GMAT Question of the Day: Daily via email | Daily via Instagram New to GMAT Club? Watch this Video

It is currently 05 Apr 2020, 22:14

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.

Close

Request Expert Reply

Confirm Cancel

a is a nonzero integer. Is a^a greater than 1?

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:

Hide Tags

Find Similar Topics 
Retired Moderator
avatar
Joined: 29 Oct 2013
Posts: 247
Concentration: Finance
GPA: 3.7
WE: Corporate Finance (Retail Banking)
GMAT ToolKit User
a is a nonzero integer. Is a^a greater than 1?  [#permalink]

Show Tags

New post Updated on: 14 Aug 2014, 10:35
2
1
26
00:00
A
B
C
D
E

Difficulty:

  45% (medium)

Question Stats:

64% (01:25) correct 36% (01:17) wrong based on 507 sessions

HideShow timer Statistics

a is a nonzero integer. Is a^a greater than 1?

(1) a < -1
(2) a is even

_________________
Please contact me for super inexpensive quality private tutoring

My journey V46 and 750 -> http://gmatclub.com/forum/my-journey-to-46-on-verbal-750overall-171722.html#p1367876

Originally posted by NoHalfMeasures on 14 Aug 2014, 10:17.
Last edited by Bunuel on 14 Aug 2014, 10:35, edited 1 time in total.
Edited the question
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 62498
Re: a is a nonzero integer. Is a^a greater than 1?  [#permalink]

Show Tags

New post 14 Aug 2014, 10:45
2
1
a is a nonzero integer. Is a^a greater than 1?

(1) a < -1. So, a could be -2, -3, -4, ... If a is a negative even integer, then a^a will be a positive fraction less than 1 (for example, if a = -2, then a^a = (-2)^(-2) = 1/4) and if a is a negative odd integer, then a^a will be a negative fraction greater than -1 (for example, if a = -3, then a^a = (-3)^(-3) = -1/27). In any case the result is less than 1. Sufficient.

(2) a is even. If a = 2, then a^a = 4 > 1 but if a = -2, then a^a = 1/4 < 1. Not sufficient.

Answer: A.

Hope it's clear.
_________________
Manager
Manager
User avatar
Status: Kitchener
Joined: 03 Oct 2013
Posts: 86
Location: Canada
Concentration: Finance, Finance
GPA: 2.9
WE: Education (Education)
a is a nonzero integer. Is a^a greater than 1?  [#permalink]

Show Tags

New post 11 Feb 2015, 16:24
Bunuel wrote:
a is a nonzero integer. Is a^a greater than 1?

(1) a < -1. So, a could be -2, -3, -4, ... If a is a negative even integer, then a^a will be a positive fraction less than 1 (for example, if a = -2, then a^a = (-2)^(-2) = 1/4) and if a is a negative odd integer, then a^a will be a negative fraction greater than -1 (for example, if a = -3, then a^a = (-3)^(-3) = -1/27). In any case the result is less than 1. Sufficient.

(2) a is even. If a = 2, then a^a = 4 > 1 but if a = -2, then a^a = 1/4 < 1. Not sufficient.

Answer: A.

Hope it's clear.



Dear Bunuel, I think that (-2)^(-2) which is -1/2^2 should be negative fraction less than 1 and equal to = (- 1/4 )
EMPOWERgmat Instructor
User avatar
V
Status: GMAT Assassin/Co-Founder
Affiliations: EMPOWERgmat
Joined: 19 Dec 2014
Posts: 16361
Location: United States (CA)
GMAT 1: 800 Q51 V49
GRE 1: Q170 V170
Re: a is a nonzero integer. Is a^a greater than 1?  [#permalink]

Show Tags

New post 11 Feb 2015, 21:57
Hi 23a2012,

Unfortunately, that's NOT how the math "works"

When dealing with a negative exponent, you have to put the entire calculation "under" the 1.

With your example, we have (-2)^(-2). This can be rewritten as....

1/[(-2)^2] = 1/4

IF....we were dealing with (-3)^(-3) though, we'd have.....

