BREAKING: Target Test Prep releases Brand New 2026 On Demand GMAT prep course

Redeem
TTP OnDemand GMAT Video Course
Featured Course

Target Test Prep GMAT OnDemand

Scott Woodbury-Stewart’s private virtual classroom — 400 hours of master-class video lessons for the GMAT Focus Edition.

  • 715+ score guarantee — highest in the industry (99th percentile)
  • 52 chapters · 1,500+ lessons · 4,000+ practice questions
  • 400 hours of video · 1,500+ instructor-led HD smartboard lessons
  • 300,000+ students accepted to Harvard, Stanford, Wharton, Booth & Sloan & more
  • 24/7 live support + weekly Zoom office hours with GMAT instructors
  • TTP AI Assist — 24/7 AI-powered virtual tutor for instant help
  • 1,200+ flashcards + AI-powered study assistant & daily calendar
  • OnDemand, LiveTeach & GMAT Bootcamp formats available
  • Also: GRE, SAT Math & Executive Assessment courses
  • MBA Admissions Consulting now available
  • 🏆 2025 EdTech Breakthrough Award: Test Prep Solution Provider of the Year
  • 200,000+ students served
  • 5-day free trial — $0 to start, no auto-billing, cancel anytime
★★★★★ 5.0 (559 reviews)
130-pt guarantee
$0 to start then $127/mo
Start Free 5-Day Trial Read 559 Reviews →

simplification

Expert replies
Post new topic Post Reply
Previous Topic Next Topic
Source: — Problem Solving |
Master | Next Rank: 500 Posts
Posts: 118
Joined: Mon May 21, 2012 10:07 pmFollowed by: 4 members
Thanked: 23 times

by das.ashmita » Sun Oct 07, 2012 12:14 pm
Hi Pritam


4^4x = 1600
4^2x = root(1600) = 40.... (1)

We need to find 4^(x-1)2 = (4^2x)/ (4^2)
Substituting (1), we get
= 40/16 = 2.5

ANS 2.5
Last edited by das.ashmita on Sun Oct 07, 2012 9:55 pm, edited 4 times in total.
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
Master | Next Rank: 500 Posts
Posts: 118
Joined: Mon May 21, 2012 10:07 pmFollowed by: 4 members
Thanked: 23 times

by das.ashmita » Sun Oct 07, 2012 12:15 pm
4^2x=|root(1600)| and how you get 400? 400^2=160000
and 4^(x-1)2 is meant to be 4^(x-1)^2 - We don't factor by 2 at the end of exponential expression
I have edited my post above. Root(1600) = 400 was a blunder on my part. :( . It should be 40.

Regarding expression "4^(x-1)2 ", it cannot possibly be "4^(x-1)^2" in this question as it would yield no result. :P

The proper interpretation is given below:
4^(x-1)2 = [4^(x-1)]^2 or 4^2(x-1)
Last edited by das.ashmita on Sun Oct 07, 2012 9:55 pm, edited 3 times in total.
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
Legendary Member
Posts: 1084
Joined: Fri Apr 15, 2011 2:33 pmFollowed by: 21 members
Thanked: 158 times

by pemdas » Sun Oct 07, 2012 1:11 pm
4^2x=|root(1600)| and how you get 400? 400^2=160000
and 4^(x-1)2 is meant to be 4^(x-1)^2 - We don't factor by 2 at the end of exponential expression :)
das.ashmita wrote:Hi Pritam


4^4x = 1600
4^2x = root(1600) = 400.... (1)

