(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

bumpbot · Answer

Automated notice from GMAT Club BumpBot: 

A member just gave Kudos to this thread, showing it’s still useful. I’ve bumped it to the top so more people can benefit. Feel free to add your own questions or solutions.

 This post was generated automatically.

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

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards

GMAT Problem Solving (PS) Questions

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

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards