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# 0.99999999/1.0001-0.99999991/1.0003

Author Message
Manager
Joined: 18 Jun 2012
Posts: 143
Concentration: Healthcare, General Management
GMAT Date: 09-14-2012

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Updated on: 31 Jan 2014, 08:06
2
7
00:00

Difficulty:

75% (hard)

Question Stats:

61% (02:04) correct 39% (01:48) wrong based on 108 sessions

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This is from OG 13, #199. The explanation is tedious and time consuming, I hope I don't see anything like this, because I'd be tempted to guess and move on.

$$\frac{0.99999999}{1.0001}-\frac{0.99999991}{1.0003}=$$

A. 10^-8
B. 3(10^-8)
C. 3(10^-4)
D. 2(10^-4)
E. 10^-4

OPEN DISCUSSION OF THIS QUESTION IS HERE: topic-144735.html

Originally posted by RoyHalladay on 11 Aug 2012, 12:54.
Last edited by Bunuel on 31 Jan 2014, 08:06, edited 2 times in total.
Renamed the topic.
Director
Joined: 22 Mar 2011
Posts: 600
WE: Science (Education)

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11 Aug 2012, 14:00
13
6
This is from OG 13, #199. The explanation is tedious and time consuming, I hope I don't see anything like this, because I'd be tempted to guess and move on.

$$\frac{0.99999999}{1.0001}-\frac{0.99999991}{1.0003}=$$

A. 10^-8
B. 3(10^-8)
C. 3(10^-4)
D. 2(10^-4)
E. 10^-4

Well, you need a little bit of algebra here...

The question is meant to test the formula $$a^2-b^2=(a+b)(a-b).$$
The clue is in the answers, explicitly the powers of $$10$$.
You can write the given expression as follows:

$$\frac{1-10^{-8}}{1+10^{-4}}-\frac{1-9*10^{-8}}{1+3*10^{-4}}=\frac{(1+10^{-4})(1-10^{-4})}{1+10^{-4}}-\frac{(1+3*10^{-4})(1-3*10^{-4})}{1+3*10^{-4}}=1-10^{-4}-(1-3*10^{-4})=2*10^{-4}.$$

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PhD in Applied Mathematics
Love GMAT Quant questions and running.
Math Expert
Joined: 02 Sep 2009
Posts: 55732

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31 Jan 2014, 08:07
1
3
$$\frac{0.99999999}{1.0001}-\frac{0.99999991}{1.0003}=$$

A. 10^-8
B. 3(10^-8)
C. 3(10^-4)
D. 2(10^-4)
E. 10^-4

$$\frac{0.99999999}{1.0001}-\frac{0.99999991}{1.0003}=\frac{1-10^{-8}}{1+10^{-4}}-\frac{1-9*10^{-8}}{1+3*10^{-4}}$$

Now apply $$a^2-b^2=(a+b)(a-b)$$:

$$\frac{1-10^{-8}}{1+10^{-4}}-\frac{1-9*10^{-8}}{1+3*10^{-4}}=\frac{(1+10^{-4})(1-10^{-4})}{1+10^{-4}}-\frac{(1+3*10^{-4})(1-3*10^{-4})}{1+3*10^{-4}}=(1-10^{-4})-(1-3*10^{-4})=2*10^{-4}$$.

OPEN DISCUSSION OF THIS QUESTION IS HERE: topic-144735.html
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Posts: 11399

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17 Aug 2018, 05:54
Hello from the GMAT Club BumpBot!

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Re: 0.99999999/1.0001-0.99999991/1.0003   [#permalink] 17 Aug 2018, 05:54
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