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Bunuel
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1 − 0.000001 = [#permalink] New post  29 Jul 2018, 23:29
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72% (01:31) correct 28% (01:34) wrong based on 1489 sessions

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1 − 0.000001 =

A. (1.01)(0.99)
B. (1.11)(0.99)
C. (1.001)(0.999)
D. (1.111)(0.999)
E. (1.0101)(0.0909)


NEW question from GMAT® Quantitative Review 2019


(PS00918)
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chetan2u
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Re: 1 − 0.000001 = [#permalink] New post  30 Jul 2018, 02:15
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Bunuel wrote:
1 − 0.000001 =

A. (1.01)(0.99)
B. (1.11)(0.99)
C. (1.001)(0.999)
D. (1.111)(0.999)
E. (1.0101)(0.0909)


NEW question from GMAT® Quantitative Review 2019


(PS00918)


Two ways..

1) algebraic..
\(1-0.000001=1^2-(0.001)^2=(1+0.001)(1-0.001)=1.001*0.999\)

2) choices
1-0.000001=0.999999
So the answer will have 6 decimal point.
A and B have 2+2=4 decimal points so eliminate
E has 4+4=8, so out
Left C and D
D is 1.111*0.999 the multiple cannot have all 9s as 11*99=1098 and also it will surely be >1.... eliminate

Left is C
1.001*0.999 will be <1 and will give all 9s
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1) Absolute modulus : http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html
3) effects of arithmetic operations : https://gmatclub.com/forum/effects-of-arithmetic-operations-on-fractions-269413.html
4) Base while finding % increase and % decrease : https://gmatclub.com/forum/percentage-increase-decrease-what-should-be-the-denominator-287528.html


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BrentGMATPrepNow
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Re: 1 − 0.000001 = [#permalink] New post  05 Aug 2018, 07:15
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Bunuel wrote:
1 − 0.000001 =

A. (1.01)(0.99)
B. (1.11)(0.99)
C. (1.001)(0.999)
D. (1.111)(0.999)
E. (1.0101)(0.0909)

NEW question from GMAT® Quantitative Review 2019


(PS00918)


1 = 1²
0.000001 = 1/1,000,000 = 1/1,000² = (1/1,000)² = = (0.001)²

So, 1 and 0.000001 are SQUARES
This means 1 - 0.000001 is a difference of squares

We can factor a difference of squares as follows: x² - y² = (x + y)(x - y)

Likewise....
1 - 0.000001 = 1² - (0.001)²
= (1 + 0.001)(1 - 0.001)
= (1.001)(0.999)

Answer: C

Cheers,
Brent
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Bismarck
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Re: 1 − 0.000001 = [#permalink] New post  29 Jul 2018, 23:53
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Bunuel wrote:
1 − 0.000001 =

A. (1.01)(0.99)
B. (1.11)(0.99)
C. (1.001)(0.999)
D. (1.111)(0.999)
E. (1.0101)(0.0909)


NEW question from GMAT® Quantitative Review 2019


(PS00918)

OA:C
\(1 − 0.000001 =1-10^{-6}=1^2-(10^{-3})^2=(1+10^{-3})(1-10^{-3})=(1.001)(0.999)\)
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GMATbuster92
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Re: 1 − 0.000001 = [#permalink] New post  29 Jul 2018, 23:46
1
when you will do subtraction , you will get = 0.999999 or 999999 * \(10^{-6}\)
now you need to find factors of 999999 = 999 * 1001
(for example you need factors of 99 = 9 * 11 , 9999 = 99 * 101 and so on if 9 is repeated even times...)

so in answer choices option C , (1.001) * (0.999) is answer
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1 − 0.000001 = [#permalink] New post  30 Jul 2018, 02:03
2
Bunuel wrote:
1 − 0.000001 =

A. (1.01)(0.99)
B. (1.11)(0.99)
C. (1.001)(0.999)
D. (1.111)(0.999)
E. (1.0101)(0.0909)


NEW question from GMAT® Quantitative Review 2019


(PS00918)


1^2-(0.001)^2= (1+0.001) (1-0.001)= (1.001)(0.999)

Hence the answer is C
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PKN
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Re: 1 − 0.000001 = [#permalink] New post  05 Aug 2018, 06:50
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Bunuel wrote:
1 − 0.000001 =

A. (1.01)(0.99)
B. (1.11)(0.99)
C. (1.001)(0.999)
D. (1.111)(0.999)
E. (1.0101)(0.0909)


NEW question from GMAT® Quantitative Review 2019


(PS00918)


We have, 1−0.000001=0.999999

Let's check the answer choices.

