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
OA [spoiler]B
[/spoiler]
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At Western Springs School there are 150 total students
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gmat_winter
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Since 150 students play either soccer, tennis, or both -- and not one of these 150 students plays neither sport -- use the following matrix:gmat_winter 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?
(1) 50 students don't play soccer
(2) 80 students don't play tennis
OA [spoiler]B
[/spoiler]
Statement 1: 50 students don't play soccer
Since total NS = 50, the following matrix is yielded:
Test EXTREMES.
Case 1: Both tennis and soccer = 0
In this case, total soccer = 100 and total tennis = 50.
Since more students play soccer than tennis, the answer to the question stem is YES.
Case 2: Both tennis and soccer = 100
In this case, total soccer = 100 and total tennis = 150.
Since more students play tennis than soccer, the answer to the question stem is NO.
Since the answer is YES in Case 1 but NO in Case 2, INSUFFICIENT.
Statement 2: 80 students don't play tennis
Since total NT = 80, the following matrix is yielded:
Again, test EXTREMES.
Case 3: Both tennis and soccer = 0
The following matrix is yielded:
In this case, total soccer = 80 and total tennis = 70.
Since more students play soccer than tennis, the answer to the question stem is YES.
Case 4: Both tennis and soccer = 70
The following matrix is yielded:
In this case, total soccer = 150 and total tennis = 70.
Since more students play soccer than tennis, the answer to the question is YES.
Since the answer is YES in both cases, SUFFICIENT.
The correct answer is B.
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Hi gmat_winter,
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. Mitch's approach goes by a number of different names (the Tic-Tac-Toe Board, the Matrix, etc.), but it's essentially just about organizing data.
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.
Final Answer: B
GMAT assassins aren't born, they're made,
Rich
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. Mitch's approach goes by a number of different names (the Tic-Tac-Toe Board, the Matrix, etc.), but it's essentially just about organizing data.
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.
Final Answer: B
GMAT assassins aren't born, they're made,
Rich
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It's worth noting that Mitch's Double Matrix approach can be used for most questions featuring a population in which each member has two characteristics associated with it.
Here, we have a population of students, and the two characteristics are:
- play soccer or don't play soccer
- play tennis or don't play tennis
This question type is VERY COMMON on the GMAT, so be sure to master the technique.
To learn more about the Double Matrix Method, watch our free video: https://www.gmatprepnow.com/module/gmat- ... ems?id=919
Once you're familiar with this technique, you can attempt these additional practice questions:
Easy Problem Solving questions
- https://www.beatthegmat.com/the-aam-aadm ... 72242.html
- https://www.beatthegmat.com/finance-majo ... 67425.html
Medium Problem Solving questions
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Difficult Problem Solving questions
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- https://www.beatthegmat.com/fractions-t264254.html
- https://www.beatthegmat.com/overlapping- ... 64092.html
- https://www.beatthegmat.com/mba/2011/05/ ... question-2
Easy Data Sufficiency questions
- https://www.beatthegmat.com/for-what-per ... 70596.html
- https://www.beatthegmat.com/ds-quest-t187706.html
Medium Data Sufficiency questions
- https://www.beatthegmat.com/sets-matrix-ds-t271914.html
- https://www.beatthegmat.com/each-of-peop ... 71375.html
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Difficult Data Sufficiency questions
- https://www.beatthegmat.com/double-set-m ... 71423.html
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- https://www.beatthegmat.com/mba/2011/05/ ... question-3
Cheers,
Brent
Here, we have a population of students, and the two characteristics are:
- play soccer or don't play soccer
- play tennis or don't play tennis
This question type is VERY COMMON on the GMAT, so be sure to master the technique.
To learn more about the Double Matrix Method, watch our free video: https://www.gmatprepnow.com/module/gmat- ... ems?id=919
Once you're familiar with this technique, you can attempt these additional practice questions:
Easy Problem Solving questions
- https://www.beatthegmat.com/the-aam-aadm ... 72242.html
- https://www.beatthegmat.com/finance-majo ... 67425.html
Medium Problem Solving questions
- https://www.beatthegmat.com/probability- ... 73360.html
- https://www.beatthegmat.com/posted-speed ... 72374.html
- https://www.beatthegmat.com/motel-t271938.html
- https://www.beatthegmat.com/of-the-appli ... 70255.html
- https://www.beatthegmat.com/opening-nigh ... 64869.html
- https://www.beatthegmat.com/ds-french-ja ... 22297.html
- https://www.beatthegmat.com/prblem-solving-t279424.html
Difficult Problem Solving questions
- https://www.beatthegmat.com/ratio-problem-t268339.html
- https://www.beatthegmat.com/overlapping- ... 65223.html
- https://www.beatthegmat.com/fractions-t264254.html
- https://www.beatthegmat.com/overlapping- ... 64092.html
- https://www.beatthegmat.com/mba/2011/05/ ... question-2
Easy Data Sufficiency questions
- https://www.beatthegmat.com/for-what-per ... 70596.html
- https://www.beatthegmat.com/ds-quest-t187706.html
Medium Data Sufficiency questions
- https://www.beatthegmat.com/sets-matrix-ds-t271914.html
- https://www.beatthegmat.com/each-of-peop ... 71375.html
- https://www.beatthegmat.com/a-manufacturer-t270331.html
- https://www.beatthegmat.com/in-costume-f ... 69355.html
- https://www.beatthegmat.com/mba/2011/05/ ... question-1
Difficult Data Sufficiency questions
- https://www.beatthegmat.com/double-set-m ... 71423.html
- https://www.beatthegmat.com/sets-t269449.html
- https://www.beatthegmat.com/mba/2011/05/ ... question-3
Cheers,
Brent
Brent Hanneson - Creator of GMATPrepNow.com
