NEW HERE? LEARN MORE
closeclose
Last visit was: 16 May 2024, 11:05 It is currently 16 May 2024, 11:05
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

The value of (2/3)^99 is closest to which of the following?

SORT BY:
Date
Kudos
Tags:
Find Similar Topics 
Show Tags
Hide Tags
User avatar
G
yrozenblum
Intern
Intern
Joined: 29 Mar 2020
Posts: 27
Own Kudos [?]: 419 [17]
Given Kudos: 23
Send PM
The value of (2/3)^99 is closest to which of the following? [#permalink] New post   29 Oct 2023, 10:38
17
Bookmarks
00:00
A
B
C
D
E

Difficulty:

45% (medium)

Question Stats:

64% (01:08) correct 36% (01:19) wrong based on 222 sessions
Hide Show timer Statistics
The value of \((\frac{-2}{3})^{99}\) is closest to which of the following?

A. \(-1\)
B. \(-\frac{1}{2}\)
C. \(0\)
D. \(\frac{1}{2}\)
E. \(1\)­


Show Spoiler
ShowHide Answer
Official Answer
C
User avatar
L
KarishmaB
Tutor
Joined: 16 Oct 2010
Posts: 14892
Own Kudos [?]: 65315 [4]
Given Kudos: 431
Location: Pune, India
Send PM
Forum Quiz Mode
Re: The value of (2/3)^99 is closest to which of the following? [#permalink] New post   24 Feb 2024, 08:46
4
Kudos
Expert Reply
 
yrozenblum wrote:
The value of \((\frac{-2}{3})^{99}\) is closest to which of the following?

A. \(-1\)
B. \(-\frac{1}{2}\)
C. \(0\)
D. \(\frac{1}{2}\)
E. \(1\)


 


Looks like a good candidate for estimation. 

\((\frac{-2}{3})^{99} = (-0.6)^{99}\)

Now note: 0.6*0.6 = 0.36 
0.36*0.6 = 0.216

As we take higher powers of (0.6), the absolute value of the result is reducing. So (0.6)^99 will be a very small number like 0.00...001..
So (-0.6)^99 will simply be - 0.00...001... something that is very close to 0 on the left side of the number line. 
It will certainly be much farther away from 1 or 1/2 or any other such values on the number line. 

Answer (C)
Here is a video on Estimation: https://youtu.be/4Wy7BrQrjkM



­­­
User avatar
L
gmatophobia
Quant Chat Moderator
Joined: 22 Dec 2016
Posts: 3130
Own Kudos [?]: 4386 [3]
Given Kudos: 1854
Location: India
Concentration: Strategy, Leadership
Send PM
CAT Tests Forum Quiz Mode
Re: The value of (2/3)^99 is closest to which of the following? [#permalink] New post   29 Oct 2023, 12:00
2
Kudos
1
Bookmarks
yrozenblum wrote:
The value of \((\frac{-2}{3})^{99}\) is closest to which of the following?

A. \(-1\)
B. \(-\frac{1}{2}\)
C. \(0\)
D. \(\frac{1}{2}\)
E. \(1\)



\((\frac{-2}{3})^{99}\) = \((-0.XX)^{99}\)

\((-0.XX)^{99}\) indicates that we are multiplying (-0.XX) 99 times, hence the value will be very close to zero.

Option C
User avatar
D
sayan640
Director
Director
Joined: 29 Oct 2015
Posts: 691
Own Kudos [?]: 325 [0]
Given Kudos: 452
Send PM
Reviews Badge CAT Tests Forum Quiz Mode
Re: The value of (2/3)^99 is closest to which of the following? [#permalink] New post   23 Feb 2024, 03:20
gmatophobia wrote:
yrozenblum wrote:
The value of \((\frac{-2}{3})^{99}\) is closest to which of the following?

A. \(-1\)
B. \(-\frac{1}{2}\)
C. \(0\)
D. \(\frac{1}{2}\)
E. \(1\)



\((\frac{-2}{3})^{99}\) = \((-0.XX)^{99}\)

\((-0.XX)^{99}\) indicates that we are multiplying (-0.XX) 99 times, hence the value will be very close to zero.

Option C

­Could you please elaborate on your answer ?
User avatar
D
sayan640
Director
Director
Joined: 29 Oct 2015
Posts: 691
Own Kudos [?]: 325 [0]
Given Kudos: 452
Send PM
Reviews Badge CAT Tests Forum Quiz Mode
Re: The value of (2/3)^99 is closest to which of the following? [#permalink] New post   23 Feb 2024, 03:22
yrozenblum wrote:
The value of \((\frac{-2}{3})^{99}\) is closest to which of the following?

A. \(-1\)
B. \(-\frac{1}{2}\)
C. \(0\)
D. \(\frac{1}{2}\)
E. \(1\)

­KarishmaB , Could you please provide your explanation for this one ?
User avatar
B
Yeetyeti38
Intern
Intern
Joined: 16 May 2023
Posts: 13
Own Kudos [?]: 3 [0]
Given Kudos: 3
Send PM
Re: The value of (2/3)^99 is closest to which of the following? [#permalink] New post   23 Feb 2024, 07:31
If you square the fraction just once it is already below half; if you raise to the power of 4 you have 16/81, which is already closer 0 than it is to 1/2. So you can infer that doing so 99 times will be closer to 0 than any other number.
GMAT Club Bot
gmatclubot
Re: The value of (2/3)^99 is closest to which of the following? [#permalink]
23 Feb 2024, 07:31
Moderators:
Bunuel
Math Expert
93312 posts
yashikaaggarwal
Senior Moderator - Masters Forum
3136 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