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Adding exponents

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by aman88 » Fri Dec 28, 2012 1:03 am
IMO 10

I think this question asks for a closest value of (10^8 - 10^2)/(10^7-10^3).
I remember doing this question in one of the practice tests.

Numerator: (10^8 - 10^2)
Taking 10^2 common...
10^2(10^6-1)

Denominator: (10^7-10^3)
Taking 10^3 common...
10^3(10^4-1)

-> 10^2(10^6-1)/10^3(10^4-1)
-> 10^6-1/10(10^4-1) (we canceled out 10^2 with 10^3)
10^6-1 is very close to 10^6 and similarly, 10^4-1 is very close to 10^4)
-> 10^6/10(10^4)
-> 10^6/10^5
-> 10

Thanks.
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by Brent@GMATPrepNow » Fri Dec 28, 2012 8:50 am
Bunmiafolabi wrote:Hi, please who can help with a solution for (10^8 - 10^2 )divided by (10^7-10^3)?

Thanks
The official question is:

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 our 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) [approximately]
= 10^1 = B

Cheers,
Brent
Brent Hanneson - Creator of GMATPrepNow.com
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