OG13 199

[massi2884]

0.99999999/1.0001 - 0.99999991/1.0003 =

10^-8
3(10^-8)
3(10^-4)
2(10^-4)
10^-4

[neelgandham]

0.99999999/1.0001 - 0.99999991/1.0003 =

10^-8
3(10^-8)
3(10^-4)
2(10^-4)
10^-4

~ (1/1.0001 - 1/1.0003)*0.999999999
~ (0.0002/(1.0001*1.0003))*0.999999999
~ 0.000199x *0.999999999
~ 0.000199

I don't see any answer choice which is close to 0.0002.
Is this a GMAT question ? Can you please post the source please

p.s: I will respond to your PM in a bit. Sorry for that.

[aneesh.kg]

@neelgandham: Look at Option(D)

[neelgandham]

awwww thanks for pointing out !

[Anurag@Gurome]

0.99999999/1.0001 - 0.99999991/1.0003 =

10^-8
3(10^-8)
3(10^-4)
2(10^-4)
10^-4

(0.99999999 / 1.0001) - (0.99999991 / 1.0003) = ?
Let us assume that x = 0.0001 = 10^(-4)
x² = 0.00000001 = 10^(-8)

We can write 0.99999999 = 1 - 0.00000001 = 1 - 10^(-8) = 1 - x²
1.0001 = 1 + x
0.99999991 = 1 - 9x² = 1 - (3x)²
1.0003 = 1 + 3x

Therefore, (0.99999999 / 1.0001) - (0.99999991 / 1.0003) = [(1 - x²)/(1 + x)] - [(1 - (3x)²)/(1 + 3x)] = [(1 - x)(1 + x)/(1 + x)] - [(1 - 3x)(1 + 3x))/(1 + 3x)] = [(1 - x)] - [(1 - 3x)] = 1 - x -1 + 3x = 3x - x = 2x
= 2 * 0.0001 = 0.0002 = [spoiler]2 * 10^(-4) [/spoiler]

The correct answer is D.

[GMATGuruNY]

0.99999999/1.0001 - 0.99999991/1.0003 =

10^-8
3(10^-8)
3(10^-4)
2(10^-4)
10^-4

(9999.9999)/10001 - (9999.9991)/10003

≈ (10^4)/10001 - (10^4)/10003

≈ (10^4)(1/10001 - 1/10003)

≈ (10^4)(10003-10001) / (10001)(10003)

≈ (10^4)(2 / (10^4)(10^4))

≈ 2(10^-4).

The correct answer is D.

[cholda.ct]

Hi Mitch,

I dont quite understand the first step:

(9999.9999)/10001 - (9999.9991)/10003

≈ (10^4)/10001 - (10^4)/10003

Since you can round up 9999.9999 to 10^4, why couldn't 10001 and 10003 both become 10^4.
I was a bit confuse because in the final step, you round both 10001 and 10003 to 10^4 as shown below:

≈ (10^4)(10003-10001) / (10001)(10003)

≈ (10^4)(2 / (10^4)(10^4))

Please clarify. Thank you!

[GMATGuruNY]

Hi Mitch,

I dont quite understand the first step:

(9999.9999)/10001 - (9999.9991)/10003

≈ (10^4)/10001 - (10^4)/10003

Since you can round up 9999.9999 to 10^4, why couldn't 10001 and 10003 both become 10^4.
I was a bit confuse because in the final step, you round both 10001 and 10003 to 10^4 as shown below:

≈ (10^4)(10003-10001) / (10001)(10003)

≈ (10^4)(2 / (10^4)(10^4))

Please clarify. Thank you!

The trick is to make RELATIVELY small changes.

At the beginning of the process, I rounded 9999.9999 up by .0001 and 9999.9991 up by .0009.
I left 10001 and 10003 alone because I knew that these values would be brought into the numerator when I put the fractions over a common denominator.
Thus, rounding 10001 down by 1 and 10003 down by 3 would result in a RELATIVELY much greater change than rounding 9999.9999 up by .0001 and 9999.9991 up by .0009.

Once I was near the end of the process -- with 10�(10003-10001) / (10001)(10003) -- I examined the answer choices.
10003-10001 = 2.
Relative to 2, rounding 10�/(10001)(10003) to 10¯� is a very small change, implying that the correct answer is D: 2*10¯