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
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(1.00001)(0.99999) - (1.00002)(0.99998)
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1.00001 = 1+10ˉ�(1.00001)(0.99999) - (1.00002)(0.99998) =
a. 0
b. 10^-10
c. 3(10^-10)
d. 10^-5
e. 3(10^-5)
.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.
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Followed here and elsewhere by over 1900 test-takers.
I have worked with students based in the US, Australia, Taiwan, China, Tajikistan, Kuwait, Saudi Arabia -- a long list of countries.
My students have been admitted to HBS, CBS, Tuck, Yale, Stern, Fuqua -- a long list of top programs.
As a tutor, I don't simply teach you how I would approach problems.
I unlock the best way for YOU to solve problems.
For more information, please email me (Mitch Hunt) at [email protected].
Student Review #1
Student Review #2
Student Review #3
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.
(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.
