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Sets

This topic has 3 expert replies and 3 member replies

Sets

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In a School, 250 students participate in debate or
student government of both. If 40 of these students participate
in both debate and student government, how many of these
students do not participate in debate?
(1) 80 of the students do not participate in student
government.
(2) In a School, 150 students do not participate
in either debate or student government.

OA is A

P.S.-According to me,it is C using formula;Total=only A+ only B-Both+Neither

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GMAT/MBA Expert

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We want to know how many of the 250 students mentioned in the stem are in student government but not in debate (everyone is in at least one of the two groups, so if someone is not in debate, he or she must be in government only).

Using Statement 1, we know 80 are not in government, so the rest, or 250 - 80 = 170, must be in government. The stem tells us that 40 of these people are also in debate, so the rest, or 170 - 40 = 130, are not in debate.

I'd use a Venn diagram, but that's a bit hard to draw here!

If you were trying to use a formula here when only looking at Statement 1, notice that the 250 in the question does not include the 'neither' group. So 250 is only equal to the "only A + only B + both" part of your formula (and the minus sign in your formula in front of "Both" needs to be a plus sign). When you use Statement 2, you discover that Neither = 150, and the Total is therefore 400 (not 250), but we don't need that information to answer the question.

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tapanmittal wrote:
In a School, 250 students participate in debate or
student government of both. If 40 of these students participate
in both debate and student government, how many of these
students do not participate in debate?
(1) 80 of the students do not participate in student
government.
(2) In a School, 150 students do not participate
in either debate or student government.

OA is A

P.S.-According to me,it is C using formula;Total=only A+ only B-Both+Neither
Total students = Debate only + Government only + Both + Neither
250 = D + G + DG + 0 = D + G + GB = D + G + 40

If a student does not participate in debate, it means he participate in government only
therefore the question "how many of these students do not participate in debate" means
how many students particpate in government only? What is G in equation?

(1) 80 of the students do not participate in student government
therefore 80 students particpate in debate only
250 = D + G + 40 = 80 + G + 40
250 = 120 + G
G = 130
statement is sufficent

(2) In a School, 150 students do not participate in either debate or student government

Total students = Debate only + Government only + Both + Neither
250 + 150 = D + G + DG + neither = D + G + GB + 150 = D + G + 40 + 150
400 = D + G + 190
We cant find G because we dont know D.
Therfore statement is insufucient

Answer = A

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GMAT/MBA Expert

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A clearer wording might be as follows:

tapanmittal wrote:
In School X, a total of 250 students are members of Club Y. Every member of Club Y participates in debate or student government or both. If 40 members of Club Y participate in both debate and student government, how many members of Club Y do not participate in debate?

(1) 80 members of Club Y do not participate in student government.
(2) In School X, 150 students do not participate in either debate or student government.
Since the 250 members participate in debate or government or both, we get:
Only Debate + Only Government + Both = 250.

Since 40 members participate in both, we get:
Only Debate + Only Government + 40 = 250
Only Debate + Only Government = 210.

To determine how many members do not participate in debate -- in other words, to determine how many participate only in government -- we need to know how many participate only in debate.

Question stem, rephrased:
How many members of Club Y participate only in debate?

Statement 1: 80 members of Club Y do not participate in student government.
Implication:
These 80 members participate only in debate.
SUFFICIENT.

Statement 2: In School X, 150 students do not participate in either debate or student government.
Implication:
Since every member of Club Y participates in debate or student government or both, these 150 students are not members of Club Y.
No way to determine how many members of Club Y participate only in debate.
INSUFFICIENT.

The correct answer is A.

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Hi Experts ,

Can you please explain this question by Double Matrix.

Thanks.

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Option2:

No info about club Y students.

Therefore answer is A

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GMAT/MBA Expert

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I thought I'd point out that iwgi's approach (known as the Double Matrix Method) 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:
- participates in debate or doesn't participate in debate
- participates in student government or doesn't participate in student government

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: http://www.gmatprepnow.com/module/gmat-word-problems?id=919

Once you’re familiar with this technique, you can attempt these additional practice questions:

Easy Problem Solving questions
- http://www.beatthegmat.com/the-aam-aadmi-party-t272242.html
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- http://www.beatthegmat.com/at-least-100-students-at-a-certain-high-school-study-japanes-t274669.html
- http://www.beatthegmat.com/prblem-solving-t279424.html

Difficult Problem Solving questions
- http://www.beatthegmat.com/ratio-problem-t268339.html
- http://www.beatthegmat.com/overlapping-sets-question-t265223.html
- http://www.beatthegmat.com/fractions-t264254.html
- http://www.beatthegmat.com/overlapping-sets-t264092.html
- http://www.beatthegmat.com/mba/2011/05/09/random-double-matrix-question-2

Easy Data Sufficiency questions
- http://www.beatthegmat.com/for-what-percent-of-those-tested-for-a-certain-t270596.html
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Medium Data Sufficiency questions
- http://www.beatthegmat.com/sets-matrix-ds-t271914.html
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- http://www.beatthegmat.com/a-manufacturer-t270331.html
- http://www.beatthegmat.com/in-costume-for-halloween-t269355.html
- http://www.beatthegmat.com/mba/2011/05/05/random-double-matrix-question-1

Difficult Data Sufficiency questions
- http://www.beatthegmat.com/double-set-matrix-question-t271423.html
- http://www.beatthegmat.com/sets-t269449.html
- http://www.beatthegmat.com/mba/2011/05/16/random-double-matrix-question-3

Cheers,
Brent

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