We need to find 4^(x-1)2 = (4^2x)/ (4^2)
Substituting (1), we get
= 400/16 = 25

ANS 25
Success doesn't come overnight!
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
Legendary Member
Posts: 1084
Joined: Fri Apr 15, 2011 2:33 pmFollowed by: 21 members
Thanked: 158 times

by pemdas » Sun Oct 07, 2012 1:39 pm
pritam.ryders wrote:If 4^4x = 1600 then what is the value of 4^(x-1)2 ?
the required is 4^(x-1)^2 along with 4^(x^2-2x+1) or (4^(x-1))^2 ??
I hope the latter is our needed condition, as with 4^(x-1)^2 we fall to the given 4^4x=1600, 4^2x=|40| and 4^2x=|4*10| and consider positive case first, 4^(2x-1)=10. From the above expression we have an exponent (x^2-2x+1) and we can rewrite 4^(2x-1)=10 as 4^(-2x+1)=1/10. So we have 1/10 * 4^(x^2) where 4^(x^2) is unknown.

If are given (4^(x-1))^2, then 4^(2x-2) is sought for solution. Since 4^(2x-1)=10, 4^(2x-2)=10/4=2.5
Success doesn't come overnight!
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
User avatar
GMAT Instructor
Posts: 15539
Joined: Tue May 25, 2010 12:04 pmFollowed by: 1906 members
Location: New York, NY
Thanked: 13060 times
GMAT Score:790

by GMATGuruNY » Sun Oct 07, 2012 2:57 pm
pritam.ryders wrote:If 4^4x = 1600, then what is the value of (4^(x-1))² ?

40
20
10
5/2
5/4
Rephrase (4^(x-1))² into a form resembling 4^4x:
(4^(x-1))²

= 4^(2x-2)

= (4^2x)/4²

= (4^2x)/16.

Use 4^4x = 1600 to determine the value of 4^2x:
4^2x = (4^4x)^(½) = 1600^(½) = 40.

Substitute 4^2x = 40 into (4^2x)/16:
(4^2x)/16 = 40/16 = 5/2.

The correct answer is D.
Last edited by GMATGuruNY on Mon Oct 08, 2012 2:51 am, edited 1 time in total.
Private tutor exclusively for the GMAT and GRE, with over 20 years of experience.
Followed here and elsewhere by over 1900 test-takers.
I have worked with students based in the US, Australia, Taiwan, China, Tajikistan, Kuwait, Saudi Arabia -- a long list of countries.
My students have been admitted to HBS, CBS, Tuck, Yale, Stern, Fuqua -- a long list of top programs.

As a tutor, I don't simply teach you how I would approach problems.
I unlock the best way for YOU to solve problems.

For more information, please email me (Mitch Hunt) at [email protected].
Student Review #1
Student Review #2
Student Review #3
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
Legendary Member
Posts: 1084
Joined: Fri Apr 15, 2011 2:33 pmFollowed by: 21 members
Thanked: 158 times

by pemdas » Mon Oct 08, 2012 12:33 am
But Mitch with your notation, 4^(x-1)^2 falls into 4^(x^2-2x+1)

should not this be (4^(x-1))^2 by squaring the entire expression?
Success doesn't come overnight!
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
User avatar
GMAT Instructor
Posts: 15539
Joined: Tue May 25, 2010 12:04 pmFollowed by: 1906 members
Location: New York, NY
Thanked: 13060 times
GMAT Score:790

by GMATGuruNY » Mon Oct 08, 2012 2:57 am
pemdas wrote: Should not this be (4^(x-1))^2 by squaring the entire expression?
Yes, indeed. The problem asks for the value of (4^(x-1))². I've corrected the notation in my post above.
Private tutor exclusively for the GMAT and GRE, with over 20 years of experience.
Followed here and elsewhere by over 1900 test-takers.
I have worked with students based in the US, Australia, Taiwan, China, Tajikistan, Kuwait, Saudi Arabia -- a long list of countries.
My students have been admitted to HBS, CBS, Tuck, Yale, Stern, Fuqua -- a long list of top programs.

As a tutor, I don't simply teach you how I would approach problems.
I unlock the best way for YOU to solve problems.

For more information, please email me (Mitch Hunt) at [email protected].
Student Review #1
Student Review #2
Student Review #3
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
Post new topic Post Reply
• Page 1 of 1