Find all School-related info fast with the new School-Specific MBA Forum

 It is currently 27 Apr 2015, 09:48

### 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

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

# Events & Promotions

###### Events & Promotions in June
Open Detailed Calendar

# Each of the following equations has at least one solution

 Question banks Downloads My Bookmarks Reviews Important topics
Author Message
TAGS:
Director
Joined: 24 Aug 2009
Posts: 507
Schools: Harvard, Columbia, Stern, Booth, LSB,
Followers: 10

Kudos [?]: 444 [0], given: 241

Each of the following has at least one solution EXCEPT [#permalink]  23 Aug 2012, 03:45
OA has to be A because
Equation 1 simplifies to (2)^n (2)^n (-1)^n= -1 has no solution for any value of n
Rest of options have at least 1 solution
_________________

If you like my Question/Explanation or the contribution, Kindly appreciate by pressing KUDOS.
Kudos always maximizes GMATCLUB worth
-Game Theory

If you have any question regarding my post, kindly pm me or else I won't be able to reply

Moderator
Joined: 02 Jul 2012
Posts: 1227
Location: India
Concentration: Strategy
GMAT 1: 740 Q49 V42
GPA: 3.8
WE: Engineering (Energy and Utilities)
Followers: 79

Kudos [?]: 836 [0], given: 116

Re: Each of the following equations has at least one solution [#permalink]  08 Oct 2012, 04:00
if -2^n means -(2^n), the answer is A. Otherwise I find 0 to satisfy all equations.
_________________

Did you find this post helpful?... Please let me know through the Kudos button.

Thanks To The Almighty - My GMAT Debrief

GMAT Reading Comprehension: 7 Most Common Passage Types

Math Expert
Joined: 02 Sep 2009
Posts: 27123
Followers: 4187

Kudos [?]: 40493 [1] , given: 5540

Re: Each of the following equations has at least one solution [#permalink]  08 Oct 2012, 04:26
1
KUDOS
Expert's post
Intern
Joined: 16 Sep 2012
Posts: 15
Concentration: Finance, General Management
GMAT 1: 710 Q47 V41
Followers: 0

Kudos [?]: 4 [0], given: 2

Re: Exponents [#permalink]  14 Oct 2012, 07:05
Bunuel wrote:
gurpreetsingh wrote:
all seems to have n=0 as solution....? whats the OA

$$n=0$$ is not a solution of the equation $$-2^n = (-2)^{-n}$$ (in fact this equation has no solution):

$$-2^n=-(2^n)=-(2^{0})=-1$$ but $$(-2)^{-n}=(-2)^{0}=1$$.

Thank you for your response.

I would like to double check why we say that n=0 could be a solution in case of $$(-2)^{-n}$$
as $$(-2)^{-n} = (-2)^{1/n}$$ and then we can not divide by zero?

Nik
Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 5433
Location: Pune, India
Followers: 1325

Kudos [?]: 6720 [0], given: 176

Re: Exponents [#permalink]  14 Oct 2012, 22:12
Expert's post
NikRu wrote:
I would like to double check why we say that n=0 could be a solution in case of $$(-2)^{-n}$$
as $$(-2)^{-n} = (-2)^{1/n}$$ and then we can not divide by zero?

Nik

$$(-2)^{-n} = 1/(-2)^n$$ not $$(-2)^{1/n}$$
_________________

Karishma
Veritas Prep | GMAT Instructor
My Blog

Veritas Prep GMAT course is coming to India. Enroll in our weeklong Immersion Course that starts March 29!

Veritas Prep Reviews

Senior Manager
Joined: 03 Dec 2012
Posts: 367
Followers: 0

Kudos [?]: 51 [0], given: 291

Re: Each of the following equations has at least one solution [#permalink]  26 Oct 2013, 03:40
Can somebody please explain if (–2)^n = 1 or -1 (if n=0)
Math Expert
Joined: 02 Sep 2009
Posts: 27123
Followers: 4187

Kudos [?]: 40493 [1] , given: 5540

Re: Each of the following equations has at least one solution [#permalink]  26 Oct 2013, 03:44
1
KUDOS
Expert's post
mohnish104 wrote:
Can somebody please explain if (–2)^n = 1 or -1 (if n=0)

Check here: each-of-the-following-equations-has-at-least-one-solution-94119.html#p738365
_________________
SVP
Joined: 06 Sep 2013
Posts: 2026
Concentration: Finance
GMAT 1: 710 Q48 V39
Followers: 24

