It is currently 21 Oct 2017, 14:50

### 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

Author Message
TAGS:

### Hide Tags

Manager
Joined: 28 Oct 2009
Posts: 89

Kudos [?]: 148 [1], given: 42

Each of the following equations has at least one solution [#permalink]

### Show Tags

12 May 2010, 10:12
1
KUDOS
29
This post was
BOOKMARKED
00:00

Difficulty:

95% (hard)

Question Stats:

36% (01:04) correct 64% (01:28) wrong based on 406 sessions

### HideShow timer Statistics

Each of the following equations has at least one solution EXCEPT

A. –2^n = (–2)^-n
B. 2^-n = (–2)^n
C. 2^n = (–2)^-n
D. (–2)^n = –2^n
E. (–2)^-n = –2^-n
[Reveal] Spoiler: OA

Kudos [?]: 148 [1], given: 42

Senior Manager
Joined: 24 Jul 2009
Posts: 287

Kudos [?]: 167 [3], given: 0

### Show Tags

12 May 2010, 11:53
3
KUDOS
2
This post was
BOOKMARKED
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

Kudos [?]: 167 [3], given: 0

CEO
Status: Nothing comes easy: neither do I want.
Joined: 12 Oct 2009
Posts: 2761

Kudos [?]: 1887 [0], given: 235

Location: Malaysia
Concentration: Technology, Entrepreneurship
Schools: ISB '15 (M)
GMAT 1: 670 Q49 V31
GMAT 2: 710 Q50 V35

### Show Tags

12 May 2010, 12:09
all seems to have n=0 as solution....? whats the OA
_________________

Fight for your dreams :For all those who fear from Verbal- lets give it a fight

Money Saved is the Money Earned

Jo Bole So Nihaal , Sat Shri Akaal

GMAT Club Premium Membership - big benefits and savings

Gmat test review :
http://gmatclub.com/forum/670-to-710-a-long-journey-without-destination-still-happy-141642.html

Kudos [?]: 1887 [0], given: 235

Math Expert
Joined: 02 Sep 2009
Posts: 41892

Kudos [?]: 129160 [0], given: 12194

### Show Tags

12 May 2010, 15:01
Expert's post
3
This post was
BOOKMARKED
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 $$(-2)^{-n}=(-2)^{0}=1$$.
_________________

Kudos [?]: 129160 [0], given: 12194

CEO
Status: Nothing comes easy: neither do I want.
Joined: 12 Oct 2009
Posts: 2761

Kudos [?]: 1887 [0], given: 235

Location: Malaysia
Concentration: Technology, Entrepreneurship
Schools: ISB '15 (M)
GMAT 1: 670 Q49 V31
GMAT 2: 710 Q50 V35

### Show Tags

12 May 2010, 16:13
yes right i didnt read it closely
_________________

Fight for your dreams :For all those who fear from Verbal- lets give it a fight

Money Saved is the Money Earned

Jo Bole So Nihaal , Sat Shri Akaal

GMAT Club Premium Membership - big benefits and savings

Gmat test review :
http://gmatclub.com/forum/670-to-710-a-long-journey-without-destination-still-happy-141642.html

Kudos [?]: 1887 [0], given: 235

Intern
Joined: 15 Mar 2010
Posts: 25

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

Re: Manhattan Gmat prep Q [#permalink]

### Show Tags

14 May 2010, 07:56
Hi,

it's really elegant question

0 is a solution for second and third equations.
1 is a solution for the last two equations.

So answer is A. Really if n is not equal to 0 then absolute value of left part is greater than 1 and right part is less than 1. In case when n is equal to 0 we will get -1=1.
_________________

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

Manager
Joined: 16 Feb 2010
Posts: 179

Kudos [?]: 34 [0], given: 17

### Show Tags

14 May 2010, 13:49
great explanation Bunuel, thanks

Kudos [?]: 34 [0], given: 17

Senior Manager
Joined: 05 Oct 2008
Posts: 270

Kudos [?]: 538 [0], given: 22

### Show Tags

15 Jun 2010, 14:15
Thanks for merging.

Do you mean a negative number raised to the power of 0 yields -1?? I didn't know that!

Kudos [?]: 538 [0], given: 22

Math Expert
Joined: 02 Sep 2009
Posts: 41892

Kudos [?]: 129160 [3], given: 12194

### Show Tags

15 Jun 2010, 14:32
3
KUDOS
Expert's post
1
This post was
BOOKMARKED
study wrote:
Thanks for merging.

Do you mean a negative number raised to the power of 0 yields -1?? I didn't know that!

No.

