is closest to which of the following?

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b.gowthamkumar: Newbie | Next Rank: 10 Posts; Posts: 8; Joined: Fri Aug 13, 2010 7:58 am; Thanked: 2 times

by b.gowthamkumar » Mon Sep 13, 2010 10:37 am

Maybe silly, but can anyone let me how this is derived?

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Source: Beat The GMAT — Problem Solving | Mon Sep 13, 2010 10:37 am

Gurpinder: Legendary Member; Posts: 659; Joined: Mon Dec 14, 2009 8:12 amFollowed by: 3 members; Thanked: 32 times

by Gurpinder » Mon Sep 13, 2010 10:51 am

.......opps

Last edited by Gurpinder on Mon Sep 13, 2010 10:58 am, edited 1 time in total.

"Do not confuse motion and progress. A rocking horse keeps moving but does not make any progress."
- Alfred A. Montapert, Philosopher.

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Brian@VeritasPrep: GMAT Instructor; Posts: 1031; Joined: Thu Jul 03, 2008 1:23 pmFollowed by: 255 members; Location: Malibu, CA; Thanked: 716 times; GMAT Score:750

by Brian@VeritasPrep » Mon Sep 13, 2010 10:57 am

Whoa - careful!

10^8 - 10^2 is NOT 10^6. It's actually almost exactly 10^8. If you expand them you'll see:

10^8 = 100,000,000
10^2 = 100

If you subtract the two, you're not subtracting very much at all. The same goes for 10^7 - 10^3 which is NOT 10^4

10^7 = 10,000,000
10^4 = 1,000

Again, if you subtract the two, you don't end up very far at all from 10^7.

So....

For this one you can simply estimate, given the knowledge that the magnitude of the larger exponents renders the smaller ones insignificant (the answer choices all differ by a factor of 10), and get:

10^8 / 10^7 = 10

OR, you can factor the numerator and denominator to get even closer to a quick estimate:

10^8 - 10^2 = 10^2 * (10^6 - 1)
10^7 - 10^3 = 10^3 * (10^4 - 1)

Then divide those two. 10^2 / 10^ 3 gives you 1/10
And (10^6 - 1) / (10^4 - 1) is a pretty easy estimate to 10^2.

So with 10^2 / 10 you'd get to 10.

The biggest key here is to recognize the order of magnitude for exponents. 10^8 and 10^7 are so large that 10^2 and 10^3 really don't matter at all in comparison.

Brian Galvin
GMAT Instructor
Chief Academic Officer
Veritas Prep

Looking for GMAT practice questions? Try out the Veritas Prep Question Bank. Learn More.

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b.gowthamkumar: Newbie | Next Rank: 10 Posts; Posts: 8; Joined: Fri Aug 13, 2010 7:58 am; Thanked: 2 times

by b.gowthamkumar » Tue Sep 14, 2010 1:21 am

Hi Brian,

Thanks for that. I answered it right, but just wanted to confirm.
Thanks again.

Gowtham.

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