NEW HERE? LEARN MORE
closeclose
Last visit was: 26 Apr 2024, 01:40 It is currently 26 Apr 2024, 01:40
Decision Tracker
My Rewards
New posts
New comers' posts

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.
Go to My Error Log Learn more
Close
Request Expert Reply
Confirm Cancel

If n is not 0, for how many integers is |n|^n = n * n

SORT BY:
Date
Kudos
Tags:
Find Similar Topics 
Show Tags
Hide Tags
User avatar
D
Hoozan
Director
Director
Joined: 28 Sep 2018
Posts: 734
Own Kudos [?]: 559 [16]
Given Kudos: 248
GMAT 1: 660 Q48 V33 (Online)
GMAT 2: 700 Q49 V37
Send PM
Reviews Badge
If n is not 0, for how many integers is |n|^n = n * n [#permalink] New post   14 Feb 2021, 00:46
2
Kudos
14
Bookmarks
00:00
A
B
C
D
E

Difficulty:

55% (hard)

Question Stats:

49% (01:17) correct 51% (01:16) wrong based on 339 sessions
Hide Show timer Statistics
If n is not 0, for how many integers is \(|n|^n = n * n\)

(A) 0
(B) 1
(C) 2
(D) 3
(E) more than 3

Similar Question: https://gmatclub.com/forum/for-how-many ... 26963.html
ShowHide Answer
Official Answer
D
User avatar
L
chetan2u
RC & DI Moderator
Joined: 02 Aug 2009
Status:Math and DI Expert
Posts: 11178
Own Kudos [?]: 31935 [2]
Given Kudos: 290
Send PM
Reviews Badge
Re: If n is not 0, for how many integers is |n|^n = n * n [#permalink] New post   14 Feb 2021, 09:00
2
Bookmarks
Expert Reply
Hoozan wrote:
If n is not 0, for how many integers is \(|n|^n = n * n\)

(A) 0
(B) 1
(C) 2
(D) 3
(E) more than 3

Similar Question: https://gmatclub.com/forum/for-how-many ... 26963.html


\(|n|^n = n * n\)
\(|n|^n = n ^2\)
Surely one value is when n=2.
The other values are possible when both sides are 1, and n^2=1, when n is 2 or -2
So three values :
1) 1 : \(|1|^1=1^2......1=1\)
2) -1 : \(|-1|^{-1}=(-1)^2......1=1\)
3) 2 : \(|2|^2=2^2......4=4\)

D
User avatar
D
philipssonicare
Senior Manager
Senior Manager
Joined: 15 Feb 2018
Posts: 424
Own Kudos [?]: 385 [0]
Given Kudos: 2380
Send PM
Re: If n is not 0, for how many integers is |n|^n = n * n [#permalink] New post   01 Mar 2021, 19:18
Incase you're an idiot like me and forgot to note that n≠0

\(0^2=0\)
\(0^0\) is undefined.

So it can't work anyway
avatar
B
zamis
Intern
Intern
Joined: 14 Oct 2020
Posts: 4
Own Kudos [?]: 3 [3]
Given Kudos: 78
Send PM
Re: If n is not 0, for how many integers is |n|^n = n * n [#permalink] New post   05 Mar 2021, 02:32
3
Kudos
In case someone dumb like me, who initially didn't understand, why not -2 other than 1, -1 & 2

|-2|^-2=-2*-2
=> 1/4#4
User avatar
D
BrushMyQuant
Tutor
Joined: 05 Apr 2011
Status:Tutor - BrushMyQuant
Posts: 1777
Own Kudos [?]: 2094 [1]
Given Kudos: 100
Location: India
Concentration: Finance, Marketing
Schools: XLRI (A)
GMAT 1: 700 Q51 V31
GPA: 3
WE:Information Technology (Computer Software)
Send PM
Re: If n is not 0, for how many integers is |n|^n = n * n [#permalink] New post   08 Jul 2023, 06:52
1
Kudos
Expert Reply
Top Contributor
Given that n is not 0 and we need to find for how many integers is \(|n|^n = n*n\)

We can solve this by Substitution

\(|n|^n = n*n\) = \(n^2\)

Definitely 1 and 2 are two possible choices



Case n = 1 or n = 2
-n = 1
=> \(|1|^1 = 1^2\)
=> 1 = 1
=> n = 1 is SOLUTION		-n = 2
=> \(|2|^2 = 2^2\)
=> 4 = 4
=> n = 2 is SOLUTION


As we have Absolute value on left side and square on right side so let's try with -1 and -2 also



Case n = -1 or n = -2
-n = -1
=> \(|-1|^{-1} = (-1)^2\)
=> 1 = 1
=> n = -1 is SOLUTION		-n = -2
=> \(|-2|^{-2} = (-2)^2\)
=> \(1/4\) ≠ 4
=> n = -1 is NOT a SOLUTION


Now, there will be no other integer for which we will have \(|n|^n = n^2\)
As, n raised to its own power will always be greater or smaller than n to the power of 2

So, Answer will be D
Hope it helps!

Watch the following video to learn the Basics of Absolute Values

GMAT Club Bot
gmatclubot
Re: If n is not 0, for how many integers is |n|^n = n * n [#permalink]
08 Jul 2023, 06:52
Moderators:
Bunuel
Math Expert
92921 posts
yashikaaggarwal
Senior Moderator - Masters Forum
3137 posts

Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne
Main navigation
GMAT Resources
Partners
MBA Resources
www.gmac.com|www.mba.com | | GMAT Club Rules | Terms and Conditions