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# m11#30

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m11#30 [#permalink]  31 Dec 2008, 21:20
In a certain office 25% of the computers are equipped with built-in modems and infra-red 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 infra-red ports
2. 35% of all computers are equipped with infra-red ports but do not have built-in modems

REVISED VERSION OF THIS QUESTION IS HERE: m11-74398.html#p1216370

[Reveal] Spoiler:
From S_1 we know that 25% of all computers have built-in modems but do not have infra-red ports. However, without knowing the percentage of the computers with infra-red ports but without built-in modems, we cannot answer the question. S_2 gives the opposite information. We cannot answer the question without knowing the percentage of the computers with built-in modems but without infra-red ports. From S_1 and S_2 combined it follows that 25% + 25% + 35% = 85% of all computers are equipped with at least one of the devices. Therefore, 15% are equipped with neither of them.

My question is: How did the explanation deduce that S_1 = 25%? S_1 only says HALF of the computer with built-in modems. But we don't even know how many computers have built-in modem.
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Re: m11#30 [#permalink]  01 Jan 2009, 00:12
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georgechanhc wrote:
In a certain office 25% of the computers are equipped with built-in modems and infra-red 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 infra-red ports
2. 35% of all computers are equipped with infra-red ports but do not have built-in modems

From S_1 we know that 25% of all computers have built-in modems but do not have infra-red ports. However, without knowing the percentage of the computers with infra-red ports but without built-in modems, we cannot answer the question. S_2 gives the opposite information. We cannot answer the question without knowing the percentage of the computers with built-in modems but without infra-red ports. From S_1 and S_2 combined it follows that 25% + 25% + 35% = 85% of all computers are equipped with at least one of the devices. Therefore, 15% are equipped with neither of them.

My question is: How did the explanation deduce that S_1 = 25%? S_1 only says HALF of the computer with built-in modems. But we don't even know how many computers have built-in modem.

I had to do it twice as I lost the connection for some reason and I lost my response write up. That okie.

1. computers with built-in modems and infra-red ports = B&I
2. computers with only built-in modems = B
3. total computers with built-in modems (TB) = B + B&I

4. computers with only infra-red ports = I
5. total computers with infra-red ports (TI) = I + B&I

(Note: Make sure to understand the difference between "2 & 3", and "4 and 5". they are very confusing and look similar but they are not)

6. computers with neither = N

7. total computers (T) = B&I + B + I + N
T = (TB + TI - B&I) + N = (B + B&I) + (I + B&I) - B&I + N = B + I + B&I + N

St 1: "Half of the computers that are equipped with built-in modems do not have infra-red ports" means these are the computers with only B. using the above notations,

1/2 (TB) = B
TB = 2B
B + B&I = 2B
B = B&I (since B = 25%, B&I should also be 25%).

Hopy you get it. If any doubt, try with drawing ven diagram, which is very useful especially in set problems.

St 2: I = 35%.

Togather:
T = B&I + B + I + N = 25% +
100% = 25% + 25% + 35% + N
N = 15%
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Re: m11#30 [#permalink]  19 Apr 2011, 04:22
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Let total # of Computers be 100

With Modems = M

With IR Port = P

(1)

0.5M + 25 = M

=> M = 50

But nothing about Ports, (1) is insufficient.

(2)

Only P = 35, So P = 35 + 25 = 60

100 = Only Modem + 25 + 35 + Neither

So (2) is insufficient

(1) and (2)

Only Modem = 25

So Neither = 100 - 85 = 15

The attached Venn diagram should make things clear.
Attachments

m11Q30.png [ 7.64 KiB | Viewed 6121 times ]

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Re: m11#30 [#permalink]  22 Apr 2011, 18:25
2
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Quote:
In a certain office 25% of the computers are equipped with built-in modems and infra-red 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 infra-red ports
2. 35% of all computers are equipped with infra-red ports but do not have built-in modems

Let the total number of computers be 100. Initial table looks like:

Statement 1 tells:

Not sufficient since it doesn't tell you % of computers that are not equipped with either of these devices.
A,D Eliminated. Down to B,C,E.

Statement 2 tells:

Not sufficient. Eliminate B.

Considering 1 & 2:

We can deduce what % of computers are neither equipped with modem nor IR.

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Re: m11#30 [#permalink]  15 Apr 2010, 09:47
1
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@ Igor010
let M = computers with built-in modems ONLY; IR = those with Infra red ONLY ; N = none
M n IR = Modems AND Infra red
100 = M + IR + (M n IR) + N ...agreed?

