1 0.000001 =

Question

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)

(PS00918)

chetan2u · Accepted Answer

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

Bismarck · Answer

OA:C
 1 − 0.000001 =1-10^{-6}=1^2-(10^{-3})^2=(1+10^{-3})(1-10^{-3})=(1.001)(0.999)

GMATbuster92 · Answer

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

HUNTdGMAT · Answer

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

Hence the answer is C

PKN · Answer

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)

BrentGMATPrepNow · Answer

1 = 1^2

And  0.000001 = \frac{1}{1,000,000} = \frac{1}{1,000^2} = (\frac{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

ScottTargetTestPrep · Answer

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

jabhatta2 · Answer

Hi

Per the purple

-- how do you know the multiple does 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 !

tanveer7d · Answer

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!

karan.tkr · Answer

I also used exactly same thought process but It’s not Practical though. If answer choices were closer enough? Pls help

karan.tkr · Answer

OMG! Thanks! Understood I didn’t see that hidden   formula

Vegita · Answer

Hi  ScottTargetTestPrep

By looking at the question, we instantly know that 1-0.000001 = 0.999999. But how did you determine that we have to go the a^2-b^2 route to get to the answer as 0.999999 is not presented in the option?

ScottTargetTestPrep · Answer

We should always take a quick look at answer choices before we attempt to solve a question. We know from the answer choices that we should express our answer as a product of two numbers, and we should notice that some of the answer choices are in the form of (1 + x)(1 - x). The first thing that comes to mind at this point is to use the difference of two squares. If you were able to determine that the answer is 0.999999 but using the difference of two squares did not come to your mind, you could always multiply the two numbers in the answer choices. It will take a little longer, but since the factors have a lot of 1's and 0's, it won't be that bad.

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