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Source: — Problem Solving |

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by Brent@GMATPrepNow » Sun Aug 01, 2010 4:03 pm
lukeposada wrote:Need some help understanding this one:

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
the answer is b
It's important to note that the question asks us to to find the closest value here.

The fast approach is to recognize that 10^8 (100 billion) is wayyyyyyyyyyy larger than 10^2 (100). In fact 10^2 is quite insignificant compared to 10^8

So, 10^8 - 10^2 is pretty close in value to 10^8 (Aside: If you had $100 billion dollars and you lost $100 dollars, you still pretty much have $100 billion dollars)

The same applies to 10^7 - 10^3 (10^7=10 billion, and 10^3=1000). So, 10^7 - 10^3 is pretty close to 10^7

So, (10^8 - 10^2)/(10^7 - 10^3) is very close to (10^8)/(10^7) and (10^8)/(10^7) = 10^1 = 10

Choose B.
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by GMATGuruNY » Sun Aug 01, 2010 4:27 pm
lukeposada wrote:Need some help understanding this one:

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

the answer is b
Here's an alternate approach.

Whenever you see things being added or subtracted, ask yourself:

What is the GCF (the greatest common factor) that can be factored out of each term?

10^2 is the GCF of 10^8 and 10^2:
10^8 - 10^2
= 10^2(10^6 - 1)
= 10^2(10^6) approximately
= 10^8 approximately

10^3 is the GCF of 10^7 and 10^3:
10^7 - 10^3
= 10^3(10^4 - 1)
= 10^3(10^4) approximately
= 10^7 approximately

So (10^8 - 10^2)/(10^7 - 10^3)
= 10^8/10^7 approximately
= 10 approximately

The correct answer is B.
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by pradeepkaushal9518 » Mon Aug 02, 2010 2:10 am
really we have great instructors and experts. thanks to BTG
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