approximation

The easiest approach to solve this question is to use a calculator

Just kidding...Ok you can do the following steps:

k=1.001
=1001/1000

(k^2-1)^-1 = ?
Ignore the ^-1 for the time being.

(k^2-1)

[(1001/1000)^2] - 1

[(1001/1000)^2] - [(1000/1000)]

[(999+2)/1000)]^2 - [(999+1)/1000]^2

Just take the numerator

(999+2)^2 - (999+1)^2

(999^2+4*999+4)-(999^2+2*999+1)
Open the brackets

4*999-2*999+4-1
999(4-2)+3
2*999+3 = 2001 or 2000 approx

So your fraction will be

[2000/(1000)^2]^-1

1000*1000/2000 = 500

Answer is B

1.001 x 1.001 = 1.002001 - 1 = .002001

So

(.002001)^-1 =

1/ .002001 = Approx 500

jnellaz wrote:1.001 x 1.001 = 1.002001 - 1 = .002001
So
(.002001)^-1 =
1/ .002001 = Approx 500

Yes, calculator is the easiest way

mals24, your approach is perfect! thanx!
pls, chck the DS section. there r some good DS i posted

4meonly wrote:Looking for the easiest approach to this Q

[spoiler] OA B[/spoiler]

= 1/[(k+1)x(k-1)]
= 1/ [(2.001) x (0.001)]

1/0.001 = 1000 so divide by 2 = 500

>>Yes, calculator is the easiest way

No calculator used here, my friend. Math 101 only

Multiplying the numbers
1.001 x 1.001 should not be a big deal to come up with 1.002001. Should take less than 15 seconds.

Now subtracting 1 from 1.002001 comes to .002001

When it comes to dividing .002001 into 1, I made things easy by moving the decimal point over 3 places for .002001 AND 1. So you should have:

2.001 Divided into 1000. Now 2.001 goes into 1000 approximately 500.

Answer: B.

k=1.001
=1/k^2-1^2
this of the form (k+1)(k-1)
1/(1.001+1)(.001)
1/(2.001)*10^-3
10^3/2
500 IMO

vishu

1 / k^2 - 1
= 1/ (1.001) ^ 2 - 1
= 1/ (1.001) ^ 2 - (1) ^ 2 (1^2 =1)
= 1/ (1.001+1) (1.001-1) (A^2-B^2 = (A+B) (A-B) A=1.001 B =1)
= 1/ 2.0001 * .001 (.001 = 1/1000 and 2.0001~= 2)
= 1000/2 = 500

B)

jnellaz,
logitech,
vishubn,
cramya,

thanx, each of your solutions is interesting!
All of them are very useful!

forget -1 (raise to the power)
k^2-1
= (k-1)(K+1)
put k = 1.001
k-1 = .001
k+1 =2.001 ~ =2
putting back we get 2*.001 =2/1000
now it is raise to the power = -1
so 1000/2 =500
Hope it helps ~