Problem Solving

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

(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.

thank you!

Huge fan of your comments about those questions are not actual GMAT style, but I believe that "Fair Use" enables folks to post actual OG questions (citations would be good). As long as its less than 10% of the material and neither party profits, then this stuff can be used. You guys over at MGMAT might nor be able to do it, but I think (emphasis on "think") that here its all good. Don't take my word for it - check out the Fair Use Doctrine.

But PLEASE keep up your comments about whether questions are "real" or not. I send a lot of students this way with heavy warnings about unrealistic questions.