GMATPrep Question Help...

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GMATPrep Question Help...

by illini1980 » Wed Jun 17, 2009 5:10 pm
I am struggling with easy/simple questions such as the following. I am taking too long to answer them. Any short cut help?

10^8 - 10^2 / 10^7 - 10^3

a) 1

b) 10

c) 10^2

d) 10^3

e) 10^4

There has to be a quick and simple way. Thanks!

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by raleigh » Wed Jun 17, 2009 6:25 pm
Did you write this problem incorrectly? Should there be paranethesis or anything? I approximate this to be 10^7.

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by illini1980 » Thu Jun 18, 2009 4:55 am
Here is the edited version. Sorry about that:

(10^8 - 10^2) / (10^7 - 10^3)

a) 1

b) 10

c) 10^2

d) 10^3

e) 10^4

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by raleigh » Thu Jun 18, 2009 8:24 am
The question says approximately, right?

Since each term is base 10, we can factor the numerator and the denominator. Since it's addition/subtraction we have no other way of combining terms.

Numerator: (10^8 - 10^2) = 10^2(10^6-1)

Denominator: (10^7 - 10^3) = 10^3(10^4-1)

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

10^2(10^6 - 1)
_____________ =
10^3(10^4 - 1)

(10^6 - 1)
_____________ =
10(10^4 - 1)

99999
______ but this isn't an answer so they must want an approximation.
9990

That's messy, but we can approximate 10 from it. It's easier to look at it like this: 10^6 - 1 = 99999 which is close enough to 10^6 = 100000 for an approximation. Similarly, 10^4 is close enough to 10^4 - 1 for an approximation. Using these approximations:

(10^6 - 1)
_____________ ~ 10^6/(10*10^4) = 10^6/10^5 = 10.
10(10^4 - 1)

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by illini1980 » Thu Jun 18, 2009 11:24 am
Yes, it states approximately. Thanks!

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by raleigh » Thu Jun 18, 2009 11:53 am
You're welcome. Please take the time to write out the exact question so everything is clear to the people helping.

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by kevincanspain » Thu Jun 18, 2009 1:17 pm
Realize that the numerator is practically 10^8 and the denominator is practically 10^7. The quotient is practically 10

If you have 10,000,000 dollars and spend 100, you have about 10,000,000 dollars left.

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