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

 It is currently 05 Dec 2013, 08:10

# Events & Promotions

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

# What is the value of (-1)^{g^4 + g - 1} ? 1. g is an

Author Message
Director
Joined: 01 Aug 2008
Posts: 772
Followers: 3

Kudos [?]: 45 [0], given: 99

What is the value of (-1)^{g^4 + g - 1} ? 1. g is an [#permalink]  21 Dec 2008, 08:55
What is the value of (-1)^{g^4 + g - 1} ?

1. g is an integer
2. g is even

* Statement (1) ALONE is sufficient, but Statement (2) ALONE is not sufficient
* Statement (2) ALONE is sufficient, but Statement (1) ALONE is not sufficient
* BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient
* EACH statement ALONE is sufficient
* Statements (1) and (2) TOGETHER are NOT sufficient

[Reveal] Spoiler: OA
D

Source: GMAT Club Tests - hardest GMAT questions

shouldn't we consider negative values for option 1? ( 'g' is integer)? in this case, then A wont fit right?
 Kaplan Promo Code Knewton GMAT Discount Codes GMAT Pill GMAT Discount Codes
Current Student
Joined: 28 Dec 2004
Posts: 3421
Location: New York City
Schools: Wharton'11 HBS'12
Followers: 12

Kudos [?]: 141 [0], given: 2

Re: m06 # 4 [#permalink]  21 Dec 2008, 09:17
you have to realize that if you have fractions then we will have a imaginary number and that we dont consider in GMAT.

so 1) is sufficient..if g is ODD, and even it its negative

if g=1, then (-1)^1 if g=-1, g= (-1)^-1 i.e 1

if g=2 then (-1)^odd is -1..
so sufficient

2) sufficient..
Director
Joined: 01 Aug 2008
Posts: 772
Followers: 3

Kudos [?]: 45 [0], given: 99

Re: m06 # 4 [#permalink]  21 Dec 2008, 09:46
I think I miss calculated ... thanks for the correction ...
Intern
Joined: 19 Dec 2008
Posts: 13
Followers: 0

Kudos [?]: 11 [0], given: 0

Re: m06 # 4 [#permalink]  22 Dec 2008, 09:15
Why 1) Sufficient? It is either 1 or -1 so we can't tell...While 2) is definitely -1
Director
Joined: 01 Aug 2008
Posts: 772
Followers: 3

Kudos [?]: 45 [0], given: 99

Re: m06 # 4 [#permalink]  22 Dec 2008, 10:52
I too was thinking in the same way when i was taking the test that statement can be 1 or -1 .... but looks like I am not able to get +1 scenario no w... can you write up ur test case which produces +1?
Founder
Status: Costa Rica!
Affiliations: UA-1K, SPG-G, HH-D
Joined: 04 Dec 2002
Posts: 11226
Location: United States (WA)
GMAT 1: 750 Q49 V42
GPA: 3.5
WE: Information Technology (Hospitality and Tourism)
Followers: 1768

Kudos [?]: 5623 [1] , given: 3318

Re: m06 # 4 [#permalink]  22 Dec 2008, 11:51
1
KUDOS
Expert's post
FYI - here is the latest official explanation (not updated yet in the tests database - we are editing them offline).

Statement (1). Sufficient. If g is an integer, for any value of g (positive or negative or zero), the end result will always be (-1). That's because we subtract 1 from an always even number (which means the exponent will never be 0, even if g = 0). Therefore, (-1) will be always taken to an odd power, and the expression will always result into (-1), as long as g is an integer. For example: let's try 3 and 2 as values of g: 3^4 +3 -1 =81 +2 = 83 or2^4 +2 - 1 = 16 + 1 = 17. Both are odd and (-1) to the odd power results into (-1).

Statement (2) provides that g is even and therefore an even integer - applying the logic from Statement (1) - Sufficient.
_________________

Founder of GMAT Club

Just starting out with GMAT? Start here... | Want to know your GMAT Score? Try GMAT Score Estimator
Need GMAT Book Recommendations? Best GMAT Books

Co-author of the GMAT Club tests

CEO
Joined: 29 Aug 2007
Posts: 2510
Followers: 44

Kudos [?]: 422 [0], given: 19

Re: m06 # 4 [#permalink]  22 Dec 2008, 21:16
ugimba wrote:
What is the value of (-1)^{g^4 + g - 1} ?

1. g is an integer
2. g is even

Thats a good question.

