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(1.00001)(0.99999)  (1.00002)(0.99998) =
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24 Nov 2012, 11:39
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58% (02:11) correct 42% (02:01) wrong based on 440 sessions
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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. \(3(10^{5})\) 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?
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Re: (1.00001)(0.99999)  (1.00002)(0.99998) =
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24 Nov 2012, 12:33
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) 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 \(a^2b^2=(a+b)(ab)\). \(1.00001*0.999991.00002*0.99998=(1+0.00001)(10.00001)(1+0.00002)(10.00002)=\) \(=1^20.00001^21^2+0.00002^2=0.00002^20.00001^2\). Next, \(0.00002^20.00001^2=(0.00002+0.00001)(0.000020.00001)=0.00003*0.00001=3*10^{5}*10^{5}=3*10^{10}\). Answer: C.
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Re: (1.00001)(0.99999)  (1.00002)(0.99998) =
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24 Nov 2012, 12:41
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) 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. Kudos Please... If my post helped.
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Re: (1.00001)(0.99999)  (1.00002)(0.99998) =
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24 Nov 2012, 12:28
(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+99999100000*999982*99998 = 100000+999992*99998 = 100000+999992*(999991)=100000+999992*99999+2=10000099999+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) =
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Updated on: 27 Aug 2014, 03:12
I wrote it in a simple way: \((1 + \frac{1}{10^5}) (1  \frac{1}{10^5})  (1 + \frac{2}{10^5}) (1  \frac{2}{10^5})\) \(= 1  \frac{1}{10^{10}}  (1  \frac{4}{10^{10}})\) \(= \frac{4}{10^{10}}  \frac{1}{10^{10}}\) \(= \frac{3}{10^{10}}\) Answer = C
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Originally posted by PareshGmat on 30 May 2013, 02:51.
Last edited by PareshGmat on 27 Aug 2014, 03:12, edited 3 times in total.



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Re: (1.00001)(0.99999)  (1.00002)(0.99998) =
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30 May 2013, 02:59
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 +.
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Re: (1.00001)(0.99999)  (1.00002)(0.99998) =
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17 Nov 2016, 15:31
In short, this is a very messy way of dealing with factoring.
Think (a+1)(a1), etc.
1. We need to rewrite decimals, so they are in fractional form.
{[100,001/100,000][999,999/100,000]}  {[100,002/100,000][99998/100,000]}
2. Trick here is to recognize that we can write each of the numerator as a process applied to 100,000 (i.e. x, , +, etc)
{[(100,000+1)(100,0001)]/(10,000,000,000)}  {(100,000+2)(100,0002)/(10,000,000,000)}
3. Simplify by using knowledge that (a+1)(a1) = a^2  1 & (a+2)(a2) = a^2 4
{(10,000,000,0001) (10,000,000,0004)}/(10^10) > 3x10^(10)



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Re: (1.00001)(0.99999)  (1.00002)(0.99998) =
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10 Jan 2017, 04:35
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) 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? 1.00001*0.99999 .... ends in 9, and 1.00002*0.99998 ends in 6 , thus answer has to be in the form 3*10^x , option c or E but since multiplication of each term around the subtraction operation will yield 10^x < 10^5 thus x > 5 .... thus option c



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Re: (1.00001)(0.99999)  (1.00002)(0.99998) =
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03 Nov 2017, 03:47
Does anyone know of similar question types for additional practise?



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Re: (1.00001)(0.99999)  (1.00002)(0.99998) =
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Re: (1.00001)(0.99999)  (1.00002)(0.99998) =
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03 Nov 2017, 22:11
Bunuel wrote: Thank you very much for this.



