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**Jai Ganesh****Administrator**- Registered: 2005-06-28
- Posts: 42,136

SL # 1

In a school, it is found that 100 students play cricket, 70 play hockey, 60 play basketball, 41 play cricket and hockey, 33 play basketball and hockey and 27 play basketball and cricket. In total, 140 students play either one of more of these three games. Find the number of students who play all the three games.

It appears to me that if one wants to make progress in mathematics, one should study the masters and not the pupils. - Niels Henrik Abel.

Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.

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**espeon****Real Member**- Registered: 2006-02-05
- Posts: 2,586

11?

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**krassi_holmz****Real Member**- Registered: 2005-12-02
- Posts: 1,905

Correct!!!

How did you get this?

I got it with a system.

IPBLE: Increasing Performance By Lowering Expectations.

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**Jai Ganesh****Administrator**- Registered: 2005-06-28
- Posts: 42,136

Excellent, espeon and krassi_holmz!

It appears to me that if one wants to make progress in mathematics, one should study the masters and not the pupils. - Niels Henrik Abel.

Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.

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**Jai Ganesh****Administrator**- Registered: 2005-06-28
- Posts: 42,136

SL # 2

In a survey of 100 computer professionals, it was found that 48

read *'Byte'*, 39 read* 'PC World'* and 44 read *'PC Magazine'*. It was also found that 17 read both Byte and PC World, 18 read both PC World and PC Magazine and 22 read both Byte and PC Magazine and the balance 20 read none of these 3 magazines. Determine the number of professionals who read exactly one magazine.

It appears to me that if one wants to make progress in mathematics, one should study the masters and not the pupils. - Niels Henrik Abel.

Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.

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**Ricky****Moderator**- Registered: 2005-12-04
- Posts: 3,791

"In the real world, this would be a problem. But in mathematics, we can just define a place where this problem doesn't exist. So we'll go ahead and do that now..."

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**Jai Ganesh****Administrator**- Registered: 2005-06-28
- Posts: 42,136

Try again, Ricky!

Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.

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**Ricky****Moderator**- Registered: 2005-12-04
- Posts: 3,791

Ah, I missed the last part about the 20. That makes it:

"In the real world, this would be a problem. But in mathematics, we can just define a place where this problem doesn't exist. So we'll go ahead and do that now..."

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**Jai Ganesh****Administrator**- Registered: 2005-06-28
- Posts: 42,136

I get a different answer, Ricky!

Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.

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**Jai Ganesh****Administrator**- Registered: 2005-06-28
- Posts: 42,136

This is how I solved the problem:-

n(A U B U C) =

n(A) + n(B) + n(C) - n(AnB) - n(BnC) - n(AnC) + n(AnBnC)

Here, n(A U B U C) = 100-20 = 80

n(A) = 48, n(B) = 39, n(C)=44,

n(AnB)=17, n(BnC)=18, n(AnC)=22, n(AnBnC)=?.

Therefore, 80 = 48+39+44-17-18-22+n(AnBnC)

Therefore, n(AnBnC)=6.

Only A = 48-17-22+6 = 15

Only B = 39-17-18+6=10

Only C = 44-18-22+6=10.

Therefore, the number of professionals who read only one magazine is 15+10+10=35.

Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.

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**Sudeep****Member**- Registered: 2008-07-21
- Posts: 20

In a survey of political preference,78% of those asked were in favoured of at least one of the proposals: I, II and III. 50% of those asked favored proposal III. If 50% of those asked favoured all three of the proposals, what percentage of those asked favoured more than one of the 3 proposals.

Give explaination of your approach with your answer

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**Sudeep****Member**- Registered: 2008-07-21
- Posts: 20

In a survey of 200 students of a higher secondary school, it was found that 120 studied mathematics; 90 studied physics; 70 studied chemistry; 40 studied mathematics and physics; 30 studied physics and chemistry; 50 studied chemistry and mathematics, and 20 studied none of these subjects. Find the number of students who studied all the three subjects?

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**Sudeep****Member**- Registered: 2008-07-21
- Posts: 20

In a survey of 100 persons it was found that 39 subscribed to TV Guide, 26 subscribed to Time and 6 subscribed to Scientific American. A total of 15 subscribed to at least two of these magazines and 2 subscribed to all three. How many persons did not subscribe to any of the three?

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**TheDude****Member**- Registered: 2007-10-23
- Posts: 361

Wrap it in bacon

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**prithvi3459****Member**- Registered: 2011-07-15
- Posts: 2

ganesh wrote:

SL # 1

In a school, it is found that 100 students play cricket, 70 play hockey, 60 play basketball, 41 play cricket and hockey, 33 play basketball and hockey and 27 play basketball and cricket. In total, 140 students play either one of more of these three games. Find the number of students who play all the three games.

39 nos

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**Jai Ganesh****Administrator**- Registered: 2005-06-28
- Posts: 42,136

Hi prithvi3459,

The answer is 11.

140 = 100 + 70 + 60 - 41 - 33 - 27 + x

x = 11

Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.

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**Stormtangent****Member**- Registered: 2011-09-03
- Posts: 33

*Last edited by Stormtangent (2011-09-05 12:40:04)*

"Have you ever had a dream that you were so sure was real? What if you were unable to wake from that dream? How would you know the difference between the dream world and the real world? "

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**Stormtangent****Member**- Registered: 2011-09-03
- Posts: 33

"Have you ever had a dream that you were so sure was real? What if you were unable to wake from that dream? How would you know the difference between the dream world and the real world? "

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**Jai Ganesh****Administrator**- Registered: 2005-06-28
- Posts: 42,136

Hi Stormtangent,

The solutions #1 and #2 are correct. Excellent!

Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.

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