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Math Expert

Joined: 02 Sep 2009

Posts: 59087

1 − 0.000001 = [#permalink]

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30 Jul 2018, 00:29

00:00

Difficulty:

25% (medium)

Question Stats:

72% (01:33) correct

28% (01:34) wrong

based on 713 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)

Spoiler: OA

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Math Expert

Joined: 02 Aug 2009

Posts: 8179

Re: 1 − 0.000001 = [#permalink]

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30 Jul 2018, 03:15

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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Joined: 18 Jun 2018

Posts: 257

Re: 1 − 0.000001 = [#permalink]

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30 Jul 2018, 00:53

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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Re: 1 − 0.000001 = [#permalink]

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30 Jul 2018, 00:46

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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Intern

Joined: 25 Jan 2013

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Concentration: Marketing, Strategy

Schools: HEC Montreal '21, DeGroote"20

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1 − 0.000001 = [#permalink]

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30 Jul 2018, 03:03

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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Director

Status: Learning stage

Joined: 01 Oct 2017

Posts: 995

WE: Supply Chain Management (Energy and Utilities)

Re: 1 − 0.000001 = [#permalink]

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05 Aug 2018, 07:50

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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GMAT Club Legend

Joined: 12 Sep 2015

Posts: 4064

Location: Canada

Re: 1 − 0.000001 = [#permalink]

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05 Aug 2018, 08:15

Top Contributor

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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Affiliations: Target Test Prep

Joined: 14 Oct 2015

Posts: 8383

Location: United States (CA)

Re: 1 − 0.000001 = [#permalink]

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10 Aug 2018, 18:53

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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Re: 1 − 0.000001 = [#permalink]

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14 Aug 2019, 13:43

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