 32689
Own Kudos [?]: 822 [0]
Given Kudos: 0
Send PM
Re: If k is an integer, is 2^k + 3^k = m ? [#permalink] New post   10 Oct 2017, 10:52
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 Club Bot
gmatclubot
Re: If k is an integer, is 2^k + 3^k = m ? [#permalink]
10 Oct 2017, 10:52
Moderator:
Bunuel
Math Expert
92948 posts

Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne
Main navigation
GMAT Resources
Partners
MBA Resources
www.gmac.com|www.mba.com | | GMAT Club Rules | Terms and Conditions