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

Question

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

KarishmaB · Accepted Answer

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)

intheend14 · Answer

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.

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.

BillyZ · Answer

Official solution from Veritas Prep.

Nunuboy1994 · Answer

@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?

KrishnakumarKA1 · Answer

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

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