Practice GMAT Problem Solving Question

At a technology consulting firm with x computers, all of which are desktops or laptops, 30% are laptops; if 80% of the total number of computers have more than 1GB of RAM and 10% of the computers with less than 1GB of RAM are laptops (and no computers have exactly 1GM of RAM), approximately what percent of the desktops have more than 1GB of RAM?
 A) 75% B) 60% C) 52% D) 40% E) 45%
1. In order to solve this problem, it is extremely helpful to set up a matrix, organizing the information and methodically filling it in.
2. If 30% of the computers are laptops, 70% of the computers are desktops (note: you could not make this inference unless the problem said that all the computers are "desktops or laptops").
3. If 80% of the computers have more than 1GB of RAM, 20% of the computers have less than 1GB of RAM. (Note: The problem stated that no computers had exactly 1GM of RAM).
4. If 10% of the computers with less than 1GB of RAM [known to be 20% of all computers] are laptops, then (.1)(.2) = .02 or 2% of all computers are laptops with less than 1GB of RAM.
 Laptop Desktop < 1GB of RAM 2% 20% > 1GB of RAM 80% 30% 70% x
5. Since the percents rows must add up, you can fill in the values:
 Laptop Desktop < 1GB of RAM 10% of 20% = 2% 90% of 20% = 18% 20% > 1GB of RAM 28% 52% 80% 30% 70% x
6. The final graph is as follows:
 Laptop Desktop < 1GB of RAM 2% 18% 20% > 1GB of RAM 28% 52% 80% 30% 70% x
7. Since the question asks "what percent of the desktops [not total number of computers] have more than 1GB of RAM," the correct answer is (percent of desktops with more than 1GB of RAM) / (percent of desktops) = 52%/70% = about 75%
8. Note: If the concept of dividing percents is causing you trouble, let x = 100 and fill in accordingly.
 Laptop Desktop < 1GB of RAM 2% or 2 18% or 18 20% or 20 > 1GB of RAM 28% or 28 52% or 52 80% or 80 30% or 30 70% or 70 x = 100