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# At Western Springs School there are 150 total students

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At Western Springs School there are 150 total students [#permalink]

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04 Jan 2013, 05:04
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At Western Springs School there are 150 total students who play either tennis, soccer, or both. Are there more students who play soccer than who play tennis?

(1) 50 students don't play soccer

(2) 80 students don't play tennis
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Re: At Western Springs School there are 150 total students [#permalink]

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04 Jan 2013, 05:27
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At Western Springs School there are 150 total students who play either tennis, soccer, or both. Are there more students who play soccer than who play tennis?

150 = {Tennis} + {Soccer} - {Both}

(1) 50 students don't play soccer. This implies that 150-50=100 students play soccer. It's possible that only 50 students play tennis (so none play both) as well as it's possible that all 150 students play tennis (so 100 play both). So, we can have both {Tennis}>{Soccer} and {Tennis}<{Soccer} scenarios. Not sufficient.

(2) 80 students don't play tennis. This implies that 150-80=70 students play tennis. The number of students who play soccer cannot possibly be less than or equal to 70, since in this case total # of students comes up to be less than 150. Sufficient.

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Re: At Western Springs School there are 150 total students [#permalink]

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06 Jan 2013, 07:20
Bunuel wrote:
At Western Springs School there are 150 total students who play either tennis, soccer, or both. Are there more students who play soccer than who play tennis?

150 = {Tennis} + {Soccer} - {Both}

(1) 50 students don't play soccer. This implies that 150-50=100 students play soccer. It's possible that only 50 students play tennis (so none play both) as well as it's possible that all 150 students play tennis (so 100 play both). So, we can have both {Tennis}>{Soccer} and {Tennis}<{Soccer} scenarios. Not sufficient.

(2) 80 students don't play tennis. This implies that 150-80=70 students play tennis. The number of students who play soccer cannot possibly be less than or equal to 70, since in this case total # of students comes up to be less than 150. Sufficient.

Hi Bunuel,

Stmt 2:
Scenario 1:
Soccer : 80
Tennis : 70
Both :0
Total : 150

Scenario 2:
Soccer : 70
Tennis : 70
Both :10
Total : 150

Is this possible?

Also pls give some similar problems to work out !
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Re: At Western Springs School there are 150 total students [#permalink]

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06 Jan 2013, 07:40
shanmugamgsn wrote:
Bunuel wrote:
At Western Springs School there are 150 total students who play either tennis, soccer, or both. Are there more students who play soccer than who play tennis?

150 = {Tennis} + {Soccer} - {Both}

(1) 50 students don't play soccer. This implies that 150-50=100 students play soccer. It's possible that only 50 students play tennis (so none play both) as well as it's possible that all 150 students play tennis (so 100 play both). So, we can have both {Tennis}>{Soccer} and {Tennis}<{Soccer} scenarios. Not sufficient.

(2) 80 students don't play tennis. This implies that 150-80=70 students play tennis. The number of students who play soccer cannot possibly be less than or equal to 70, since in this case total # of students comes up to be less than 150. Sufficient.

Hi Bunuel,

Stmt 2:
Scenario 1:
Soccer : 80
Tennis : 70
Both :0
Total : 150

Scenario 2:
Soccer : 70
Tennis : 70
Both :10
Total : 150 THIS IS WRONG.

Is this possible?

Also pls give some similar problems to work out !

Total= tennis + soccer - both.
Hence the minimum number of soccer players is 80.
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Re: At Western Springs School there are 150 total students [#permalink]

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06 Jan 2013, 21:29
Marcab wrote:
shanmugamgsn wrote:
Bunuel wrote:
At Western Springs School there are 150 total students who play either tennis, soccer, or both. Are there more students who play soccer than who play tennis?

150 = {Tennis} + {Soccer} - {Both}

(1) 50 students don't play soccer. This implies that 150-50=100 students play soccer. It's possible that only 50 students play tennis (so none play both) as well as it's possible that all 150 students play tennis (so 100 play both). So, we can have both {Tennis}>{Soccer} and {Tennis}<{Soccer} scenarios. Not sufficient.

(2) 80 students don't play tennis. This implies that 150-80=70 students play tennis. The number of students who play soccer cannot possibly be less than or equal to 70, since in this case total # of students comes up to be less than 150. Sufficient.

Hi Bunuel,

Stmt 2:
Scenario 1:
Soccer : 80
Tennis : 70
Both :0
Total : 150

Scenario 2:
Soccer : 70
Tennis : 70
Both :10
Total : 150 THIS IS WRONG.

Is this possible?

Also pls give some similar problems to work out !

Total= tennis + soccer - both.
Hence the minimum number of soccer players is 80.

I'm messed up with this simple ques...
S2: 80 students don't play tennis (it doesnt mean they should play only Soccer ?)
they can even play both.
So 10 both
70 soccer and 70 tennis
where i'm going wrong..
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Re: At Western Springs School there are 150 total students [#permalink]

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07 Jan 2013, 04:07
shanmugamgsn wrote:

I'm messed up with this simple ques...
S2: 80 students don't play tennis (it doesnt mean they should play only Soccer ?)
they can even play both.
So 10 both
70 soccer and 70 tennis

where i'm going wrong..

80 students out of 150 don't play tennis means that the remaining 70 do play tennis. How else?

Next, your example is not valid: if 10 play both and 70 play tennis only, then 80 students play tennis. Isn't it? So, in this case only 70 students don't play tennis which contradict the second statement.

Hope it's clear.
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Re: At Western Springs School there are 150 total students [#permalink]

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05 Mar 2013, 07:26
How can this be a Sub-600 Level question? 87% of the people here got it wrong...
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Re: At Western Springs School there are 150 total students [#permalink]

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05 Mar 2013, 07:29
2flY wrote:
How can this be a Sub-600 Level question? 87% of the people here got it wrong...

Changed the difficulty level. Thank you.
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Re: At Western Springs School there are 150 total students [#permalink]

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03 Jun 2014, 20:16
Question should be reworded to explicitly state that all students play at least tennis or soccer.
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Re: At Western Springs School there are 150 total students [#permalink]

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04 Jun 2014, 01:12
szhuge wrote:
Question should be reworded to explicitly state that all students play at least tennis or soccer.

This is actually given there: At Western Springs School there are 150 total students who play either tennis, soccer, or both.
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At Western Springs School there are 150 total students [#permalink]

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04 Apr 2015, 04:07
At Western Springs School there are 150 total students who play either tennis, soccer, or both. Are there more students who play soccer than who play tennis?

How I Understood is:

whenever we are given that X number don't play/study one type of sports/subject or Y number don't play/study one type of sport/subject

we should consider the formula for example in this problem : Total= Those who play Tennis only +Those who play Soccer Only+Those who play Both

150= tennis only+soccer only+Both

St:(1) 50 students don't play soccer

50=tennis only

two possibilities
150=50+100+0(100 play soccer only and 0 both)

100 play soccer >50 play tennis

or 150=50+0+100(0 play tennis only and 100 play both)

100 play soccer<150 play tennis

Not Sufficient.

St:(2) 80 students don't play tennis

80=soccer only
possibilities
150=70+80+0 or 150=0+80+70 or 150=10+80+60

in any case there are more students who play soccer than who play tennis

Thus Sufficient

Ans B.
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Re: At Western Springs School there are 150 total students [#permalink]

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05 Apr 2015, 15:56
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Hi All,

The question is a "twist" on the typical Overlapping Sets question that you'll see on Test Day. Depending on the "restrictions" given in the prompt and the specific question that's asked, there are usually a few different ways to approach the work.

This particular prompt is designed in such a way that it can be solved with minimal note-taking and a bit of logic.

We're given a few facts to start off with:
1) There are 150 total students
2) They ALL play tennis, soccer OR both.

The question asks if more students play soccer than play tennis. This is a YES/NO question. The "key" to dealing with it is to remember that EVERY student plays at least one sport....

Fact 1: 50 students don't play soccer.

This tells us that these 50 students MUST play JUST tennis. But what about the other 100 students? We can deduce that they MUST play soccer, but they MIGHT also play tennis.....

IF....
All 150 students play tennis, then the answer to the question is NO.

IF.....
99 play tennis, then the answer to the question is YES.
Fact 1 is INSUFFICIENT

Fact 2: 80 students don't play tennis.

This tells us that these 80 students MUST play JUST soccer. The other 70 students MUST play tennis, but it can't be any more than those 70. They might also play soccer, but whether they play soccer or not does NOT impact the question. We're asked if MORE students play soccer than play tennis. With this info, we know that the answer to the question MUST be YES.
Fact 2 is SUFFICIENT.

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At Western Springs School there are 150 total students [#permalink]

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21 May 2015, 07:03
At Western Springs School there are 150 total students who play either tennis, soccer, or both. Are there more students who play soccer than who play tennis?

My Approach:

Consider t, s, b to be the number of students playing tennis only, soccer only and both tennis and soccer respectively.

What is provided to us:: 150 = t + s + b

we just need to find if s > t?

Now,
(1) states 50 students don't play soccer

=> t = 50 (students who don't play soccer=>play tennis only)

So, 50 + s + b = 150
=> s + b = 100.

This is Not Sufficient. Because, for any value of b > 50 we will get s < t, and for any value of b < 50 we will get s > t.

(2) states 80 students don't play tennis

=> s = 80 (students who don't play tennis=>play soccer only)

So, t + 80 + b = 150
=> t + b = 70.

Here whatever be the value of b, t will have value less than or equal to 70. So, t <=70 and s = 80. So, s > t.

Thus Sufficient

Ans:: B.
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Re: At Western Springs School there are 150 total students [#permalink]

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27 May 2015, 02:18
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Drawing a Venn diagram in such cases helps in visualization of the problem statement and the question asked.

Interpreting the given info
We are told that students in a school play either tennis or soccer or both and the total number of students in the school are 150. Let's represent this information through a Venn diagram

Since the total number of students are 150, we can write a + b + c + d = 150. We are also told that the students play either of the games i.e. there is no student who does not play any of the games. So d = 0 which leaves us with a + b + c = 150

We are asked if the number of students playing soccer is more than the number of students playing tennis. This can be written as

a + b > b + c i.e. a > c ?

Let's see if the statements provide us the required information to get to our answer.

Statement-I
St-I tells us that 50 students don't play soccer. This is equal to the number of students who play only tennis i.e. c = 50. That leaves us with a + b = 100. So a > c or a < c.

Hence st-I is insufficient to answer the question.

Statement-II
St-II tells us that 80 students don't play tennis. This is equal to the number of students who play only soccer i.e. a = 80. That leaves us with b + c = 70. We observe here that c can take a maximum value of 70. Hence a > c.

St-II is sufficient to answer the question.

Hope this helps

Regards
Harsh
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Re: At Western Springs School there are 150 total students   [#permalink] 27 May 2015, 02:18
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