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Closest value problem

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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
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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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by LFalken » Tue Aug 25, 2009 11:17 am
Perfect, Thank you!
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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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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
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