Agree with D.
_________________
Director
Joined: 29 Aug 2005
Posts: 885
Followers: 6

Kudos [?]: 119 [0], given: 7

Re: m06 # 4 [#permalink]  20 Jan 2009, 05:52
ugimba wrote:
What is the value of (-1)^{g^4 + g - 1} ?

1. g is an integer
2. g is even

D.
Stmt1: We need to test with odd and even integers.
odd integer: (-1)^{odd^4 + odd - 1} => (-1)^{odd}=-1
even integer: (-1)^{even^4 + even - 1} => (-1)^{even}=-1
Suff.

Stmt2: As we have seen in Stmt 1, g=even integer results in -1. Suff
Manager
Joined: 29 Nov 2009
Posts: 109
Location: United States
Followers: 1

Kudos [?]: 21 [0], given: 5

Re: m06 # 4 [#permalink]  08 Dec 2009, 06:45
if g = -1... (-1)^(1-1-1) = (-1)^(-1) = -1... so negative numbers result in -1 also making A sufficient.
SVP
Affiliations: HEC
Joined: 28 Sep 2009
Posts: 1584
Concentration: Economics, Finance
GMAT 1: 730 Q48 V44
Followers: 76

Kudos [?]: 437 [0], given: 411

Re: m06 # 4 [#permalink]  08 Dec 2009, 07:20
Expert's post
Oh, good question. I even got this one right!

Just for fun, I raised the number to a negative power and came up with the same answer. For instance, if g=0, then -1 is raised to the negative first power (0+0-1). The reciprical of -1 is 1/-1, which still equals -1.
Intern
Joined: 15 Nov 2009
Posts: 17
Followers: 0

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

Re: m06 # 4 [#permalink]  08 Dec 2009, 07:46
I read the question incorrectly. I thought it was: (-1)^(g^4+g^(-1)). I didn't know to tackle it.
Joined: 20 Aug 2009
Posts: 314
Location: Tbilisi, Georgia
Schools: Stanford (in), Tuck (WL), Wharton (ding), Cornell (in)
Followers: 12

Kudos [?]: 78 [0], given: 69

Re: m06 # 4 [#permalink]  08 Dec 2009, 08:03
so, g^4+g-1 is even for any integer g, am I right?
Manager
Joined: 29 Nov 2009
Posts: 109
Location: United States
Followers: 1

Kudos [?]: 21 [0], given: 5

Re: m06 # 4 [#permalink]  08 Dec 2009, 08:10
No, odd:

1^4+1-1 = 1
2^4+2-1 = 17
-1^4-1-1 = -1
Manager
Joined: 20 Oct 2009
Posts: 114
Followers: 6

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

Re: m06 # 4 [#permalink]  08 Dec 2009, 10:43
_________________

Dream the impossible and do the incredible.

Live. Love. Laugh.

VP
Status: The last round
Joined: 18 Jun 2009
Posts: 1322
Concentration: Strategy, General Management
GMAT 1: 680 Q48 V34
Followers: 50

Kudos [?]: 412 [0], given: 156

Re: m06 # 4 [#permalink]  08 Dec 2009, 21:11
seofah wrote:
(-1)^{even}=-1

I think its a typo. (-1)^even= 1
_________________

[ From 470 to 680-My Story ] [ My Last Month Before Test ]
[ GMAT Prep Analysis Tool ] [ US. Business School Dashboard ] [ Int. Business School Dashboard ]

I Can, I Will

Intern
Joined: 09 Nov 2009
Posts: 1
Followers: 0

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

Re: m06 # 4 [#permalink]  08 Dec 2009, 21:47
Since we need to find the value of (-1) raise to something we just need to know wheteher the power is odd or even.
Statement one tells us its integer, but it can be odd or even. So we will get two value i.e -1 and 1.
Statement 2 tells us its an vene integer so we can clearly conclude what would be the value
SVP
Affiliations: HEC
Joined: 28 Sep 2009
Posts: 1584
Concentration: Economics, Finance
GMAT 1: 730 Q48 V44
Followers: 76

Kudos [?]: 437 [0], given: 411

Re: m06 # 4 [#permalink]  08 Dec 2009, 22:11
Expert's post
bb wrote:
FYI - here is the latest official explanation (not updated yet in the tests database - we are editing them offline).

