Closest value problem

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LFalken: Senior | Next Rank: 100 Posts; Posts: 44; Joined: Wed May 13, 2009 5:40 am; Location: MN; Thanked: 1 times; GMAT Score:580

by LFalken » Tue Aug 25, 2009 10:48 am

Looking for a quick and efficient way to do this problem, during my gmat prep I did it long hand (sort of ) to get the right answer and it took way to long. What is the best way to go about this one? If anyone could shed some light that would be great. Thanks!

The value of (10^8-10^2)/(10^7-10^3) is closest to which of the following?

a)1
b)10 (correct answer)
C)10^2
d)10^3
e)10^4

LFAL

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Source: Beat The GMAT — Problem Solving | Tue Aug 25, 2009 10:48 am

shanrizvi: Senior | Next Rank: 100 Posts; Posts: 73; Joined: Tue Aug 11, 2009 2:30 am; Thanked: 2 times; GMAT Score:720

by shanrizvi » Tue Aug 25, 2009 11:03 am

Well, just simply the equation.

Question: (10^8-10^2) / (10^7-10^3)

10^2[(10^6)-1] / 10^3[(10^4)-1]

[(10^6)-1] / 10^(3-2).[(10^4)-1]

[(10^6)-1] / 10.[(10^4)-1]

[(10^6)-1] / [(10^5)-10]

When numbers are as big as 1,000,000 and 1,00,000, addition/subtraction of 1 or 10 won't make that much of a difference. As you only have to estimate the value, ignore the -1 and -10.

10^6/10^5 = 10

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LFalken: Senior | Next Rank: 100 Posts; Posts: 44; Joined: Wed May 13, 2009 5:40 am; Location: MN; Thanked: 1 times; GMAT Score:580

by LFalken » Tue Aug 25, 2009 11:17 am

Perfect, Thank you!

LFAL

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luiscarlos59: Senior | Next Rank: 100 Posts; Posts: 61; Joined: Sun Mar 13, 2011 12:34 pm; Thanked: 1 times

by luiscarlos59 » Sun Apr 17, 2011 2:20 pm

Another solution:

10^2 (10^6-1) / 10^3(10^4-1)

10^8 / 10^7 = 10^(8-7) = 10^1

Ans 10.

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Brent@GMATPrepNow: 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 » Sun Apr 17, 2011 3:29 pm

LFalken wrote:Looking for a quick and efficient way to do this problem, during my gmat prep I did it long hand (sort of ) to get the right answer and it took way to long. What is the best way to go about this one? If anyone could shed some light that would be great. Thanks!

The value of (10^8-10^2)/(10^7-10^3) is closest to which of the following?
a)1
b)10 (correct answer)
C)10^2
d)10^3
e)10^4

Since the answer choices are so spread out, we can be quite aggressive with out estimation.

First, 10^8 - 10^2 can be rounded to 10^8

Is this reasonable? Well, 10^8 equals 100,000,000, so subtracting 10^2 (aka 100) from 100,000,000 still leaves us with about 100,000,000

Similarly, 10^7 - 10^3 can be rounded to 10^7 (10,000,000 - 1000 is pretty close to 10,000,000)

So, by estimating, we get:
(10^8 - 10^2)/(10^7 - 10^3) = (10^8)/(10^7) = 10^1 = 10

Brent Hanneson - Creator of GMATPrepNow.com

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