Is there an easy way to solve the below question:
0.99999999/1.0001- 0.99999991/1.0003
1) 10^-8
2) 3(10^-8)
3) 3(10^-4)
4) 2(10^-4)
5) 10^-4
Thank you,
Prerna
OG PS query
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(x+y)(x-y) = x² - y².0.99999999/1.0001 - .99999991/1.0003 =
10^-8
3(10^-8)
3(10^-4)
2(10^-4)
10^-4
In the identity above, x+y and x-y are called CONJUGATES.
It is possible to rephrase decimals as follows:
1.01 = 1 + .01.
.99 = 1 - .01.
Notice that (1 + .01) and (1 - .01) are CONJUGATES:
= (1 + .01)(1 - .01)
= 1² - (.01)²
= 1 - .0001
= .9999.
Notice also that the product of these conjugates (.9999) is ALMOST IDENTICAL to one of the numerators in the problem above (.99999999).
The two DENOMINATORS in the problem above can be rephrased as follows:
1.0001 = 1 + .0001
1.0003 = 1 + .0003.
In order for these two denominators to CANCEL OUT, the two NUMERATORS are almost certainly composed of the following sets of CONJUGATES:
(1 + .0001)(1 - .0001)
(1 + .0003)(1 - .0003).
Thus:
0.99999999/1.0001 - .99999991/1.0003
= [(1 + .0001)(1 - .0001) / (1 + .0001)] - [(1 + .0003)(1 - .0003) / (1 + .0003)]
= (1 - .0001) - (1 - .0003)
= .0002
= 2 * 10^(-4).
The correct answer is D.
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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
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