I think the updated explanation is very clear. But when do you think these edits will be finished and updated in the test database? It sounds like a difficult and time consuming task. Good luck!
Manager
Joined: 23 Oct 2010
Posts: 89
Location: India
Followers: 3

Kudos [?]: 17 [0], given: 6

Re: m06 # 4 [#permalink]  15 Dec 2010, 06:44
A

Rephrase the question: is g^4 + g -1 odd or even? If we determine this then we can know for sure the value of the complete expression
S1: g is an integer -->
if g is odd then g^4 - g - 1= O + O - 1 = E - 1 = O
if g is even then g^4 - g - 1 = E + E -1 = E - 1 = O
this is true for special cases such as g = -1, 0, 1
Manager
Joined: 23 Oct 2010
Posts: 89
Location: India
Followers: 3

Kudos [?]: 17 [0], given: 6

Re: m06 # 4 [#permalink]  15 Dec 2010, 06:48
sleekmover wrote:
A

Rephrase the question: is g^4 + g -1 odd or even? If we determine this then we can know for sure the value of the complete expression
S1: g is an integer -->
if g is odd then g^4 - g - 1= O + O - 1 = E - 1 = O
if g is even then g^4 - g - 1 = E + E -1 = E - 1 = O
this is true for special cases such as g = -1, 0, 1

Well I got excited and arrived at the answer too early. Obviously S2 also provides the answer as it says g is Even (a possibility that is considered already in explanation of S1)
(Though this is kind of wierd question in which one solution is a subset of information provided the first solution)

Correct ans: D
Manager
Status: Trying to get into the illustrious 700 club!
Joined: 18 Oct 2010
Posts: 81
Followers: 1

Kudos [?]: 18 [1] , given: 58

Re: m06 # 4 [#permalink]  15 Dec 2010, 09:19
1
KUDOS
ugimba wrote:
What is the value of (-1)^{g^4 + g - 1} ?

1. g is an integer
2. g is even

* Statement (1) ALONE is sufficient, but Statement (2) ALONE is not sufficient
* Statement (2) ALONE is sufficient, but Statement (1) ALONE is not sufficient
* BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient
* EACH statement ALONE is sufficient
* Statements (1) and (2) TOGETHER are NOT sufficient

[Reveal] Spoiler: OA
D

Source: GMAT Club Tests - hardest GMAT questions

shouldn't we consider negative values for option 1? ( 'g' is integer)? in this case, then A wont fit right?

I actually got the concept tested on this question but didn't bother to test the variable G in statement 1) so I got it wrong selecting B

First the concept is testing the special case of -1 as a base along with the exponent (even or odd). If the exponent is an even number then the answer will be 1, but if the exponent is an odd number the answer will be -1 (because a negative base will take the same sign if the exponent is odd..in addition this is a special case of 1 so the value won't change and will be -1)

Here is how I did it the 2nd time around.

I chose the integers 2 and 3.

-1^(2^4)+(2-1)
-1^(even)+(odd) <---even + odd = odd
so -1 will be raised to an odd power which will result in -1 as the answer

-1^(3^4)+(3-1)
-1^(odd)+(even) <-------odd + even = odd
so -1 will be raised to an odd power which will result in -1 as the answer

Statement 1) is sufficient

For statement 2 if g is even then any number raised to an even integer such as 4 will yield EVEN.

G-1 will equal ODD because an even - odd = odd

We take the result of even + odd and we get ODD for the exponent
-1^odd exponent will equal -1 SUFFICIENT
_________________

I'm trying to not just answer the problem but to explain how I came up with my answer. If I am incorrect or you have a better method please PM me your thoughts. Thanks!

Re: m06 # 4   [#permalink] 15 Dec 2010, 09:19
Similar topics Replies Last post
Similar
Topics:
If g is a the square of an integer, then what is the value 3 20 Sep 2006, 14:53
What is the value of (-1)^{g^4 + g - 1} ? 1. g is an integer 4 17 Jan 2008, 23:34
2 What is the value of (-1)^{g^4 + g - 1} ? 1. g is an 26 21 Dec 2008, 08:55
If f(g(3))=12, what is f(g(4))? 1) g(x) = 2x + 2 2) f(g(5)) 3 20 Jun 2011, 19:58
1 If f(x) = x^3 + 1, and g(x) = 2x, for what value of x does 3 10 Jul 2013, 11:52
Display posts from previous: Sort by

# What is the value of (-1)^{g^4 + g - 1} ? 1. g is an

 Go to page    1   2    Next  [ 27 posts ]

Moderator: Bunuel

 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®.