St1: M = (1/2)(M + 25)
2M = M + 25
=> M is 25%
nothing about N - so, Insuff.

St2: Insuff
combining:
100 = M + IR + (M n IR) + N
100 = 25 + 35 + 25 + N
N = 100-85 = 15%
OA = C.

Please i stand to be corrected.
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Re: m11#30 [#permalink]  15 Apr 2010, 10:23
1
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the best way to solve the problems like this it is draw the cirlce - 100% and then draw smaller circles...
I did this problem in 20 seconds. ANd get the right answer C, 15 %
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Re: m11#30 [#permalink]  15 Apr 2010, 22:09
1
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To make things simpler :

Main statement: Let the total no. of computers are 100.
25 computers have both Modem and Infra-red.

Statement 1: Half of the computers that are equipped with built-in modems do not have infra-red ports. Reverse of this statement is half(50%) of computers with modem have infrared, which is 25 computers.

So total Computers with modem =(computers with only moden and no infra-red) + (computers with both infrared and modem)
So (computers with only moden and no infra-red) = (computers with both infrared and modem) = 25

Statement 2: Computers with only Infra-red = 35.

So total = 25+25+35 = 85 computers

So both statements required.
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Re: m11#30 [#permalink]  23 Apr 2012, 07:43
1
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The best way to solve this problem is through visualizing it on paper as a diagram. I've come to the right answer without doing so, but it took me too much time, and I am pretty sure that such kind of a problem is very likely to occur on the real GMAT.
Look at what subhashghosh has attached. It is so unusual to make a mistake here, just instert the relevant values in the circles and you'll see what leaves outside them.
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Re: m11#30 [#permalink]  25 Apr 2012, 08:21
1
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Expert's post
harshavmrg wrote:
mniyer wrote:
Quote:
In a certain office 25% of the computers are equipped with built-in modems and infra-red 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 infra-red ports
2. 35% of all computers are equipped with infra-red ports but do not have built-in modems

Let the total number of computers be 100. Initial table looks like:

Statement 1 tells:

Not sufficient since it doesn't tell you % of computers that are not equipped with either of these devices.
A,D Eliminated. Down to B,C,E.

Statement 2 tells:

Not sufficient. Eliminate B.

Considering 1 & 2:

We can deduce what % of computers are neither equipped with modem nor IR.

can somebody explain how the 1st point "Half of the computers that are equipped with built-in modems do not have infra-red ports" equals 25%... i am confused here... i very well know that answer should be either C or E...can some expert please explain this to me

(1) Half of the computers that are equipped with built-in modems do not have infra-red ports --> hence another half of computers that are equipped with built-in modems DO have infra-red ports. So, two boxes in "With Modem" row are equal, since stem says that # of computers with modems and infra-red ports is 25 then # of computers with modems but without infra-red ports is also 25.

Hope it's clear.
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Re: m11#30 [#permalink]  15 Apr 2010, 09:40
I understand why the answer is C but I am trying to arrive at the answer.

Can someone explain through a ven diagram why the amount of modems

This is the answer I am arriving at

25 Modem
(collectively 50%)
25 Both
(collectively 35%)
10 Infra red

= 60%

With Out Both
= 40%???

Because 85% for each - 25% for both ??
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Re: m11#30 [#permalink]  15 Apr 2010, 11:14
C = Both statements together are sufficient, neither statement alone is sufficient

100% - total computers
25% - have both components
25% - have only a built-in modem
35% - have only an infra-red port

so add those up and subtract them from 100% and you'll be left 15% that have neither
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Re: m11#30 [#permalink]  15 Apr 2010, 11:23
proccountant wrote:
C = Both statements together are sufficient, neither statement alone is sufficient

100% - total computers
25% - have both components
25% - have only a built-in modem
35% - have only an infra-red port

so add those up and subtract them from 100% and you'll be left 15% that have neither

I guess I am interpreting statement 1 incorrectly. Why is it only 25% for modems only?
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Re: m11#30 [#permalink]  19 Apr 2011, 04:25
Since is asks for the percentage the first thing to do is assume the total number of computers is 100
Now the information we have is number of computers with modem (m) and infra red port (i), so I can divide my set as follows :

x : number of computers with modem but not infra red port
y : number of computers with modem and infra red port
z : number of computers with infra red port but not modem

thus total number of computers equipped with either is x+y+z and we only need to determine 100-(x+y+z). If I have three independent equations in x, y and z my job is done.

the question statement says y=25

S1 : Half of the computers that are equipped with built-in modems do not have infra-red ports
$$1/2$$(x+y) = x => y = x
we have no information on z and hence not sufficient

S2 : 35% of all computers are equipped with infra-red ports but do not have built-in modems
z = 35
no information on x and not sufficient

combining S1 and S2 we will have our required three equations, so the answer is (C)
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Re: m11#30 [#permalink]  19 Apr 2011, 12:07
In a certain office 25% of the computers are equipped with built-in modems and infra-red 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 infra-red ports
2. 35% of all computers are equipped with infra-red ports but do not have built-in modems

Say there are 100 computers in all -so 25 computers are equipped with built-in Modems and IR ports
1) says 50 computers are equipped with built in modems BUT NO IR ports ->
This does not tell how many have IR ports and no modem - so NOT SUFFICIENT

2) says 35 of all computers have IR ports but no inbuilt modems.
This does not tell how many have built-in modem and not IR ports - so NOT SUFFICIENT

(1) and (2) combined tells us, there are 50 computers with built-in modems and no IR port and 35 computers with IR ports but no built in modem.

If there are 25 computers which has both IR ports and Modem, total number of computers is 50+35+25 > 100, this question is wrong.
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Re: m11#30 [#permalink]  20 Apr 2011, 01:21
information given

25% computers are equipped with BM and IR.

sentense 1: half of BM have no IR.
however no information on total is gven.

sentense 2: 35% of total computers have IR but no BM.
so 35% + 25% = 60% have IR
howver no information is availabe about only BM in 40%

putting both sentenses together

25% have only BM as 1/2 BM are not having IR.

hence 60- 25 = 15 % are not having BM or IR

I hope this clarifies
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Re: m11#30 [#permalink]  20 Apr 2011, 01:28
nishtil wrote:
information given

25% computers are equipped with BM and IR.

sentense 1: half of BM have no IR.
however no information on total is gven.

sentense 2: 35% of total computers have IR but no BM.
so 35% + 25% = 60% have IR
howver no information is availabe about only BM in 40%

putting both sentenses together

25% have only BM as 1/2 BM are not having IR.

hence 60- 25 = 15 % are not having BM or IR

I hope this clarifies

everything is straight forward except one thing. I am unable to understand how you got "60 -25 = 15"
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Re: m11#30 [#permalink]  20 Apr 2011, 14:54
Let M, I be the Modem and Infrared computers respectively.
(M and I) = 25 %

1. M/2 = (M only and no I) = 25%

no info on I. so not sufficient.

2. I = 60% , no info on M. Not sufficient.

Together we have M and I = 25 %
M only not I = 25 %
I only not M = 35 %
=> none = 100 - (25+25+35) % = 15%

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Re: m11#30 [#permalink]  24 Apr 2012, 19:02

Enough explanations given above..

DO remember that in DS questions, the actual answer figure doesnt matter as much as the ability to get a unique one using the statements.

i.e. If you could just visualize the whole thing and be sure of getting an answer, you dont need to actually find it.
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Re: m11#30 [#permalink]  25 Apr 2012, 06:05
mniyer wrote:
Quote:
In a certain office 25% of the computers are equipped with built-in modems and infra-red 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 infra-red ports
2. 35% of all computers are equipped with infra-red ports but do not have built-in modems

Let the total number of computers be 100. Initial table looks like:

Statement 1 tells:

Not sufficient since it doesn't tell you % of computers that are not equipped with either of these devices.
A,D Eliminated. Down to B,C,E.

Statement 2 tells:

Not sufficient. Eliminate B.

Considering 1 & 2:

We can deduce what % of computers are neither equipped with modem nor IR.

can somebody explain how the 1st point "Half of the computers that are equipped with built-in modems do not have infra-red ports" equals 25%... i am confused here... i very well know that answer should be either C or E...can some expert please explain this to me
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Re: m11#30 [#permalink]  24 Apr 2013, 04:19
Expert's post
BELOW IS REVISED VERSION OF THIS QUESTION:
In a certain office, 25% of the computers are equipped with built-in modems and infrared ports, what percentage of the computers that 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. Look at the double set matrix below:
Attachment:

1.png [ 4.63 KiB | Viewed 3746 times ]
As you can see we can not get the value of the yellow box. Not sufficient.

To elaborate more on this statement: Half of the computers that are equipped with built-in modems do not have infra-red ports --> hence another half of computers that are equipped with built-in modems DO have infra-red 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 infra-red 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:
Attachment:

2.png [ 5.43 KiB | Viewed 3740 times ]
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:
Attachment:

1%2B2.png [ 6.48 KiB | Viewed 3745 times ]
So, we have that 15% of the computers are not equipped with either of these devices.

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