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# Of the students who eat in a certain cafeteria, each student

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Of the students who eat in a certain cafeteria, each student [#permalink]

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26 Apr 2006, 03:26
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65% (02:23) correct 35% (02:00) wrong based on 126 sessions

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Of the students who eat in a certain cafeteria, each student either likes or dislikes lima beans and each student either likes or dislikes brussels sprouts. Of these students, 2/3 dislike lima beans; and of those who dislike lima beans, 3/5 also dislike brussels sprouts. How many of the students like brussels sprouts but dislike lima beans?

(1) 120 students eat in the cafeteria
(2) 40 of the students like lima beans

OPEN DISCUSSION OF THIS QUESTION IS HERE: of-the-students-who-eat-in-a-certain-cafeteria-each-student-95246.html
[Reveal] Spoiler: OA

Last edited by Bunuel on 20 Mar 2014, 06:15, edited 1 time in total.
Renamed the topic, edited the question, added the OA and moved to DS forum.
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26 Apr 2006, 08:32
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I think it is D.

See attached picture.

1) x = 120, Hence 4*x/15 = 4*120/15 = 32
2) 1/3*x = 120 => x = 120, so 4*x/15 = 32
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beans.gif [ 3.56 KiB | Viewed 2865 times ]

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30 Oct 2006, 07:19
Hi guys,

some of us (like me for example ) have difficulty using the matrix method ... this is a tree branch method that may help with some questions.

Thought i'd share it here ...

Cheers,
Dennis
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BursselSprouts.JPG [ 32.93 KiB | Viewed 2735 times ]

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30 Oct 2006, 17:50
Good explanation by giddi77 and dennisquah
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Re: Of the students who eat in a certain cafeteria, each student [#permalink]

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20 Mar 2014, 05:28
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Re: Of the students who eat in a certain cafeteria, each student [#permalink]

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20 Mar 2014, 06:16
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Of the students who eat in a certain cafeteria, each student either likes or dislikes lima beans and each student either likes or dislikes brussels sprouts. Of these students, 2/3 dislike lima beans; and of those who dislike lima beans, 3/5 also dislike brussels sprouts. How many of the students like brussels sprouts but dislike lima beans?

Make a matrix:

Note that:
"2/3 dislike lima beans" means 2/3 of total dislike lima;
"of those who dislike lima beans, 3/5 also dislike brussels sprouts" means of those who dislike lima $$1-\frac{3}{5}=\frac{2}{5}$$ like sprout, or $$\frac{2}{3}*\frac{2}{5}=\frac{4}{15}$$ of total dislike lima but like sprouts. So to calculate # of students who dislike lima but like sprouts we should now total # of students (t).

(1) 120 students eat in the cafeteria --> $$t=120$$ --> $$x=\frac{4}{15}t=32$$. Sufficient.

(2) 40 of the students like lima beans --> total students who like lima + total students who dislike lima = total --> $$40+\frac{2}{3}t=t$$ --> $$t=120$$ --> $$x=\frac{4}{15}t=32$$. Sufficient.

OPEN DISCUSSION OF THIS QUESTION IS HERE: of-the-students-who-eat-in-a-certain-cafeteria-each-student-95246.html
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Re: Of the students who eat in a certain cafeteria, each student   [#permalink] 20 Mar 2014, 06:16
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