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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. The correct answer is C.

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.

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. The correct answer is C.

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%
_________________

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.

@ 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.
_________________

KUDOS me if you feel my contribution has helped you.

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 %

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.
_________________

The only way of finding the limits of the possible is by going beyond them into the impossible.

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.
_________________

KUDOS needed URGENTLY. Thank you in advance and be ACTIVE!

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.

Answer: C (which is 15%)

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 halfof 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.

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)
_________________

http://pyarapopat.wordpress.com

Last edited by pyarapopat on 23 Apr 2011, 13:46, edited 1 time in total.

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.

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.

Answer: C (which is 15%)

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
_________________

Regards, Harsha

Note: Give me kudos if my approach is right , else help me understand where i am missing.. I want to bell the GMAT Cat

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 4253 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 halfof 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 4248 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 4252 times ]

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