The Quantitative Comparison section emphasizes shortcuts, insight, and quick techniques. Long and/or involved mathematical computation is unnecessary and is contrary to the purpose of this section.
Remember that your answers will conform to the following:

if the quantity in Column A is greater;

if the quantity in Column B is greater;

if the two quantities are equal;

if the comparison cannot be determined from the information given.
Sample 1
Column A 
Column B 
(.9)8 
(1.01)4 
In Column A, a fractional value (a value less than 1) is multiplied by itself many times. So its value becomes increasingly smaller. (For example, 1⁄2 x 1⁄2 = 1⁄4; 1⁄4 x 1⁄2 = 1⁄8, and so forth.) In Column B, a number greater than 1 is multiplied by itself; its value grows larger. So Column B is greater.
The correct answer is B.
Sample 2
Column A 
Column B 
(10)100 
(10)101 
A negative number multiplied an even number of times will yield a positive product. A negative number multiplied an odd number of times will yield a negative product. Since Column A will be positive and Column B will be negative, A is greater.
The correct answer is A.
Sample 3
Column A 
Column B 
.05  .125 
.1 
Subtracting in Column A, you get .05  .125 = .075. Our difference is a negative number. Thus, the positive value in Column B must be greater.
The correct answer is B.
Sample 4
Column A 
Column B 
a, b, c, all greater than 0 
a(b + c) 
ab + ac 
Using the distributive property on Column A to simplify gives ab and ac; therefore, the columns are equal.
The correct answer is C.
Sample 5
Column A 
Column B 
a > 0
b > 0
c > 0 
(3a)(3b)(3c) 
3abc 
Multiplying column A gives (3a)(3b)(3c) = 27abc. Because a, b, and c are all positive values, 9abc will always be greater than 3abc.
The correct answer is A.
Sample 6
Column A 
Column B 
Number of prime numbers between 3 and 19 
5 
The prime numbers between 3 and 19 are 5, 7, 11, 13, and 17. The correct answer is C, since there are 5 primes.