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GMAT Prep Exam 1- Factor

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by nsuen » Sun Jun 12, 2016 6:05 am
Hi-

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

my thinking process

Factor out 10^2( 10^6-1)/ ( 10^3( 10^4-1) -> 1(10^6-1)/10^1(10^4-1). I tried to think of different way to factor but still couldn't get the answer 10. Thanks!
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by Brent@GMATPrepNow » Sun Jun 12, 2016 6:32 am
The value of (10� - 10²)/(10� - 10³) is closest to which of the following?

a)1
b)10
C)10²
d)10³
e)10�
Since the answer choices are so spread out, we can be quite aggressive with out estimation.

First, 10� - 10² can be rounded to 10�

Is this reasonable? Well, 10� equals 100,000,000, so subtracting 10² (aka 100) from 100,000,000 still leaves us with about 100,000,000

Similarly, 10� - 10³ can be rounded to 10� (10,000,000 - 1000 is pretty close to 10,000,000)

So, by estimating, we get:
(10� - 10²)/(10� - 10³) ≈ (10�)/(10�) = 10¹ = 10 = B
Brent Hanneson - Creator of GMATPrepNow.com
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by [email protected] » Sun Jun 12, 2016 10:21 am
Hi nsuen,

Instead of factoring, consider how 10^8 compares to (10^8 - 10^2)....

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

Difference = 99,999,900

Since we're asked which of the answers is CLOSEST to the exact calculation, the prompt is essentially telling us to estimate the result. As far as this question is concerned, 100,000,000 is essentially the same as 99,999,900. Now, think about the denominator in the same terms... and you'll be just a couple of steps away from the correct answer.

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by OptimusPrep » Wed Jun 15, 2016 8:09 pm
nsuen wrote:Hi-

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

my thinking process

Factor out 10^2( 10^6-1)/ ( 10^3( 10^4-1) -> 1(10^6-1)/10^1(10^4-1). I tried to think of different way to factor but still couldn't get the answer 10. Thanks!
If we go by what you have done,

1(10^6-1)/10^1(10^4-1) can be written as (1/10)*10^6/10^4
Since subtracting 1 from 10^4 and 10^6 and then dividing the two will not change anything,

Now, (1/10)*10^6/10^4 = 1/10*100 = 10
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by Matt@VeritasPrep » Thu Jun 23, 2016 4:48 pm
If you think of the problem as

100,000,000 - 100
------------------
10,000,000 - 1000

it's easier to see that the subtract does almost nothing, so we still have

≈100,000,000
------------
≈10,000,000

or ≈10.
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