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 →

4+2^2+2^3+2^4+2^5+2^6+2^7=

Expert replies
Post new topic Post Reply
Previous Topic Next Topic
Source: — Problem Solving |

GMAT/MBA Expert

User avatar
GMAT Instructor
Posts: 16207
Joined: Mon Dec 08, 2008 6:26 pmFollowed by: 1268 members
Location: Vancouver, BC
Thanked: 5254 times
GMAT Score:770

by Brent@GMATPrepNow » Fri Sep 29, 2017 7:29 pm
Vincen wrote:4+2^2+2^3+2^4+2^5+2^6+2^7=

A) 2^7
B) 2^8
C) 2^16
D) 2^28
E) 2^29
Let's look for a pattern...

We want: 4 + 2^2 + 2^3 + 2^4 + 2^5 + 2^6 + 2^7 = ?

4 + 2^2 = 4 + 4 = 8 = 2^3
So, 4 + 2^2 + 2^3 + 2^4 + 2^5 + 2^6 + 2^7 = 2^3 + 2^3 + 2^4 + 2^5 + 2^6 + 2^7

2^3 + 2^3 = 2(2^3) = 2^4
So, 2^3 + 2^3 + 2^4 + 2^5 + 2^6 + 2^7 = 2^4 + 2^4 + 2^5 + 2^6 + 2^7

2^4 + 2^4 = 2(2^4) = 2^5
So, 2^4 + 2^4 + 2^5 + 2^6 + 2^7 = 2^5 + 2^5 + 2^6 + 2^7

Continuing the pattern, we get: 4 + 2^2 + 2^3 + 2^4 + 2^5 + 2^6 + 2^7 = 2^8

Answer: B

Cheers,
Brent
Brent Hanneson - Creator of GMATPrepNow.com
Image
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY

GMAT/MBA Expert

User avatar
Elite Legendary Member
Posts: 10392
Joined: Sun Jun 23, 2013 6:38 pmFollowed by: 511 members
Location: Palo Alto, CA
Thanked: 2867 times
GMAT Score:800

by [email protected] » Sat Sep 30, 2017 3:52 pm
Hi Vincen,

With a little math and a bit of logic, you can get to the correct answer here without too much trouble. To start, you have to recognize what it really means to raise 2 to higher and higher exponents. With each increase of 1 to the exponent, the total DOUBLES.

2^1 = 2
2^2 = 4
2^3 = 8
2^4 = 16
2^5 = 32
Etc.

Thus, at higher and higher exponents, the numbers are NOT close together. From the sum of terms given to us, we can see that the largest term will be 2^7 and (when we word 'down' the list) we're adding smaller and smaller numbers to it. Clearly the sum will be GREATER than 2^7, but not that much greater (relatively speaking). Looking at the answer choices, there's only one option that makes sense...

Final Answer: B

GMAT assassins aren't born, they're made,
Rich
Contact Rich at [email protected]
Image
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
User avatar
GMAT Instructor
Posts: 555
Joined: Wed Oct 04, 2017 4:18 pmFollowed by: 12 members
Thanked: 180 times

by EconomistGMATTutor » Tue Oct 10, 2017 1:20 pm
Vincen wrote:4+2^2+2^3+2^4+2^5+2^6+2^7=

A) 2^7
B) 2^8
C) 2^16
D) 2^28
E) 2^29

The OA is B.

Is there any way to make this PS question without using a calculator?
Hi Vincen,
Let's take a look at your question.

4+2^2+2^3+2^4+2^5+2^6+2^7
We can write the first term of the sum 4 as 2^2,
=(2^2+2^2)+2^3+2^4+2^5+2^6+2^7
= 2(2^2)+2^3+2^4+2^5+2^6+2^7

We know that 2(2^2) = 2^3, so
= (2^3+2^3)+2^4+2^5+2^6+2^7

Add 2^3 + 2^3 = 2(2^3)
= 2(2^3) + 2^4+2^5+2^6+2^7
= 2^4 + 2^4+2^5+2^6+2^7

Add 2^4 + 2^4 = 2(2^4)
= 2(2^4) +2^5+2^6+2^7
=( 2^5 + 2^5)+2^6+2^7

Add 2^5 + 2^5 = 2(2^5)
= 2(2^5) + 2^6+2^7
=( 2^6+2^6)+2^7

Add 2^6 + 2^6 = 2(2^6)
= 2(2^6)+2^7
= 2^7+2^7
= 2(2^7)
= 2^8

Therefore, Option B is correct.

I am available if you'd like any follow up.
GMAT Prep From The Economist
We offer 70+ point score improvement money back guarantee.
Our average student improves 98 points.

Image
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY

GMAT/MBA Expert

User avatar
GMAT Instructor
Posts: 8149
Joined: Sat Apr 25, 2015 10:56 amFollowed by: 29 members
Location: Los Angeles, CA
Thanked: 43 times

Re: 4+2^2+2^3+2^4+2^5+2^6+2^7=

by Scott@TargetTestPrep » Sun Feb 02, 2020 10:09 am
Vincen wrote: ↑
Fri Sep 29, 2017 6:37 pm
 4+2^2+2^3+2^4+2^5+2^6+2^7=

A) 2^7
B) 2^8
C) 2^16
D) 2^28
E) 2^29

The OA is B.

Is there any way to make this PS question without using a calculator?
We can use the rule that 2^n + 2^n = 2^(n+1).

Starting with the first two terms, we have:

2^2 + 2^2 = 2^3

Then we have:

2^3 + 2^3 = 2^4

If we continue this pattern, we end with:

2^7 + 2^7 = 2^8.

Answer: B

Scott Woodbury-Stewart
Founder and CEO
[email protected]

Image

See why Target Test Prep is rated 5 out of 5 stars on BEAT the GMAT. Read our reviews

ImageImage
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
Post new topic Post Reply
• Page 1 of 1