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Junior | Next Rank: 30 Posts
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by dunnec3 » Fri Dec 04, 2015 5:58 am
Help! Is there a quick way to solve (10^8 - 10^2)/(10^7 - 10^3) that I'm missing?
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by GMATGuruNY » Fri Dec 04, 2015 6:27 am
Please post the COMPLETE problem, ALONG WITH THE ANSWER CHOICES.
The value of (10�-10²)/(10�-10³) is closest to which of the following?

A. 1
B. 10
C. 10²
D. 10³
E. 10�
In the expression above, the values in blue are HUGE, while the values in red are RELATIVELY SMALL.
Since the question stems asks for an APPROXIMATION -- and the answer choices are spread out -- we can safely ignore the values in red:

(10�-10²)/(10�-10³) ≈ 10�/10� = 10.

The correct answer is B.
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by Brent@GMATPrepNow » Fri Dec 04, 2015 6:54 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 apart, 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 = [spoiler]10 = B[/spoiler]

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by [email protected] » Fri Dec 04, 2015 11:51 am
Hi dunnec3,

To prove the point that Mitch made, consider 10^8 vs. (10^8 - 10^2)....

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

Difference = 99,999,900

As far as this question is concerned, 100,000,000 is essentially the same as 99,999,900.

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