Exponent pls help

This topic has expert replies
Newbie | Next Rank: 10 Posts
Posts: 3
Joined: Wed Aug 27, 2008 8:35 am

Exponent pls help

by ramandeepn » Fri Apr 10, 2009 8:19 am
Please tell me how to solve this question from GMAT PREP

2+2+2^2+2^3+2^4+2^5+2^6+2^7+2^8

Ans:2^9

User avatar
Community Manager
Posts: 1049
Joined: Sun Apr 06, 2008 5:15 pm
Location: Pittsburgh, PA
Thanked: 113 times
Followed by:27 members
GMAT Score:710

by dmateer25 » Fri Apr 10, 2009 8:30 am
2+2+2^2+2^3+2^4+2^5+2^6+2^7+2^8

2(2+2+2^2+2^3+2^4+2^5+2^6+2^7)
2^2(2+2+2^2+2^3+2^4+2^5+2^6)
2^3(2+2+2^2+2^3+2^4+2^5)
2^4(2+2+2^2+2^3+2^4)
2^5(2+2+2^2+2^3)
2^6(2+2+2^2)
2^7(2 + 2)
2^8(2)
2^9

Newbie | Next Rank: 10 Posts
Posts: 6
Joined: Fri Apr 10, 2009 9:38 am
Thanked: 1 times

by milqman » Fri Apr 10, 2009 10:37 am
That solution is actually not quite right.

There is an error in the first line of work shown (pulling a 2 out would not leave you with 2's on the inside like that).

Later on the 2^8 line: 2^7*(2+2) does not equal 2^8

I think the easiest way to do this is to evaluate the first handful, then factor out of the remainder and evaluate again.

2+2+2^2+2^3+2^4+2^5+2^6+2^7+2^8

2+2+4+8+16 + (2^4*(2+2^2+2^3+2^4))

32 + (16*(30))

32 + 480

512

2^9

Does that make sense?

Newbie | Next Rank: 10 Posts
Posts: 3
Joined: Wed Aug 27, 2008 8:35 am

by ramandeepn » Fri Apr 10, 2009 10:44 am
Thank you so much. Now i understand it... :)

Master | Next Rank: 500 Posts
Posts: 353
Joined: Sat Jan 20, 2007 1:29 am
Location: Italy
Thanked: 7 times
GMAT Score:720

by mjjking » Fri Apr 10, 2009 10:44 am
There are many ways to reach the solution, but I agree that grouping them and multiplying is the easiest one.
Beat The GMAT - 1st priority
Enter a top MBA program - 2nd priority
Loving my wife: MOST IMPORTANT OF ALL!

REAL THING 1 (AUG 2007): 680 (Q43, V40)
REAL THING 2 (APR 2009): 720 (Q47, V41)

Legendary Member
Posts: 1578
Joined: Sun Dec 28, 2008 1:49 am
Thanked: 82 times
Followed by:9 members
GMAT Score:720

by maihuna » Fri Apr 10, 2009 11:07 am
the first time when i saw this question in my test itself I was kind of taken by surprise...but in a moment i found this pattern:

2+2 = 2^2
2^2 + 2^2 = 2^3
2^3 + 2^3= 2^4

r u able to see a pattern, previous two terms equate to next term in series...

that way the last two will be : 2^8 + 2^8 = 2^9

User avatar
Community Manager
Posts: 1049
Joined: Sun Apr 06, 2008 5:15 pm
Location: Pittsburgh, PA
Thanked: 113 times
Followed by:27 members
GMAT Score:710

by dmateer25 » Fri Apr 10, 2009 1:45 pm
milqman wrote:That solution is actually not quite right.

Later on the 2^8 line: 2^7*(2+2) does not equal 2^8


2^7 *(4) = 2^8 *(2)

I just showed it as 2^7 *(2+2)

Pulling out the 2 leaves you with 2^8 * (1+1) = 2^8 * (2)