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1 − 0.000001 =

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1 − 0.000001 =  [#permalink]

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New post 30 Jul 2018, 00:29
26
00:00
A
B
C
D
E

Difficulty:

  25% (medium)

Question Stats:

71% (01:34) correct 29% (01:32) wrong based on 674 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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Re: 1 − 0.000001 =  [#permalink]

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New post 30 Jul 2018, 03:15
10
7
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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Re: 1 − 0.000001 =  [#permalink]

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New post 30 Jul 2018, 00:53
12
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)

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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New post 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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1 − 0.000001 =  [#permalink]

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New post 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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Re: 1 − 0.000001 =  [#permalink]

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New post 05 Aug 2018, 07:50
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)


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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Re: 1 − 0.000001 =  [#permalink]

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New post 05 Aug 2018, 08:15
1
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

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Brent
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Re: 1 − 0.000001 =  [#permalink]

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New post 10 Aug 2018, 18:53
1
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] 10 Aug 2018, 18:53
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