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Re: (1.00001)(0.99999)  (1.00002)(0.99998) =
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06 Nov 2017, 17:30
anon1 wrote: \((1.00001)(0.99999)  (1.00002)(0.99998) =\)
A. 0
B. \(10^{10}\)
C. \(3(10^{10})\)
D. \(10^{5}\)
E. \(3(10^{5})\) Let’s rewrite the expressions using scientific notation: (1 + 10^5)(1  10^5)  (1 + 2 x 10^5)(1  2 x 10^5) 1^2  (10^5)^2  [1^2  2^2 x (10^5)^2] 1  10^10  1 + 4 x 10^10 3 x 10^10 Answer: C
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Re: (1.00001)(0.99999)  (1.00002)(0.99998) =
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28 Jan 2018, 15:00
Hi All, This question actually has a really big shortcut built into it that will allow you to avoid most of the "long math": The first part of the calculation... (1.00001)(0.99999) …will have 10 decimal places (5 decimal points x 5 decimal points = 10 total decimal points) and the last digit will be a 9 (1 x 9 = 9 The second part of the calculation…. (1.00002)(0.99998) ….will also have 10 decimal places (for the same reason that the first part has 10 decimal points) and the last digit will be a 6 (2 x 8 = 16) From the answers, we know that we'll be dealing with 10 to some "negative power"; subtracting the second number from the first would give us… ._ _ _ _ _ _ _ _ _ 9 ._ _ _ _ _ _ _ _ _ 6 __________________ ._ _ _ _ _ _ _ _ _ 3 So, which answer has a "3" in it and implies 10 decimal points? Final Answer: GMAT assassins aren't born, they're made, Rich
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(1.00001)(0.99999)  (1.00002)(0.99998) =
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02 Jul 2019, 03:14
EMPOWERgmatRichC wrote: Hi All, This question actually has a really big shortcut built into it that will allow you to avoid most of the "long math": The first part of the calculation... (1.00001)(0.99999) …will have 10 decimal places (5 decimal points x 5 decimal points = 10 total decimal points) and the last digit will be a 9 (1 x 9 = 9 The second part of the calculation…. (1.00002)(0.99998) ….will also have 10 decimal places (for the same reason that the first part has 10 decimal points) and the last digit will be a 6 (2 x 8 = 16) From the answers, we know that we'll be dealing with 10 to some "negative power"; subtracting the second number from the first would give us… ._ _ _ _ _ _ _ _ _ 9 ._ _ _ _ _ _ _ _ _ 6 __________________ ._ _ _ _ _ _ _ _ _ 3 So, which answer has a "3" in it and implies 10 decimal points? Final Answer: GMAT assassins aren't born, they're made, Rich EMPOWERgmatRichCI wanted to dobthis math like you, but can't figure out the decimal part! Why not E? Does the highlighted part always introduce the first part like option C ( 3(10^10) and E ( 3(10^5) ? Thanks__
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Re: (1.00001)(0.99999)  (1.00002)(0.99998) =
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02 Jul 2019, 14:51
Hi Asad, To start, it's important to remember a couple of things about GMAT questions: 1) NOTHING about a GMAT question is ever "random"; each prompt is carefully designed to 'test' you on specific concepts  and in many cases, provide you with potential shortcuts that you can use to avoid a longwinded, mathheavy approach (and that's because the Quant section is NOT a 'math test'  it's a 'critical thinking test' that requires lots of little calculations as you work through it). 2) Even the answer choices are specifically designed  often with patterns in mind  that can help you to think about what the question is asking for. The exact format that the answers take can vary  and sometimes it's actually beneficial to 'rewrite' the answer choices in a different format (for example, changing fractions to decimals; in this case, it's thinking of "negative powers of 10" as decimals). Answer E won't be correct because it only has 5 decimal places  and the correct answer will have TEN decimal places GMAT assassins aren't born, they're made, Rich
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Re: (1.00001)(0.99999)  (1.00002)(0.99998) =
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02 Jul 2019, 15:04
EMPOWERgmatRichC wrote: Hi Asad,
To start, it's important to remember a couple of things about GMAT questions:
1) NOTHING about a GMAT question is ever "random"; each prompt is carefully designed to 'test' you on specific concepts  and in many cases, provide you with potential shortcuts that you can use to avoid a longwinded, mathheavy approach (and that's because the Quant section is NOT a 'math test'  it's a 'critical thinking test' that requires lots of little calculations as you work through it).
2) Even the answer choices are specifically designed  often with patterns in mind  that can help you to think about what the question is asking for. The exact format that the answers take can vary  and sometimes it's actually beneficial to 'rewrite' the answer choices in a different format (for example, changing fractions to decimals; in this case, it's thinking of "negative powers of 10" as decimals).
Answer E won't be correct because it only has 5 decimal places  and the correct answer will have TEN decimal places
GMAT assassins aren't born, they're made, Rich So, if the question asks: \(0.001×0.0040.002×0.001\)= ?Can I easily write the answer like 2×10^(6) ? Calculation: The last digit of first part (after multiplication) is 4 and The last digit of 2nd part (after multiplication) is 2 So, 42=2 and the decimal point is total 6.
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Re: (1.00001)(0.99999)  (1.00002)(0.99998) =
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02 Jul 2019, 19:09
Hi Asad, You picked a remarkably simple example, but that example DOES fit. Keep in mind that if you change ANY of those individual 0's to a non0 digit, then the calculation will NOT fit that pattern. One of the reasons why I was able to use the approach I used was because the answer choices (with the exception of Answer A) were all written as a decimal, followed by a bunch of zeroes, and ending in a non0 digit. Thus, I knew that almost all of the digits in the overall calculation would 'cancel out' and I'd be left with a decimal, a string of 0s and a single digit. GMAT assassins aren't born, they're made, Rich
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Re: (1.00001)(0.99999)  (1.00002)(0.99998) =
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