Math Problem 4

n is an odd positive integer

Compare two values:

Column A	Column B
The number of prime factors of n	The number of prime factors of 2n

Solution for GRE Math Problem 3:

Lets consider three possibilities: numbers x and y can be bot positive, negative and positive and 0 and 1. (They both can't be negative, because their sum is x+y=1>0).

In the first case, as x>0, y>0, x+y=1, we can say that x<1 and y<1, so their product will be less than 1.

In the second case, the product of positive and negative values is negative, so, less than one.

And for the pair (1;0), xy=0<1. That's why column B is always bigger.

Answer: B

See also these GRE problems: