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

[Needgmat]

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

A) 0

B) 10^-10

C) 3(10^-10)

D) 10^-5

E) 3(10^-5)

OAC

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Hi Needgmat,

This question actually has a really big shortcut built into it that will allow you to avoid most of the "long math":

The first part of the calculation...

(1.00001)(0.99999)

...will have 10 decimal places (5 decimal points x 5 decimal points = 10 total decimal points) and the last digit will be a 9 (1 x 9 = 9

The second part of the calculation....

(1.00002)(0.99998)

....will also have 10 decimal places (for the same reason that the first part has 10 decimal points) and the last digit will be a 6 (2 x 8 = 16)

From the answers, we know that we'll be dealing with 10 to some "negative power"; subtracting the second number from the first would give us...

._ _ _ _ _ _ _ _ _ 9
._ _ _ _ _ _ _ _ _ 6
__________________
._ _ _ _ _ _ _ _ _ 3

So, which answer has a "3" in it and implies 10 decimal points?

Final Answer: C

GMAT assassins aren't born, they're made,
Rich

[GMATGuruNY]

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

a. 0
b. 10^-10
c. 3(10^-10)
d. 10^-5
e. 3(10^-5)

1.00001 = 1+10ˉ�
.99999 = 1-10ˉ�
1.00002 = 1+2(10ˉ�)
.99998 = 1-2(10ˉ�)

Thus:
(1.00001)(0.99999) - (1.00002)(0.99998)

= (1+10ˉ�)(1-10ˉ�) - (1 + 2*10ˉ�)(1 - 2*10ˉ�) [Note the difference of two squares: (x+y)(x-y) = x²-y²]

= (1 - 10ˉ¹�) - (1 - 4*10ˉ¹�)

= 3*10ˉ¹�

The correct answer is C.

[Matt@VeritasPrep]

Another idea: pick a friendly number! All of these are close to 1, so we've got

(1 + 1/100000)(1 - 1/100000) - (1 + 2/100000)(1 - 2/100000)

Let's call 1/100,000 x to make our lives easier. Now we've got

(1 + x)(1 - x) - (1 + 2x)(1 - 2x)

and this is difference of squares!

(1² - x²) - (1² - (2x)²)

or

x² - (-4x²)

or

3x²

So the answer is 3 * (1/100000)², or C.