Percents Problem

Let total computers = 100

laptops = 30 (and) Desktops = 70

80 comps > 1 GB RAM

therefore, 20 comps < 1 GB RAM

10% of 20 = 2 laptops < 1GB RAM

Desktops with < 1GB RAM = 20 - 2 = 18

% Desktop > 1GB RAM = (70-18)/70 * 100 ~ [spoiler]75%[/spoiler] IMO

theldot wrote:I get stuck about halfway through this. I would like to see how this is worked out with equations. The explanation uses a matrix. Can someone guide me through this using equations and fractions?

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%

Lets say there are 100 computers

Total no of Desktops = 70
Total no of Laptops = 30


Total no of computers with less than 1GB RAM = 20
No of laptops with less than 1GB RAM = 10% of 20 = 2
No of desktops with less than 1GB RAM = 18
No of desktops with more than 1GB RAM = 70-18 = 52

percentage of desktops having more than 1GB of RAM = 52/70 *100 = 74.28%

Option A

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%

Let me write down each sentence in to a mathematical expression.
At a technology consulting firm with x computers.
Total number of computers = x

all of which are desktops or laptops, 30% are laptops
Total number of laptops = (30/100) * x
Total number of desktops = x - ((30/100) * x) = (70/100)*x

if 80% of the total number of computers have more than 1GB of RAM and no computers have exactly 1GM of RAM
Total number of computers that have more than 1GB of RAM = (80/100) * x
Total number of computers that have less than 1GB of RAM = x - ((80/100) * x) = (20/100) * x

10% of the computers with less than 1GB of RAM are laptops
Total number of computers that have less than 1GB of RAM and that are laptops = (10/100)*(20/100) * x = (2/100)*x

We know that the total number of laptops = (30/100) * x and also
Total number of laptops with less than 1GB of RAM = (2/100)*x then
Total number of laptops with greater than 1GB of RAM = (30/100) * x - (2/100)*x = (28/100)*x

We know that the total number of computers with greater than 1GB of RAM = (80/100)*x and
Total number of laptops with greater than 1GB of RAM = (28/100)*x
Total number of Desktops with greater than 1GB of RAM = (80/100) * x - (28/100)*x = (52/100)*x

what percent of the desktops have more than 1GB of RAM ?
= Total number of Desktops with greater than 1GB of RAM / Total number of Desktops
= (52/100)*x/(70/100)*x
= 52/70
= 74.x ~ 75%

IMO

A

For a step-by-step description of how a group grid can be used to solve this problem, check here:

https://www.beatthegmat.com/650-800-ques ... tml#309483

This is embarassingly easy now that I see the steps. Thanks so much everyone.