A. (1.01)(0.99)=(1+0.01)(0.99)=0.99+0.0099=0.9999
B. (1.11)(0.99)=(1+0.1+0.01)(0.99)=0.99+0.099+0.0099=1.0989
C. (1.001)(0.999)=(1+0.001)(0.999)=0.999+0.000999=0.999999
Ans. (C)
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ScottTargetTestPrep
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Re: 1 − 0.000001 = [#permalink] New post  10 Aug 2018, 17:53
1
Expert Reply
Bunuel wrote:
1 − 0.000001 =

A. (1.01)(0.99)
B. (1.11)(0.99)
C. (1.001)(0.999)
D. (1.111)(0.999)
E. (1.0101)(0.0909)


Let’s first re-express 0.000001 in exponential form:

1 - 10^-6

Factoring the resulting expression as a difference of squares, we have:

(1 - 10^-3)(1 + 10^-3)

(1 - 0.001)(1 + 0.001) = 0.999 x 1.001

Answer: C
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jabhatta2
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Joined: 15 Dec 2016
Posts: 322
1 − 0.000001 = [#permalink] New post  27 Nov 2019, 13:25
chetan2u wrote:
Bunuel wrote:
1 − 0.000001 =

A. (1.01)(0.99)
B. (1.11)(0.99)
C. (1.001)(0.999)
D. (1.111)(0.999)
E. (1.0101)(0.0909)


NEW question from GMAT® Quantitative Review 2019


(PS00918)


Two ways..

1) algebraic..
\(1-0.000001=1^2-(0.001)^2=(1+0.001)(1-0.001)=1.001*0.999\)

2) choices
1-0.000001=0.999999
So the answer will have 6 decimal point.
A and B have 2+2=4 decimal points so eliminate
E has 4+4=8, so out
Left C and D
D is 1.111*0.999 the multiple cannot have all 9s as 11*99=1098 and also it will surely be >1.... eliminate

Left is C
1.001*0.999 will be <1 and will give all 9s


Hi

Per the purple

-- how do you know the multiple does not have all 9's [ i am assuming you did not actually calculate out on paper that the resulting number will NOT have all 9's]

Per the red colored font
-- how could you be sure the resulting number MUST BE > 1 (without calculating or pulling out a calculator) --- i thought it could be below 1 or just above 1

can you tell me, how is your thinking -- regarding how is this definitely > 1 ?

Thank you !
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tanveer7d
Intern
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Joined: 23 Dec 2019
Posts: 1
Re: 1 − 0.000001 = [#permalink] New post  04 Jan 2020, 02:29
Bunuel wrote:
1 − 0.000001 =

A. (1.01)(0.99)
B. (1.11)(0.99)
C. (1.001)(0.999)
D. (1.111)(0.999)
E. (1.0101)(0.0909)


NEW question from GMAT® Quantitative Review 2019


(PS00918)


Well, So start with, we know the difference between 1 and 0.000001 will have 6 digits AFTER the decimal point. So, use the same concept and apply to the options.

A. (1.01)(0.99) - here, multiplying a number having 2 digits after the decimal point to the same will give us answer with 4 digits after the decimal point.

Similarly, applying the same to all options, we see that the answer to Option C will have 6 digits after the decimal point.

Hope that helps!
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karan.tkr
Intern
Intern
Joined: 06 Oct 2017
Posts: 6
Re: 1 − 0.000001 = [#permalink] New post  16 Jan 2020, 08:01
chetan2u wrote:
Bunuel wrote:
1 − 0.000001 =

A. (1.01)(0.99)
B. (1.11)(0.99)
C. (1.001)(0.999)
D. (1.111)(0.999)
E. (1.0101)(0.0909)


NEW question from GMAT® Quantitative Review 2019


(PS00918)


Two ways..

1) algebraic..
\(1-0.000001=1^2-(0.001)^2=(1+0.001)(1-0.001)=1.001*0.999\)

2) choices
1-0.000001=0.999999
So the answer will have 6 decimal point.
A and B have 2+2=4 decimal points so eliminate
E has 4+4=8, so out
Left C and D
D is 1.111*0.999 the multiple cannot have all 9s as 11*99=1098 and also it will surely be >1.... eliminate

Left is C
1.001*0.999 will be <1 and will give all 9s


I also used exactly same thought process but It’s not Practical though. If answer choices were closer enough? Pls help
avatar
B
karan.tkr
Intern
Intern
Joined: 06 Oct 2017
Posts: 6
Re: 1 − 0.000001 = [#permalink] New post  16 Jan 2020, 08:02
GMATPrepNow wrote:
Bunuel wrote:
1 − 0.000001 =

A. (1.01)(0.99)
B. (1.11)(0.99)
C. (1.001)(0.999)
D. (1.111)(0.999)
E. (1.0101)(0.0909)

NEW question from GMAT® Quantitative Review 2019


(PS00918)


1 = 1²
0.000001 = 1/1,000,000 = 1/1,000² = (1/1,000)² = = (0.001)²

So, 1 and 0.000001 are SQUARES
This means 1 - 0.000001 is a difference of squares

We can factor a difference of squares as follows: x² - y² = (x + y)(x - y)

Likewise....
1 - 0.000001 = 1² - (0.001)²
= (1 + 0.001)(1 - 0.001)
= (1.001)(0.999)

Answer: C

Cheers,
Brent


OMG! Thanks! Understood I didn’t see that hidden [a^2 - b^2] formula
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