(x+y)(x-y) = x² - y².
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) looks VERY SIMILAR to the denominators in the problem below. .
TeddyBonham wrote:0.999991/0.997 - 0.999996/0.998 = ?
1. 10^-6
2. 3*10^-6
3. 10^-3
4. 2*10^-3
5. 3*10^-3
The two DENOMINATORS in the problem above can be rephrased as follows:
.997 = 1 - .003
.998 = 1 - .002.
In order for these two denominators to CANCEL OUT, the two NUMERATORS must be composed of the following sets of CONJUGATES:
(1 + .003)(1 - .003)
(1 + .002)(1 - .002).
Thus:
0.999991/0.997 - 0.999996/0.998
= [
(1 + .003)(1 - .003) /
(1 - .003)] - [
(1 + .002)(1 - .002) /
(1 - .002)]
= (1 + .003) - (1 + .002)
= .001
= 10^(-3).
The correct answer is
C.
Private tutor exclusively for the GMAT and GRE, with over 20 years of experience.
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
