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!
GMAT Prep Exam 1- Factor
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Since the answer choices are so spread out, we can be quite aggressive with out estimation.The value of (10� - 10²)/(10� - 10³) is closest to which of the following?
a)1
b)10
C)10²
d)10³
e)10�
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
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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.
GMAT assassins aren't born, they're made,
Rich
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.
GMAT assassins aren't born, they're made,
Rich
- OptimusPrep
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If we go by what you have done,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!
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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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.
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.