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

 It is currently 24 May 2013, 23:11

# Each has one solution except?

Author Message
TAGS:
Manager
Joined: 23 Sep 2009
Posts: 159
Followers: 1

Kudos [?]: 9 [1] , given: 37

Each has one solution except? [#permalink]  01 Oct 2009, 17:45
1
KUDOS
00:00

Question Stats:

42% (03:31) correct 57% (02:09) wrong based on 4 sessions
Hi folks,
I came across this problem in he MGMAT practice..Can anyone explain the solution more clearly?

Each of the following equations has at least one solution EXCEPT
1. –2n = (–2)-n
2. 2-n = (–2)n
3. 2n = (–2)-n
4. (–2)n = –2n
5. (–2)-n = –2-n

_________________

Thanks,
VP

 Manhattan GMAT Discount Codes Kaplan GMAT Prep Discount Codes GMAT Pill GMAT Discount Codes
Senior Manager
Joined: 31 Aug 2009
Posts: 426
Location: Sydney, Australia
Followers: 4

Kudos [?]: 76 [0], given: 20

Re: Each has one solution except? [#permalink]  01 Oct 2009, 20:12
I’m assuming that they are all multiples?? That -2-n means (-2)*(-n) and not (-2) subtract (n)?

Let n =1
1) -2(1) = -2(-1) Left = -2 Right = +2. No solution
2) 2(-1) = (-2)(1) Both = -2
3) 2(1) = (-2)(-1) both = +2
4) (-2)1 = -2(1) both = -2
5) (-2)(-1) = (-2)(-1) both = +2
Manager
Joined: 04 Sep 2009
Posts: 53
WE 1: Real estate investment consulting
Followers: 1

Kudos [?]: 15 [0], given: 7

Re: Each has one solution except? [#permalink]  01 Oct 2009, 22:12
vigneshpandi - it is indeed not clear whether the signes should be treated as is or you imply multiplication here. Pls, try to use the math symbols to avoid misunderstanding.

yangsta - in option 1 - what about n=0 - then it does work. Or is it that I cannot have 0 with a minus sign?
Senior Manager
Joined: 31 Aug 2009
Posts: 426
Location: Sydney, Australia
Followers: 4

Kudos [?]: 76 [0], given: 20

Re: Each has one solution except? [#permalink]  01 Oct 2009, 22:46
yangsta - in option 1 - what about n=0 - then it does work. Or is it that I cannot have 0 with a minus sign?

well 0 cannot be negative. From what I've seen on most GMAT question stems they will state if a variable can be zero.
Manager
Joined: 23 Sep 2009
Posts: 159
Followers: 1

Kudos [?]: 9 [0], given: 37

Re: Each has one solution except? [#permalink]  02 Oct 2009, 20:25
I am sorry....the question has all the terms 'n' on the powers....the actual question is:

Each of the following equations has at least one solution EXCEPT
1. –2^n = (–2)^-n
2. 2^-n = (–2)^n
3. 2^n = (–2)^-n
4. (–2)^n = –2^n
5. (–2)^-n = –2^-n

_________________

Thanks,
VP

Kaplan GMAT Instructor
Joined: 25 Aug 2009
Posts: 574
Location: Cambridge, MA
Followers: 51

Kudos [?]: 129 [1] , given: 2

Re: Each has one solution except? [#permalink]  02 Oct 2009, 22:00
1
KUDOS
vigneshpandi wrote:
I am sorry....the question has all the terms 'n' on the powers....the actual question is:

Each of the following equations has at least one solution EXCEPT
1. –2^n = (–2)^-n
2. 2^-n = (–2)^n
3. 2^n = (–2)^-n
4. (–2)^n = –2^n
5. (–2)^-n = –2^-n

While it is possible to reason out which of these choices must not work, we may not have time or the confidence to do so. However, this problem has variable in its answer choice, and relatively simple math. Therefore, an easy alternative is picking numbers.

Since we're dealing with exponents, we want to keep things as easy as possible. Hence, we'll start with the easiest exponent possible: n = 1. A, B, and C are not solved (x^-n = 1/(x^n), so we're comparing integers to fractions), but choices D and E both end up valid, eliminating them from contention.

In the process of doing this, however, we've uncovered a major clue to our next step: A, B, and C, all compared integers to fractions, and the only integer equal to it's reciprocal is 1, which is equal to 1/1. This, in turn, tells us the we need to pick n = 0. Remember, for all non-zero x, x^0 = 1.

If we plug n = 0 into choices B and C, we end up with 1 = 1 both times. Choice A, however, results in the false 1 = -1. Thus, we conclude that the first choice has no valid solutions, and is therefore the correct answer.
_________________

Eli Meyer
Kaplan Teacher
http://www.kaptest.com/GMAT

Prepare with Kaplan and save \$150 on a course!

Kaplan Reviews

Manager
Joined: 23 Sep 2009
Posts: 159
Followers: 1

Kudos [?]: 9 [0], given: 37

Re: Each has one solution except? [#permalink]  03 Oct 2009, 09:29
Thank you for the explanation....
_________________

Thanks,
VP

VP
Status: There is always something new !!
Affiliations: PMI,QAI Global,eXampleCG
Joined: 08 May 2009
Posts: 1400
Followers: 8

Kudos [?]: 84 [0], given: 10

Re: Each has one solution except? [#permalink]  03 May 2011, 07:43
1 has no solution.
others have 0,1 and 2.
hence A
_________________

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

Intern
Joined: 21 Apr 2011
Posts: 11
Followers: 0

Kudos [?]: 3 [1] , given: 4

Re: Each has one solution except? [#permalink]  25 Jun 2011, 04:37
1
KUDOS
I have a quick answer, using elimination.
If n1 is the solution of the second equation, then (-n1) must be the solution of the third question. Therefore 2nd and 3rd question must have a solution or must have no solution at the same time.
The same situation with the 4th and 5th equation.
Then we left the 1st equation which is the correct answer
Director
Joined: 01 Feb 2011
Posts: 791
Followers: 11

Kudos [?]: 63 [0], given: 42

Re: Each has one solution except? [#permalink]  25 Jun 2011, 18:42
1 has no solution , others has at least one solution.
Re: Each has one solution except?   [#permalink] 25 Jun 2011, 18:42
Similar topics Replies Last post
Similar
Topics:
Except for one class in history and one in biology, all the 13 09 Jan 2005, 08:42
Except for one class in history and one class in biology, 12 30 Apr 2006, 21:10
Except for one class in history and one in biology, all the 0 13 Nov 2006, 07:02
5 An insect has one shoe and one sock for each of its twelve 14 02 Dec 2009, 01:35
2 Each of the following equations has at least one solution 28 12 May 2010, 10:12
Display posts from previous: Sort by