Any number to the power of zero equals to 1 (except 0^0: 0^0 is undefined for GMAT and not tested).

The point here is that $$-2^n$$ means $$-(2^n)$$ and not $$(-2)^n$$. So for $$n=0$$ --> $$-2^n=-(2^n)=-(2^0)=-(1)$$. But if it were $$(-2)^n$$, then for $$n=0$$ --> $$(-2)^0=1$$.

Hope it's clear.
_________________

Kudos [?]: 129160 [3], given: 12194

Senior Manager
Joined: 05 Oct 2008
Posts: 270

Kudos [?]: 538 [0], given: 22

### Show Tags

15 Jun 2010, 23:56
So how do you know that the point here is that -2^n means -(2^n) and not (-2)^n

The actual question has no parenthesis. This is tricky!

Kudos [?]: 538 [0], given: 22

Math Expert
Joined: 02 Sep 2009
Posts: 41892

Kudos [?]: 129160 [0], given: 12194

### Show Tags

16 Jun 2010, 06:36
Expert's post
1
This post was
BOOKMARKED
study wrote:
So how do you know that the point here is that -2^n means -(2^n) and not (-2)^n

The actual question has no parenthesis. This is tricky!

I mean that $$-x^y$$ always means $$-(x^y)$$. If it's supposed to mean $$(-x)^y$$, then it would be represented this way.
_________________

Kudos [?]: 129160 [0], given: 12194

Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 7676

Kudos [?]: 17381 [2], given: 232

Location: Pune, India
Re: At least one solution [#permalink]

### Show Tags

06 Dec 2010, 09:21
2
KUDOS
Expert's post
SubratGmat2011 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

Can somebody plz help me out what is the approch for this type of problems?

The first and most straight forward approach that comes to mind is that I can see most of these equations will have n = 0 or n = 1 as a solution.
Except for the very first one:
n = 0: -2^0 = -1 while (-2)^(-0) = 1
n = 1: -2^1 = -2 while (-2)^-n = -1/2

For all other options, n = 0 or 1 satisfies the equation.
_________________

Karishma
Veritas Prep | GMAT Instructor
My Blog

Get started with Veritas Prep GMAT On Demand for \$199

Veritas Prep Reviews

Kudos [?]: 17381 [2], given: 232

Manager
Joined: 18 Jan 2011
Posts: 228

Kudos [?]: 37 [1], given: 4

### Show Tags

19 Jan 2011, 23:03
1
KUDOS
1
This post was
BOOKMARKED
Lets look at each choice -

A –2^n = (–2)^-n
=>(-1).(2)^n = 1/(-2)^n
=>(-1).(2)^n.(-2)^n = 1
=>(-1).(2)^n.(-1)^n.(2)^n = 1
=>(-1).(-1)^n.(2)^2n = 1
Above cannot be true for any value of n (No solution - answer)

B 2^-n = (–2)^n
=>1/(2)^n = (-2)^n
=>1=(-1)^n.(2)^n.(2)^n
=>1=(-1)^n.(2)^2n
Above is true for n=0, so it has atleast one solution

C 2^n = (–2)^-n
=>(2)^n = 1/(-2)^n
Rest of the steps Similar to option B

D (–2)^n = –2^n
=>(-1)^n. (2)^n = (-1).(2)^n
=>(-1)^n = (-1)
Above is true for all odd values of n

E (–2)^-n = –2^-n
=>1/[(-1)^n. (2)^n] = (-1)/(2)^n
=>1/[(-1)^n] = (-1)
=>1/(-1)^n = -1
Above is true for all odd values of n

I hope this helps.
_________________

Good Luck!!!

***Help and be helped!!!****

Kudos [?]: 37 [1], given: 4

Intern
Joined: 08 Jun 2010
Posts: 10

Kudos [?]: 4 [0], given: 1

### Show Tags

20 Jan 2011, 16:19

1. "In fact Option A doesn't have any solutions" - I disagree
LHS: (-2)^n [consider n = 0] then value will be (-2)^0 = 1 [this evaluation related to/depends on 2nd point in my post]
and
RHS: (-2)^-n [consider n = 0]then value will be (-2)^-0=(-2)^0= 1

2. "LSH actually should be read as -1 * (2)^n"
Does the rule says that if parenthesis are missing then always start with "power" first and then assign the -ve or +ve signs to the calculated number ? in that case I agree i.e it should be read as -2^n is to be read as -1[assign this last]* 2^n[solve this 1st]