Kudos [?]: 291 [0], given: 354

Re: Exponents [#permalink]  15 Jan 2014, 08:57
nverma wrote:
marcusaurelius wrote:
Each of the following equations has at least one solution EXCEPT

–2^n = (–2)^-n
2^-n = (–2)^n
2^n = (–2)^-n
(–2)^n = –2^n
(–2)^-n = –2^-n

IMHO A

a) –2^n = (–2)^-n
–2^n = 1/(–2)^n
–2^n * (–2)^n = 1, Keep it. Let's solve the other options..!!

b) 2^-n = (–2)^n
1/2^n = (–2)^n
1 = (–2)^n * (2^n)
For n=0, L.H.S = R.H.S

c) 2^n = (–2)^-n
2^n = 1/ (–2)^n
(2^n) * (–2)^n = 1
For n=0, L.H.S = R.H.S

d) (–2)^n = –2^n
(–2)^n / –2^n = 1
For n=1, L.H.S = R.H.S

e) (–2)^-n = –2^-n
1/ (–2)^n = 1/–2^n
For n=1, L.H.S = R.H.S

Why did you plug n=1 for the last two, wouldn't it be easier just to plug n=0 for all and see that A has no solution?
Just want to know if there was any specific reason why you did so

Thank you
Cheers
J

PS. Would be nice if we could get this question in code format!
Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 5433
Location: Pune, India
Followers: 1325

Kudos [?]: 6720 [0], given: 176

Re: Exponents [#permalink]  15 Jan 2014, 19:55
Expert's post
jlgdr wrote:
nverma wrote:
marcusaurelius wrote:
Each of the following equations has at least one solution EXCEPT

–2^n = (–2)^-n
2^-n = (–2)^n
2^n = (–2)^-n
(–2)^n = –2^n
(–2)^-n = –2^-n

IMHO A

a) –2^n = (–2)^-n
–2^n = 1/(–2)^n
–2^n * (–2)^n = 1, Keep it. Let's solve the other options..!!

b) 2^-n = (–2)^n
1/2^n = (–2)^n
1 = (–2)^n * (2^n)
For n=0, L.H.S = R.H.S

c) 2^n = (–2)^-n
2^n = 1/ (–2)^n
(2^n) * (–2)^n = 1
For n=0, L.H.S = R.H.S

d) (–2)^n = –2^n
(–2)^n / –2^n = 1
For n=1, L.H.S = R.H.S

e) (–2)^-n = –2^-n
1/ (–2)^n = 1/–2^n
For n=1, L.H.S = R.H.S

Why did you plug n=1 for the last two, wouldn't it be easier just to plug n=0 for all and see that A has no solution?
Just want to know if there was any specific reason why you did so

Thank you
Cheers
J

PS. Would be nice if we could get this question in code format!

We need to find the equation that has no solution. What we are trying to do is find at least one solution for 4 equations. The fifth one will obviously not have any solution and will be our answer.
Options (D) and (E) do not have 0 as a solution.
So you try n = 1 on (A), (D) and (E).
n = 1 is still not a solution for (A) but it is for (D) and (E).

(D) (–2)^n = –2^n
When you put n = 0, you get
(-2)^0 = -2^0
1 = -1 which doesn't hold.
So you try n = 1
(–2)^1 = -2^1
-2 = -2
n = 1 is a solution.

Same logic for (E)
_________________

Karishma
Veritas Prep | GMAT Instructor
My Blog

Veritas Prep GMAT course is coming to India. Enroll in our weeklong Immersion Course that starts March 29!

Veritas Prep Reviews

GMAT Club Legend
Joined: 09 Sep 2013
Posts: 4684
Followers: 291

Kudos [?]: 52 [0], given: 0

Re: No solution N: Manhattan GMAT test [#permalink]  24 Aug 2014, 15:52
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.
_________________
Re: No solution N: Manhattan GMAT test   [#permalink] 24 Aug 2014, 15:52

Go to page   Previous    1   2   [ 30 posts ]

Similar topics Replies Last post
Similar
Topics:
33 Each of 435 bags contains at least one of the following 10 20 Feb 2012, 12:12
1 At least one solution-Postive and negatives 2 12 Sep 2011, 10:01
1 Each of 435 bags contains at least one of the following thre 3 26 Mar 2011, 06:34
12 Each of the following equations has at least one solution EX 12 17 Oct 2009, 07:06
12 Each of the following equations has at least one solution 9 01 Oct 2009, 16:45
Display posts from previous: Sort by

# Each of the following equations has at least one solution

 Question banks Downloads My Bookmarks Reviews Important topics

 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®.