(1.00001)(0.99999) - (1.00002)(0.99998) =

Question

A. 0

B.  10^{-10}

C.  3(10^{-10})

D.  10^{-5}

E.  3(10^{-5})

Bunuel · Accepted Answer

Apply  a^2-b^2=(a+b)(a-b) .

1.00001*0.99999-1.00002*0.99998=(1+0.00001)(1-0.00001)-(1+0.00002)(1-0.00002)= 
 =1^2-0.00001^2-1^2+0.00002^2=0.00002^2-0.00001^2 .

Next,  0.00002^2-0.00001^2=(0.00002+0.00001)(0.00002-0.00001)=0.00003*0.00001=3*10^{-5}*10^{-5}=3*10^{-10} .

Answer: C.

GMATinsight · Answer

(1.00001)(0.99999) - (1.00002)(0.99998)  =   (1+.00001)(1-.00001)   -   (1+.00002)(1-.00002)   =   (1^2-.00001^2)   -   (1^2-.00002^2)

= -1^2*(10^{-5})^2   +   2^2*(10^{-5})^2   =   3*10^{-10}

Answer: Option C

chetan2u · Answer

(1.00001)(0.99999) - (1.00002)(0.99998) =

I.  We can see that the terms are equidistant from 1, so let us use that for   (1-a)(1+a)=1^2-a^2

(1.00001)(0.99999) - (1.00002)(0.99998) =  
 (1+0.00001)(1-0.00001) - (1+0.00002)(1-0.00002) =  
 1^2-(0.00001)^2-(1^2-0.00002^2)= 
 0.00002^2-0.00001^2=(0.00002+0.00001)(0.00002-0.00001)=   
  0.00003*0.00001=3*10^{-5}*1*10^{-5}=3*10^{-10}

II.  Make use of options

Both turn out to be product of two numbers with 5 digits after decimal. So we are looking at an answer with 5+5 or 10 digits after decimal or 10^{-5}.

Only B and C left.

Now the digit at the rightmost decimal place is 1*9-2*8=9-6=3

Option C gives the correct digit as 3.

C

Aswin12 · Answer

(1.00001)(0.99999) = (1+ 10^{-5})(1-10^{-5}) 
and 
 (1.00002)(0.99998) = (1+ 2*10^{-5})(1-2*10^{-5}) 
 
we know  (a-b)(a+b) =(a^2 - b^2) 
so the above equations can be simplified as 
 (1+ 10^{-5})(1-10^{-5}) =   
&
 (1+ 2*10^{-5})(1-2*10^{-5}) =

-   =

= 3*10^{-10}   Option C

levin343 · Answer

I realized this type of questions somehow has appeared in my last two GMAT attempts and I got frozen by it.. any way to get similar practice?

dave13 · Answer

VeritasKarishma can you pls expand the below in detailed step by step way so i got this and got stuck how to proceed further (1-10^{-5})^2 - (1-2*10^{-5})^2 BrentGMATPrepNow hi Brent maybe you could answer

Iotaa · Answer

Use aˆ{2} - bˆ{2} in the question stem,

=>(1+10ˆ{-5}) * (1-10ˆ{-5}) - (1+2*10ˆ{-5}) * (1-2* 10ˆ{-5}) 
=> (1-10ˆ{-10}) - (1-2*10ˆ{-10})
=> -10ˆ{-10} - 4* 10ˆ{-10} 
=> 3 * 10ˆ{-10}, Option C

minionbaba · Answer

Hi  Bunuel , this is a very good question but hasn't been seen by many people due to its tag.

This is available in Quant Review 2025-26. You can add that tag too. Thank you!

Please leave a kudos if this helps!

-KT

Bunuel · Answer

Could you please provide a screenshot of the question? That would be very helpful. Thank you!

minionbaba · Answer

Here https://gmatclub.com/forum/download/file.php?id=88790 GMAT-Club-Forum-qsux4cce.png

Bunuel · Answer

Added the tag. Thank you very much for your continuous help in properly tagging the questions!

(1.00001)(0.99999) - (1.00002)(0.99998) =

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