Please confirm, as always thanks for help

Kudos [?]: 4 [0], given: 1

Math Expert
Joined: 02 Sep 2009
Posts: 41892

Kudos [?]: 129160 [0], given: 12194

### Show Tags

20 Jan 2011, 16:34
pushkarajg wrote:

1. "In fact Option A doesn't have any solutions" - I disagree
LHS: (-2)^n [consider n = 0] then value will be (-2)^0 = 1 [this evaluation related to/depends on 2nd point in my post]
and
RHS: (-2)^-n [consider n = 0]then value will be (-2)^-0=(-2)^0= 1

2. "LSH actually should be read as -1 * (2)^n"
Does the rule says that if parenthesis are missing then always start with "power" first and then assign the -ve or +ve signs to the calculated number ? in that case I agree i.e it should be read as -2^n is to be read as -1[assign this last]* 2^n[solve this 1st]

Please confirm, as always thanks for help

exponents-94119.html#p724081
exponents-94119.html#p738365
exponents-94119.html#p738571
_________________

Kudos [?]: 129160 [0], given: 12194

Senior Manager
Joined: 08 Nov 2010
Posts: 394

Kudos [?]: 128 [0], given: 161

### Show Tags

18 Feb 2011, 11:22
i guess the only real way to solve it under 2 min is to plug in 0/1...

if u start with choosing 1 here as first step is not good... choosing 0 is canceling 3 choices quickly...
_________________

Kudos [?]: 128 [0], given: 161

Manager
Joined: 21 Jun 2010
Posts: 111

Kudos [?]: 171 [0], given: 0

Schools: Tuck, Duke, Cambridge, Said
No solution N: Manhattan GMAT test [#permalink]

### Show Tags

05 May 2011, 17:52
2
This post was
BOOKMARKED
I am totally lost on this one ..... can anyone help please ?

Each of the following equations has at least one solution EXCEPT
A.) –2^n = (–2)^-n
B.) 2^-n = (–2)^n
C.) 2^n = (–2)^-n
D.) (–2)^n = –2^n
E.) (–2)^-n = -2^-n

Kudos [?]: 171 [0], given: 0

Director
Joined: 01 Feb 2011
Posts: 726

Kudos [?]: 144 [0], given: 42

Re: No solution N: Manhattan GMAT test [#permalink]

### Show Tags

05 May 2011, 18:26
lets pick a value for n.

n = 0

A. cannot be true as we get -1 on LHS and 1 on RHS ( as anything to the power of 0 is 1)
B. true (LHS = RHS = 1)
C. true (LHS = RHS = 1)
D. true (LHS = RHS = 1)
E. true (LHS = RHS = 1)

Kudos [?]: 144 [0], given: 42

VP
Status: There is always something new !!
Affiliations: PMI,QAI Global,eXampleCG
Joined: 08 May 2009
Posts: 1285

Kudos [?]: 283 [0], given: 10

Re: No solution N: Manhattan GMAT test [#permalink]

### Show Tags

05 May 2011, 23:42
for B and C n = 0
for D and E n = 1.

A prevails.
_________________

Visit -- http://www.sustainable-sphere.com/
Promote Green Business,Sustainable Living and Green Earth !!

Kudos [?]: 283 [0], given: 10

Retired Moderator
Affiliations: PMI, ASQ
Joined: 16 Jun 2012
Posts: 119

Kudos [?]: 1284 [0], given: 21

GMAT 1: 710 Q49 V38
Re: Each of the following has at least one solution EXCEPT [#permalink]

### Show Tags

18 Aug 2012, 16:14
1
This post was
BOOKMARKED
arichardson26 wrote:
Each of the following has at least one solution EXCEPT

A. -2^n = (-2)^-n

B. 2^-n = (-2)^n

C. 2^n = (-2)^-n

D. (-2)^n = -2^n

E. (-2)^-n = -2^-n

[Reveal] Spoiler:
A

B, C have can be equated by using n=0
D and E have external/independent -ve signs, so 0 wont help, but using n= +1 for D and -1 for E will equate the sides.

Took more than 2 mins
_________________

Legendary Collections
1. 700 Level Quant 2. IIM Quant 3. 100 CR from LSAT 4. 100 Legendary SC 5. 5000 Practice problems 6.125 Quant 7. 38 SC 8. 10 Full Length GMAT Pen&Paper Tests
9. 1500+ RC 10. 100 Legendary CR 11. Additional Verbal Qs 12. Additional Quant Qs

My debrief |Free essay review initiative
PM me for One-on-One Webex Tutoring

Kudos [?]: 1284 [0], given: 21

Re: Each of the following has at least one solution EXCEPT   [#permalink] 18 Aug 2012, 16:14

Go to page    1   2    Next  [ 33 posts ]

Display posts from previous: Sort by