Problem Solving

VJesus12 wrote:The value of (10^8-10^2)/(10^7-10^3) is closest to which of the following?

A. 1
B. 10
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� - 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 approximately 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

Cheers,
Brent

VJesus12 wrote:The value of (10^8-10^2)/(10^7-10^3) is closest to which of the following?

A. 1
B. 10
C. 10^2
D. 10^3
E. 10^4

[spoiler]OA=B[/spoiler]

Source: GMAT Prep

We see that since 10^2 is MUCH SMALLER than 10^8 and 10^3 is MUCH smaller than 10^7, subtracting 10^2 from 10^8 does not appreciably change the value, and subtracting 10^3 from 10^7 does not appreciably change the value. Thus, the approximate value of (10^8-10^2)/(10^7-10^3) is:

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

Answer: B

Hi All,

We're asked to choose the answer that is CLOSEST in value to (10^8-10^2)/(10^7-10^3). While you might be tempted to try lots of 'math steps', if you consider how the answer choices are written, you can use a bit of estimation and logic to get to the correct answer without doing too much math.

To start, when the answer choices are based around increased exponents, it's worth noting that those answers are NOT "close" to one another. Each of the answers here is a 'power of 10', and each answer is 10 TIMES greater than the one immediately above it.

With the numerator of the given fraction, 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

100,000,000 is essentially the same as 99,999,900. Next, we can think about the denominator in the same terms...

10^7 = 10,000,000
10^3 = 1,000

Difference = 9,999,000

This means that 10,000,000 is essentially the same as 9,999,999...

Thus, we're essentially just asked to divide 10 million by 1 million... and that equals 10.

Final Answer: B

GMAT assassins aren't born, they're made,
Rich