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Of 80 students in the eighth grade, 35 played basketball and 19 made t

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Of 80 students in the eighth grade, 35 played basketball and 19 made t  [#permalink]

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New post 27 Nov 2014, 10:58
1
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A
B
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D
E

Difficulty:

  55% (hard)

Question Stats:

67% (01:08) correct 33% (01:21) 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?

1. 10 students played basketball and made the Dean’s List
2. 44 students played basketball or made the Dean’s List or both
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Re: Of 80 students in the eighth grade, 35 played basketball and 19 made t  [#permalink]

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New post 27 Nov 2014, 11:53
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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Re: Of 80 students in the eighth grade, 35 played basketball and 19 made t  [#permalink]

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New post 28 Nov 2014, 00:41
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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?

1. 10 students played basketball and made the Dean’s List
2. 44 students played basketball or made the Dean’s List or both


Attachment:
Ques3.jpg
Ques3.jpg [ 14.8 KiB | Viewed 1535 times ]

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

So if we have Both, we can get Neither.

1. 10 students played basketball and made the Dean’s List
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.

Answer (D)
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Re: Of 80 students in the eighth grade, 35 played basketball and 19 made t  [#permalink]

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New post 22 Feb 2017, 20:39
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?

1. 10 students played basketball and made the Dean’s List
2. 44 students played basketball or made the Dean’s List or both


Official solution from Veritas Prep.
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Untitled.jpg
Untitled.jpg [ 133.9 KiB | Viewed 684 times ]


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Re: Of 80 students in the eighth grade, 35 played basketball and 19 made t  [#permalink]

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New post 21 Mar 2017, 22:15
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?

1. 10 students played basketball and made the Dean’s List
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.

1. 10 students played basketball and made the Dean’s List
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.

Answer (D)


@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?
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Re: Of 80 students in the eighth grade, 35 played basketball and 19 made t  [#permalink]

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New post 22 Mar 2017, 03:43
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?

1. 10 students played basketball and made the Dean’s List
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
N (nothing) = 36. ANSWER

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

therefore 80 = N(nothing) + 44

N(nothing) = 36. ANSWER

Option D
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Re: Of 80 students in the eighth grade, 35 played basketball and 19 made t &nbs [#permalink] 22 Mar 2017, 03:43
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