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# M11-30

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Math Expert
Joined: 02 Sep 2009
Posts: 49430

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16 Sep 2014, 00:45
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Difficulty:

25% (medium)

Question Stats:

79% (01:26) correct 21% (01:43) wrong based on 105 sessions

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If in a certain office, 25% of the computers are equipped with built-in modems and infrared ports, what percentage of the computers are not equipped with either of these devices?

(1) Half of the computers that are equipped with built-in modems do not have infrared ports.

(2) 35% of all computers are equipped with infrared ports but do not have built-in modems.

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16 Sep 2014, 00:45
Official Solution:

(1) Half of the computers that are equipped with built-in modems do not have infrared ports. Look at the double set matrix below:

As you can see we can not get the value of the yellow box. Not sufficient.

To elaborate more on this statement: since half of the computers that are equipped with built-in modems do not have infra-red ports, then another half of computers that are equipped with built-in modems DO have infrared ports. So, two boxes in "Modem" column are equal, since stem says that # of computers with modems and infra-red ports is 25 then # of computers with modems but without infrared ports is also 25.

(2) 35% of all computers are equipped with infrared ports but do not have built-in modems. Look at the double set matrix below:

As you can see we can not get the value of the yellow box. Not sufficient.

(1)+(2) When we consider two statements together we get the following matrix:

So, we have that 15% of the computers are not equipped with either of these devices.

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04 Sep 2017, 10:05
how did we divide total 100 computers into 50-50? , I'm not getting this part from the question?
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Joined: 02 Sep 2009
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04 Sep 2017, 10:18
r19 wrote:
how did we divide total 100 computers into 50-50? , I'm not getting this part from the question?

For (1) first we got that # of computers with modems is 50 (see explanation for that), thus # of computers without modems is also 50.
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Joined: 24 Oct 2016
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09 Oct 2017, 19:37
Poorly worded question.
In this question the actual meaning is "built-in modems and infrared port"=="both built-in modems and infrared port"
However, it can also mean either built-in modems or infrared ports or both of these.
Initially, I got confused with what is mentioned.
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Joined: 04 May 2015
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07 Nov 2017, 02:54
from 1) its only saying half of computers with built in modems do not have infrared ports. how its conveying computers with modem are 50%?
Math Expert
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07 Nov 2017, 03:01
ank4u wrote:
from 1) its only saying half of computers with built in modems do not have infrared ports. how its conveying computers with modem are 50%?

(1) Half of the computers that are equipped with built-in modems do not have infrared ports. Look at the double set matrix below:

As you can see we can not get the value of the yellow box. Not sufficient.

To elaborate more on this statement: since half of the computers that are equipped with built-in modems do not have infra-red ports, then another half of computers that are equipped with built-in modems DO have infrared ports. So, two boxes in "Modem" column are equal, since stem says that # of computers with modems and infra-red ports is 25 then # of computers with modems but without infrared ports is also 25.
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Joined: 30 Apr 2013
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13 Dec 2017, 03:28
How do we solve this with formula?
Re: M11-30 &nbs [#permalink] 13 Dec 2017, 03:28
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# M11-30

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