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Manager
Joined: 04 Aug 2013
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Location: India
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GMAT 1: 670 Q47 V35
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27 Nov 2014, 09:58
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Difficulty:

55% (hard)

Question Stats:

71% (01:41) correct 29% (01:42) wrong based on 96 sessions

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Of 80 students in the eighth grade, 35 played basketball and 19 made the Dean’s List. How many of the students neither made the Dean’s List, nor played basketball?

2. 44 students played basketball or made the Dean’s List or both
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Joined: 12 Sep 2014
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GMAT 1: 740 Q49 V41
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27 Nov 2014, 10:53
Classic overlapping sets problem. Let a= # who only played basketball (not Dean's List), b = # who did Basketball and got on the Dean's List, c=# who got on the Dean's List (no basketball) and n=# of people who neither played basketball nor did they make the Dean's List. We're looking for n and we can set up the expression: 80 = a + c + b + n and we don't know b nor do we know n, but we do know a + b and b + c.

Statement 1 gives us the value of b, from which we can determine a and c and thus get n. N = 36 btw.
Statement 2 gives us a + b + c, from which we get n = 36.

Both are sufficient alone and the answer is D.
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27 Nov 2014, 23:41
3
anceer wrote:
Of 80 students in the eighth grade, 35 played basketball and 19 made the Dean’s List. How many of the students neither made the Dean’s List, nor played basketball?

2. 44 students played basketball or made the Dean’s List or both

Attachment:

Ques3.jpg [ 14.8 KiB | Viewed 1580 times ]

Note that
Total = n(A) + n(B) - Both + Neither
80 = 35 + 19 - Both + Neither

So if we have Both, we can get Neither.

This tells us that Both = 10. So we can get Neither. Sufficient.

2. 44 students played basketball or made the Dean’s List or both
This tells us that
44 = 35 + 19 - Both
So we can get Both from here and then get Neither. Sufficient.

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22 Feb 2017, 19:39
anceer wrote:
Of 80 students in the eighth grade, 35 played basketball and 19 made the Dean’s List. How many of the students neither made the Dean’s List, nor played basketball?

2. 44 students played basketball or made the Dean’s List or both

Official solution from Veritas Prep.
Attachments

Untitled.jpg [ 133.9 KiB | Viewed 729 times ]

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21 Mar 2017, 21:15
VeritasPrepKarishma wrote:
anceer wrote:
Of 80 students in the eighth grade, 35 played basketball and 19 made the Dean’s List. How many of the students neither made the Dean’s List, nor played basketball?

2. 44 students played basketball or made the Dean’s List or both

Attachment:
Ques3.jpg

Note that
Total = n(A) + n(B) - Both + Neither
80 = 35 + 19 - Both + Neither

So if we have Both, we can get Neither.

This tells us that Both = 10. So we can get Neither. Sufficient.

2. 44 students played basketball or made the Dean’s List or both
This tells us that
44 = 35 + 19 - Both
So we can get Both from here and then get Neither. Sufficient.

@VeritasPrepKarishma- I am have a hard time figuring out and understanding when to use set theory vs drawing a matrix- I solved this problem using set theory but in a few questions struggled and saw that a matrix provided a more succinct method? Do you just figure out which to use through practice and preference over time?
Director
Status: Come! Fall in Love with Learning!
Joined: 05 Jan 2017
Posts: 515
Location: India

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22 Mar 2017, 02:43
anceer wrote:
Of 80 students in the eighth grade, 35 played basketball and 19 made the Dean’s List. How many of the students neither made the Dean’s List, nor played basketball?

2. 44 students played basketball or made the Dean’s List or both

let the basket ball people be denoted be B and deans list be D

total = N(nothing) + N (B only) + N(D only) + N (both)
or total = N(nothing) + N (B) + N(D ) - N (both)
or 80 = N(nothing) + 35 + 19 - N (both)
or 26 = N(nothing) - N(both)

ST 1: N(both) = 10
therefore 26 = N(nothing) - 10

St 2: N (B only) + N(D only) + N (both) = 44

therefore 80 = N(nothing) + 44

Option D
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