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# At a technology consulting firm with x computers, all of which are des

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Math Expert
Joined: 02 Sep 2009
Posts: 61283
At a technology consulting firm with x computers, all of which are des  [#permalink]

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19 Dec 2019, 23:07
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Difficulty:

95% (hard)

Question Stats:

39% (02:27) correct 61% (02:20) wrong based on 56 sessions

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Competition Mode 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%

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Re: At a technology consulting firm with x computers, all of which are des  [#permalink]

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20 Dec 2019, 02:56
Laptop Desktop Total
More than 1 GB Ram 28 52 80
Less than 1 GB Ram 2 18 20
Total 30 70 X = 100

Percent of the desktops have more than 1GB of RAM = 52%
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Re: At a technology consulting firm with x computers, all of which are des  [#permalink]

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20 Dec 2019, 03:19
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%

Since answer choices are in percentage terms, let total number of computers is = 100
Only catch is '10% of the computers with less than 1GB of RAM are laptops' which means only laptops with less than 1GB RAM.
Refer snapshot.
Attachment:
File comment: Laptop Desktops

Laptop Desktop.JPG [ 29.46 KiB | Viewed 719 times ]

On calculating
10% of the computers with less than 1GB of RAM are laptops = 2

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Re: At a technology consulting firm with x computers, all of which are des  [#permalink]

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20 Dec 2019, 03:47
1
Quote:
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%

30 are Laptops, then 70 are Desktops;
80 have >1, then 20 have <1;
0.1 of <1 = 0.1*20 = 2;

x=100…D…L………T
>1……[52]…[28]…80
<1……[18]…[2]……20
Total…70…30……100

D=70, D>1=52, 52/70=26/35~25/35~5/7
5/7>3/5? 25>21? yes. 5/7 aprox. 3/4 (75%)

Ans (A)
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Re: At a technology consulting firm with x computers, all of which are des  [#permalink]

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20 Dec 2019, 14:26
1
Let’s say that x = 100 computers
—> 30 laptops and 70 desktops

80 com. > 1 GB
20 com. < 1 GB

10 % of 20 com. = 2 laptops
—> 18 desktops < 1 GB

—> 70 — 18 = 52 desktops > 1 GB
—> $$(\frac{52}{70})* 100= \frac{520}{7} ≈ 74.3 %$$

Approximately, 75% of desktops have more than 1 GB RAM.

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Re: At a technology consulting firm with x computers, all of which are des  [#permalink]

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21 Dec 2019, 02:34
1
use 2x2 matris

-----D---L---total
>1gb--52--28--80
<1gb--18--2---20
total--70---30--100
what percent of the desktops have more than 1GB of RAM
52/70 = ~ 75%
IMO 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%
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Posts: 706
Re: At a technology consulting firm with x computers, all of which are des  [#permalink]

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22 Dec 2019, 21:04
1
Let the total number of Computers, which are either laptop or desktop be 100. We are informed that 30% are laptops, hence 70% are desktop, by extension, 30 are laptops and 70 are desktops.
80 pcs have more than 1GB RAM and 20 pcs have less than 1GB RAM.
10% of pcs with less than 1GB RAM are laptops, meaning than 2 laptops have less than 1GB RAM while 18 desktops have less than 1GB RAM.

Desktops with more than 1GB RAM = 70-18 = 52
% of Desktops with more than 1GB RAM = 52*100/70 = 74.3.
From the answer choices only A=75% is close to 74.3 hence we can say approximately 75% of desktops have more than 1GB RAM.

Math Expert
Joined: 02 Sep 2009
Posts: 61283
At a technology consulting firm with x computers, all of which are des  [#permalink]

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22 Dec 2019, 21:44
Bunuel wrote:

Competition Mode 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%

OFFICIAL EXPLANATION:

In order to solve this problem, it is extremely helpful to set up a matrix, organizing the information and methodically filling it in.

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").

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).

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

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

The final graph is as follows:
Laptop Desktop
< 1GB of RAM 2% 18% 20%
> 1GB of RAM 28% 52% 80%
30% 70% x

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%

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
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Re: At a technology consulting firm with x computers, all of which are des  [#permalink]

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01 Jan 2020, 18:40
Bunuel wrote:

Competition Mode 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%

If we let x = 100, we have 30 laptops and 70 desktops. Furthermore, 80 computers have more than 1GB of RAM, and 20 computers have less than 1GB of RAM.

Therefore, 20 x 0.1 = 2 are laptops with less than 1GB of RAM, and 18 are desktop with less than 1 GB of RAM. Since there are 70 desktops, 70 - 18 = 52 desktops have more than 1 GB of RAM. So 52/70 x 100 ≈ 75 percent of the desktops have more than 1 GB Of RAM.

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Re: At a technology consulting firm with x computers, all of which are des   [#permalink] 01 Jan 2020, 18:40
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