1/[(-3)^3] = 1/-27 = -1/27

GMAT assassins aren't born, they're made,
Rich
_________________
Contact Rich at: Rich.C@empowergmat.com
Image


The Course Used By GMAT Club Moderators To Earn 750+

souvik101990 Score: 760 Q50 V42 ★★★★★
ENGRTOMBA2018 Score: 750 Q49 V44 ★★★★★
Manager
Manager
User avatar
Status: Kitchener
Joined: 03 Oct 2013
Posts: 86
Location: Canada
Concentration: Finance, Finance
GPA: 2.9
WE: Education (Education)
a is a nonzero integer. Is a^a greater than 1?  [#permalink]

Show Tags

New post 12 Feb 2015, 05:15
EMPOWERgmatRichC wrote:
Hi 23a2012,

Unfortunately, that's NOT how the math "works"

When dealing with a negative exponent, you have to put the entire calculation "under" the 1.

With your example, we have (-2)^(-2). This can be rewritten as....

1/[(-2)^2] = 1/4

IF....we were dealing with (-3)^(-3) though, we'd have.....

1/[(-3)^3] = 1/-27 = -1/27

GMAT assassins aren't born, they're made,
Rich

Ok, can you tell me how write -1/4 in the form a^a
Math Expert
avatar
V
Joined: 02 Aug 2009
Posts: 8311
Re: a is a nonzero integer. Is a^a greater than 1?  [#permalink]

Show Tags

New post 12 Feb 2015, 05:27
23a2012 wrote:
Bunuel wrote:
a is a nonzero integer. Is a^a greater than 1?

(1) a < -1. So, a could be -2, -3, -4, ... If a is a negative even integer, then a^a will be a positive fraction less than 1 (for example, if a = -2, then a^a = (-2)^(-2) = 1/4) and if a is a negative odd integer, then a^a will be a negative fraction greater than -1 (for example, if a = -3, then a^a = (-3)^(-3) = -1/27). In any case the result is less than 1. Sufficient.

(2) a is even. If a = 2, then a^a = 4 > 1 but if a = -2, then a^a = 1/4 < 1. Not sufficient.

Answer: A.

Hope it's clear.



Dear Bunuel, I think that (-2)^(-2) which is -1/2^2 should be negative fraction less than 1 and equal to = (- 1/4 )


hi ,
-2^-2= 1/(-2)^2=1/4....
_________________
EMPOWERgmat Instructor
User avatar
V
Status: GMAT Assassin/Co-Founder
Affiliations: EMPOWERgmat
Joined: 19 Dec 2014
Posts: 16361
Location: United States (CA)
GMAT 1: 800 Q51 V49
GRE 1: Q170 V170
Re: a is a nonzero integer. Is a^a greater than 1?  [#permalink]

Show Tags

New post 12 Feb 2015, 11:20
1
Hi 23a2012,

If you have an EVEN exponent, then you CANNOT have a negative outcome (unless the negative "sign" is "outside" of the exponent, and thus unaffected by the exponent).

eg
(2)^2 = 4
(2)^(-2) = 1/4

(-2)^(2) = 4
(-2)^-(2) = 1/4

(-1)[2^(-2)] = (-1)[1/4] = -1/4

GMAT assassins aren't born, they're made,
Rich
_________________
Contact Rich at: Rich.C@empowergmat.com
Image


The Course Used By GMAT Club Moderators To Earn 750+

souvik101990 Score: 760 Q50 V42 ★★★★★
ENGRTOMBA2018 Score: 750 Q49 V44 ★★★★★
GMAT Club Legend
GMAT Club Legend
User avatar
V
Joined: 11 Sep 2015
Posts: 4587
Location: Canada
GMAT 1: 770 Q49 V46
Re: a is a nonzero integer. Is a^a greater than 1?  [#permalink]

Show Tags

New post 18 Jan 2018, 06:28
Top Contributor
2
NoHalfMeasures wrote:
a is a nonzero integer. Is a^a greater than 1?

(1) a < -1
(2) a is even


Target question: Is a^a greater than 1?

Given: a is a nonzero integer.

