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# I need a quick way to work this out: The value of (10^8 -

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Manager
Joined: 19 Sep 2005
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I need a quick way to work this out: The value of (10^8 - [#permalink]  08 Nov 2005, 21:23
I need a quick way to work this out:

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

SVP
Joined: 24 Sep 2005
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Re: Powers Subtraction [#permalink]  08 Nov 2005, 21:29
Jennif102 wrote:
I need a quick way to work this out:

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 rule is that 10^2 and 10^3 are too small compared with 10^8 and 10^7 ...thus, they don't influence the outcome ( trust me, it's a rule in maths )
So , the fraction approximately equals to 10^8/10^7 =10. B it is.
Director
Joined: 21 Aug 2005
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(10^8 - 10^2)/ (10^7 - 10^3)
= [10^2(10^6 - 1)]/[10^3(10^4 - 1)]
= 10^6/[10(10^4)] = 10 (B)

(For close approximation, I considered 10^6 - 1 -> 10^6 and similarly the other one)
Director
Joined: 21 Aug 2005
Posts: 793
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Kudos [?]: 9 [0], given: 0

fresinha12 wrote:
I get 10 too

How
Current Student
Joined: 28 Dec 2004
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Location: New York City
Schools: Wharton'11 HBS'12
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approximation

10^8/10^7=10

gsr wrote:
fresinha12 wrote:
I get 10 too

How
Current Student
Joined: 23 Oct 2005
Posts: 243
Schools: Cranfield SOM
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Kudos [?]: 13 [0], given: 2

Re: Powers Subtraction [#permalink]  09 Nov 2005, 13:15
Jennif102 wrote:
I need a quick way to work this out:

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

I solved it and got B. But I think laxie's method is the fastest.

I got (10^2 * (10^3 + 1) * (10^3 - 1))/(10^3 * (10^2 - 1) * (10^2 + 1))

Assuming 10^2 = 10^2 - 1 and 10^3 = 10^3 - 1

We arrive at (10^3 + 1)/(10^2 + 1) approx = 10

Last edited by scorpioguy on 10 Nov 2005, 05:29, edited 1 time in total.
Senior Manager
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I would start to factor and cancel.....

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