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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] New post 04 Jan 2013, 04:04
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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] New post 04 Jan 2013, 04:27
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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.

Answer: B.
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Re: At Western Springs School there are 150 total students [#permalink] New post 06 Jan 2013, 06:20
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.

Answer: B.


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] New post 06 Jan 2013, 06:40
Expert's post
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.

Answer: B.


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] New post 06 Jan 2013, 20:29
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.

Answer: B.


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.


Hi Marcab, Thanks for reply.

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] New post 07 Jan 2013, 03:07
Expert's post
shanmugamgsn wrote:
Hi Marcab, Thanks for reply.

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] New post 05 Mar 2013, 06:26
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] New post 05 Mar 2013, 06:29
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Re: At Western Springs School there are 150 total students [#permalink] New post 03 Jun 2014, 19:16
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] New post 04 Jun 2014, 00:12
Expert's post
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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NEW TO MATH FORUM? PLEASE READ THIS: ALL YOU NEED FOR QUANT!!!

PLEASE READ AND FOLLOW: 11 Rules for Posting!!!

RESOURCES: [GMAT MATH BOOK]; 1. Triangles; 2. Polygons; 3. Coordinate Geometry; 4. Factorials; 5. Circles; 6. Number Theory; 7. Remainders; 8. Overlapping Sets; 9. PDF of Math Book; 10. Remainders; 11. GMAT Prep Software Analysis NEW!!!; 12. SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) NEW!!!; 12. Tricky questions from previous years. NEW!!!;

COLLECTION OF QUESTIONS:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS ; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


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Re: At Western Springs School there are 150 total students   [#permalink] 04 Jun 2014, 00:12
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