Statement 1: a < -1
Let's start TESTING some values of a and see if we discover a PATTERN

a = -2. Here a^a = (-2)^(-2) = 1/(-2)^2 = 1/4
a = -3. Here a^a = (-3)^(-3) = 1/(-3)^3 = 1/(-27) = - 1/27
a = -4. Here a^a = (-4)^(-4) = 1/(-4)^4 = 1/256
a = -5. Here a^a = (-5)^(-5) = 1/(-5)^5 = 1/(some negative value) = something negative
a = -6. Here a^a = (-6)^(-6) = 1/(-6)^6 = 1/(some positive integer) = a positive fraction that's less than 1
a = -7. Here a^a = (-7)^(-7) = 1/(-7)^7 = 1/(some negative value) = something negative
.
.
.
As we can see, when a is a NEGATIVE EVEN number, a^a = some positive fraction that's LESS THAN 1
When a is a NEGATIVE ODD number, a^a = some negative value that's LESS THAN 1
So, in both possible cases, a^a is definitely LESS THAN 1
Since we can answer the target question with certainty, statement 1 is SUFFICIENT

Statement 2: a is even
We already saw in statement 1 that if a is a NEGATIVE EVEN integer, then a^a = some positive fraction that's LESS THAN 1
What if a is a POSITIVE EVEN integer?
Let's test some possible values:
a = 2. Here a^a = (2)^(2) = 4. Here, a^a is GREATER THAN 1
So, we'll stop right here.
Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT

Answer: A

Cheers,
Brent
_________________
Test confidently with gmatprepnow.com
Image
Intern
Intern
avatar
B
Joined: 01 May 2017
Posts: 33
Re: a is a nonzero integer. Is a^a greater than 1?  [#permalink]

Show Tags

New post 02 Jan 2019, 14:58
Bunuel wrote:
a is a nonzero integer. Is a^a greater than 1?

(1) a < -1. So, a could be -2, -3, -4, ... If a is a negative even integer, then a^a will be a positive fraction less than 1 (for example, if a = -2, then a^a = (-2)^(-2) = 1/4) and if a is a negative odd integer, then a^a will be a negative fraction greater than -1 (for example, if a = -3, then a^a = (-3)^(-3) = -1/27). In any case the result is less than 1. Sufficient.

(2) a is even. If a = 2, then a^a = 4 > 1 but if a = -2, then a^a = 1/4 < 1. Not sufficient.

Answer: A.

Hope it's clear.


Hi Bunuel, But the question is if a^a is greater than 1 (not less than 1).In such a case, don't we need both ST-1 and ST-2 to answer the question?
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 62498
Re: a is a nonzero integer. Is a^a greater than 1?  [#permalink]

Show Tags

New post 03 Jan 2019, 02:49
FANewJersey wrote:
Bunuel wrote:
a is a nonzero integer. Is a^a greater than 1?

(1) a < -1. So, a could be -2, -3, -4, ... If a is a negative even integer, then a^a will be a positive fraction less than 1 (for example, if a = -2, then a^a = (-2)^(-2) = 1/4) and if a is a negative odd integer, then a^a will be a negative fraction greater than -1 (for example, if a = -3, then a^a = (-3)^(-3) = -1/27). In any case the result is less than 1. Sufficient.

(2) a is even. If a = 2, then a^a = 4 > 1 but if a = -2, then a^a = 1/4 < 1. Not sufficient.

Answer: A.

Hope it's clear.


Hi Bunuel, But the question is if a^a is greater than 1 (not less than 1).In such a case, don't we need both ST-1 and ST-2 to answer the question?


The question asks: is a^a > 1.

From (1) we get that if a < -1, (if a is -2, -3, -4, ... ) a^a < 1. So, we have a definite NO answer to the question. Recall that a definite NO to an YES/NO DS questions is sufficient the same way as a definite YES is.
_________________
Non-Human User
User avatar
Joined: 09 Sep 2013
Posts: 14468
Re: a is a nonzero integer. Is a^a greater than 1?  [#permalink]

Show Tags

New post 07 Jan 2020, 06:34
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
Re: a is a nonzero integer. Is a^a greater than 1?   [#permalink] 07 Jan 2020, 06:34
Display posts from previous: Sort by

a is a nonzero integer. Is a^a greater than 1?

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  





Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne