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Of the students who eat in a certain cafeteria, each student either 06 Sep 2021, 06:11
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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

No of students who dislike lima beans = 2/3 * 120 = 80
Out of this 80 students who dislike lima beans, no of students who dislike brussels sprouts = 3/5 * 80 = 48
That means, 80 - 48 = 32 students are there who like brussels sprouts but dislike lima beans
Hence, statement 1 is sufficient.

(2) 40 of the students like lima beans

2/3 of the students dislike lima beans means that 1/3 of the students like lima beans.

From statement 2, we can say that 1/3 of total students = 40 ==> Total no of students =40*3 = 120 which is same info as Statement 1.
Hence sufficient.

Option D is the answer.

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Of the students who eat in a certain cafeteria, each student either 10 Mar 2022, 07:44
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dimitri92
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

Show Spoiler
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del5.jpg
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Answer: Option D

Step-by-Step Video solution by GMATinsight

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Of the students who eat in a certain cafeteria, each student either 09 Apr 2022, 00:03
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we only know about 2/3 of the students , what they like and dislike but we don't know about the rest 1/3 of the students. In 1/3rd students , there could be students who like sprouts only or who like brussels only or who like them both. So as per my understanding none of the options are sufficient
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Of the students who eat in a certain cafeteria, each student either 16 Nov 2022, 18:12
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KarishmaB
dimitri92
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

Show Spoiler
Attachment:
del5.jpg

"Of the students who eat in a certain cafeteria, ... "
Say T students eat in the cafeteria

"Of these students, 2/3 dislike lima beans"
(2/3)*T dislike Lima

"and of those who dislike lima beans, 3/5 also dislike brussels sprouts"
Of (2/3)T, (3/5) also dislike brussels so (3/5)*(2/3)T = (2/5)T dislike brussels
We don't know about the rest of the (T/3) that how many of them dislike brussels.

"How many of the students like brussels sprouts but dislike lima beans?"
(2/3)T dislike Lima and (2/5)th of these like Brussels (since (3/5)th of these do not like Brussels)
So (4/15)T dislike Lima but like Brussels.

(1) 120 students eat in the cafeteria
This gives us the value of T. We need to find (4/15)T which we can now. Sufficient

(2) 40 of the students like lima beans
(2/3)T dislike Lima so (1/3)T like Lima. If (1/3)T = 40, we get T = 120.
Again, we can now find (4/15)T. Sufficient.

Answer (D)
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KarishmaB
For "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." I originally thought that this meant you cannot dislike both and you cannot like both, so I out zeroes in for likes Brussel Sprouts & Lima Beans and zeroes in for dislikes brussels sprouts and dislikes lima beans. Then, I see that these are both options. So, what does "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" mean then? Is it just a long way of saying that there are no other choices besides lima beans and Brussel sprouts?
Thank you for your time.
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Of the students who eat in a certain cafeteria, each student either 16 Nov 2022, 21:15
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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

Show Spoiler
Attachment:
del5.jpg

"Of the students who eat in a certain cafeteria, ... "
Say T students eat in the cafeteria

"Of these students, 2/3 dislike lima beans"
(2/3)*T dislike Lima

"and of those who dislike lima beans, 3/5 also dislike brussels sprouts"
Of (2/3)T, (3/5) also dislike brussels so (3/5)*(2/3)T = (2/5)T dislike brussels
We don't know about the rest of the (T/3) that how many of them dislike brussels.

"How many of the students like brussels sprouts but dislike lima beans?"
(2/3)T dislike Lima and (2/5)th of these like Brussels (since (3/5)th of these do not like Brussels)
So (4/15)T dislike Lima but like Brussels.

(1) 120 students eat in the cafeteria
This gives us the value of T. We need to find (4/15)T which we can now. Sufficient

(2) 40 of the students like lima beans
(2/3)T dislike Lima so (1/3)T like Lima. If (1/3)T = 40, we get T = 120.
Again, we can now find (4/15)T. Sufficient.

Answer (D)

KarishmaB
For "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." I originally thought that this meant you cannot dislike both and you cannot like both, so I out zeroes in for likes Brussel Sprouts & Lima Beans and zeroes in for dislikes brussels sprouts and dislikes lima beans. Then, I see that these are both options. So, what does "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" mean then? Is it just a long way of saying that there are no other choices besides lima beans and Brussel sprouts?
Thank you for your time.
Show more

No, it is along way of saying that there is no student who neither likes nor dislikes lima beans i.e. each student must fall in one of two regions - 'like beans' or 'dislike beans.' There is no 'neutral' region in which one could have no strong feeling for lima beans.
Same for Brussel sprouts.
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Of the students who eat in a certain cafeteria, each student either 03 Mar 2026, 13:24
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dimitri92
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
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Show Spoiler
D




Nick Slavkovich, GMAT/GRE tutor with 20+ years of experience

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Of the students who eat in a certain cafeteria, each student either 11 Apr 2026, 01:57
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Explanation:
This is a classic overlapping sets problem. The most efficient way to organize this data is using a Double-Matrix (Cross-Grid).
Step 1: Set up the matrix with the given ratios
Let T = Total students.
    []2/3 of the students dislike Lima Beans. (Therefore, 1/3 like them). []Of those who dislike Lima Beans (2/3T), 3/5 also dislike Brussels Sprouts.
  • Calculation for "Dislike Both": $(3/5) * (2/3)T = 6/15T = 2/5T$.
Like SproutsDislike SproutsTotal Lima
Like Lima1/3 T
Dislike LimaTARGET2/5 T2/3 T
Total SproutsT
Step 2: Solve for the Target Cell
To find the number of students who Like Sprouts but Dislike Lima, we subtract the "Dislike Both" cell from the "Total Dislike Lima" column:
Target = (2/3)T - (2/5)T$
Target = (10/15)T - (6/15)T = 4/15 T$
Conclusion: We just need the value of T to solve.


Evaluate Statement (1):
(1) 120 students eat in the cafeteria.
This gives us T = 120.
Answer = (4/15) * 120 = 32.

Sufficient.

Evaluate Statement (2):
(2) 40 of the students like lima beans.
From our matrix, the "Like Lima" total is $1/3 T.
Since we have the total, we can find the target.

Sufficient.

Final Answer: D (Each statement alone is sufficient).
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