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(1.00001)(0.99999) - (1.00002)(0.99998) =

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(1.00001)(0.99999) - (1.00002)(0.99998) = [#permalink] New post 24 Nov 2012, 10:39
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(1.00001)(0.99999) - (1.00002)(0.99998) =

A. 0
B. 10^-10
C. 3(10^-10)
D. 10^-5
E. 3(10^-5)

[Reveal] Spoiler:
The solution suggests to turn all the expressions into scientific notation and then simplify but I was wondering if anyone here had any mind boggling tricks to do this in a more elegant manner?
[Reveal] Spoiler: OA
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Re: (1.00001)(0.99999) - (1.00002)(0.99998) = [#permalink] New post 24 Nov 2012, 11:28
(1.00001)(0.99999) - (1.00002)(0.99998) = (100001/100000)*(99999/100000) - (100002/100000)*(99998/100000) =
Right here from the get go we see that the denominator of the expression above is 100000*100000 = 10^(-10) - Denominator, and we live it right there and focus on the numerator.
100001*99999 = (100000+1)*99999=100000*99999+99999
100002*99998 = (100000+2)*99998 = 100000*99998+2*99998
= 100000*99999+99999-100000*99998-2*99998 = 100000+99999-2*99998 = 100000+99999-2*(99999-1)=100000+99999-2*99999+2=100000-99999+2=3 - Numerator
Or, 3*(10^(-10) = 3/10^(10)
The numbers might look intimidating and cumbersome, but a little manipulation goes a long way. Or, once you got the denominator you can cross out some answer choices and guess in case you running out of time.
Please, feel free to correct me, if I went awry
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Re: (1.00001)(0.99999) - (1.00002)(0.99998) = [#permalink] New post 24 Nov 2012, 11:33
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anon1 wrote:
(1.00001)(0.99999) - (1.00002)(0.99998) =

A. 0
B. 10^-10
C. 3(10^-10)
D. 10^-5
E. 3(10^-5)

[Reveal] Spoiler:
The solution suggests to turn all the expressions into scientific notation and then simplify but I was wondering if anyone here had any mind boggling tricks to do this in a more elegant manner?


Apply a^2-b^2=(a+b)(a-b).

1.00001*0.99999-1.00002*0.99998=(1+0.00001)(1-0.00001)-(1+0.00002)(1-0.00002)=
=1^2-0.00001^2-1^2+0.00002^2=0.00002^2-0.00001^2.

Next, 0.00002^2-0.00001^2=(0.00002+0.00001)(0.00002-0.00001)=0.00003*0.00001=3*10^{-5}*10^{-5}=3*10^{-10}.

Answer: C.
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Re: (1.00001)(0.99999) - (1.00002)(0.99998) = [#permalink] New post 24 Nov 2012, 11:41
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anon1 wrote:
(1.00001)(0.99999) - (1.00002)(0.99998) =

A. 0
B. 10^-10
C. 3(10^-10)
D. 10^-5
E. 3(10^-5)

[Reveal] Spoiler:
The solution suggests to turn all the expressions into scientific notation and then simplify but I was wondering if anyone here had any mind boggling tricks to do this in a more elegant manner?


= (1 + 0.00001)(1 - 0.00001) - (1 + 0.00002)(1 - 0.00002)

= (1 + 10^{-5})(1 - 10^{-5}) - (1 + 2*10^{-5})(1 - 2*10^{-5})

= 1 - 10^{-10} - 1 + 4*10^{-10}

=3*10^{-10}

Answer is hence C.

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Re: (1.00001)(0.99999) - (1.00002)(0.99998) = [#permalink] New post 30 May 2013, 01:51
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I wrote it in a simple way:
(1 + 1/10^5) (1 - 1/10^5) - (1 + 2/10^5) (1 + 2/10^5) =
= 1 - 1/10^10 - (1 - 4/10^10) =
= 4/10^10 - 1/10^10
= 3/10^10
Answer = C
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Re: (1.00001)(0.99999) - (1.00002)(0.99998) = [#permalink] New post 30 May 2013, 01:59
Expert's post
somalwar wrote:
I wrote it in a simple way:
(1 + 1/10^5) (1 - 1/10^5) - (1 + 2/10^5) (1 + 2/10^5) =
= 1 - 1/10^10 - (1 - 4/10^10) =
= 4/10^10 - 1/10^10
= 3/10^10
Answer = C


That's correct. One typo though: should be - instead of +.
_________________

NEW TO MATH FORUM? PLEASE READ THIS: ALL YOU NEED FOR QUANT!!!

PLEASE READ AND FOLLOW: 11 Rules for Posting!!!

RESOURCES: [GMAT MATH BOOK]; 1. Triangles; 2. Polygons; 3. Coordinate Geometry; 4. Factorials; 5. Circles; 6. Number Theory; 7. Remainders; 8. Overlapping Sets; 9. PDF of Math Book; 10. Remainders; 11. GMAT Prep Software Analysis NEW!!!; 12. SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) NEW!!!; 12. Tricky questions from previous years. NEW!!!;

COLLECTION OF QUESTIONS:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS ; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


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Re: (1.00001)(0.99999) - (1.00002)(0.99998) =   [#permalink] 30 May 2013, 01:59
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