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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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04 Jun 2010, 00:29
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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
[Reveal] Spoiler: OA

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04 Jun 2010, 03:58
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dimitri92 wrote:
What is the best approach to tackle questions like these ?

The question is basically asking how many dislikes Lima beans but like Sprouts..

Given 2/3 of the entire student poplutation dont like LIMA.. of these 3/5 DONT like sprouts..so 2/5 like sprouts..

1) Given total students = 120 so 2/3 * 120 = 80 who dislikes lima beans out of these 2/5* 50 are the ones who likes sprouts but dislikes beans ... Hence Sufficient

2) 40 Likes beans so in thats means 120 is the total number of students... same logic as 1 -- Hence Sufficient

hope this helps..!
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04 Jun 2010, 07:42
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dimitri92 wrote:
What is the best approach to tackle questions like these ?

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?

I'd advise to make a table:
Attachment:

Lima-Sprouts.JPG [ 11.66 KiB | Viewed 28513 times ]

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.

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

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17 Aug 2010, 14:19
Bunuel wrote:
dimitri92 wrote:
What is the best approach to tackle questions like these ?

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?

I'd advise to make a table:
Attachment:
Lima-Sprouts.JPG

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).

I didn't understand this part...
means of those who dislike lima $$1-\frac{3}{5}=\frac{2}{5}$$ like sprout, or
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18 Aug 2010, 04:35
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onedayill wrote:
Bunuel wrote:
dimitri92 wrote:
What is the best approach to tackle questions like these ?

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?

I'd advise to make a table:
Attachment:
Lima-Sprouts.JPG

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).

I didn't understand this part...
means of those who dislike lima $$1-\frac{3}{5}=\frac{2}{5}$$ like sprout, or

If "of those who dislike lima beans, 3/5 (40%) also dislike brussels sprouts", hence rest of of those who dislike lima beans or 2/5 (60%) must like sprouts. As "2/3 of total dislike lima beans" then 2/3*2/5=4/15 of total dislike lima but like sprouts.

Hope it's clear.
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10 Oct 2010, 23:17
D

both 1 and 2 independently tell us what the total number of students is which in turn lets us calculate what is needed in the double-set matrix
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16 Oct 2010, 05:03
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yes...i got D too......
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Re: Of the students who eat in a certain cafeteria, each student [#permalink]

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

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01 Oct 2013, 02:12
The answer is D - Both statement are sufficient because we need to find the total number of students. And both the answer choices give us that.
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Of the students who eat in a certain cafeteria, each student [#permalink]

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29 Sep 2014, 21:57
Bunuel wrote:
dimitri92 wrote:
What is the best approach to tackle questions like these ?

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?

I'd advise to make a table:

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.

Let Total Student are t.
2/3 t dislike lima bean so 1/3 likes lima bean
Now 3/5 * 2/3 *t dislike sprout = 6/15*t dislike both LB and BS

Now we know that how many dislike and Like LB and that dislike both LB and BS
But we do not know how many like BS.
I struck here and selected E wrongly.

Can you please explain in easy language. I did not get the solution
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Re: Of the students who eat in a certain cafeteria, each student [#permalink]

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30 Sep 2014, 01:17
him1985 wrote:
Bunuel wrote:
dimitri92 wrote:
What is the best approach to tackle questions like these ?

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?

I'd advise to make a table:

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.

Let Total Student are t.
2/3 t dislike lima bean so 1/3 likes lima bean
Now 3/5 * 2/3 *t dislike sprout = 6/15*t dislike both LB and BS

Now we know that how many dislike and Like LB and that dislike both LB and BS
But we do not know how many like BS.
I struck here and selected E wrongly.

Can you please explain in easy language. I did not get the solution

We need to find how many students like brussels sprouts but dislike lima beans (box in red in my solution). Each statement is sufficient to find this value as shown above. Can you please tell me what is unclear there?
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Re: Of the students who eat in a certain cafeteria, each student [#permalink]

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22 Nov 2014, 09:45
I have a question , this is a subtle concept but i guess very important.

Like in this question , i was left little misled by the work either they like or dislike Limabean , and either they like or dislike Sproat. So i thought Neither will be 0

So when do we need to identify the Neither case . I thought here also there will be no neither case ie neither like limabean and sproat.

But i see all the 4 boxes in matrix are filled .

Bunuel wrote:
dimitri92 wrote:
What is the best approach to tackle questions like these ?

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?

I'd advise to make a table:
Attachment:
Lima-Sprouts.JPG

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.

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

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22 Nov 2014, 10:00
hanschris5 wrote:
I have a question , this is a subtle concept but i guess very important.

Like in this question , i was left little misled by the work either they like or dislike Limabean , and either they like or dislike Sproat. So i thought Neither will be 0

So when do we need to identify the Neither case . I thought here also there will be no neither case ie neither like limabean and sproat.

But i see all the 4 boxes in matrix are filled .

Bunuel wrote:
dimitri92 wrote:
What is the best approach to tackle questions like these ?

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?

I'd advise to make a table:
Attachment:
Lima-Sprouts.JPG

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.

Each student either likes or dislikes lima beans, means that there are students who does NOT like lima beans.
Each student either likes or dislikes brussels sprouts, means that there are students who does NO like brussels sprouts.

Thus, there might be students who does NOT like either lima beans or brussels sprouts.
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Re: Of the students who eat in a certain cafeteria, each student [#permalink]

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25 Jul 2015, 03:06
Bunuel wrote:
dimitri92 wrote:
What is the best approach to tackle questions like these ?

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?

I'd advise to make a table:
Attachment:
Lima-Sprouts.JPG

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.

how can we solve this using formula of set theory.

total= not like lima + not like sprouts - not like both
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Data sufficiency question - pls help with solution [#permalink]

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26 Jul 2015, 21:06
Hi,
Pls answer this question with explanation as I was unable to solve correctly.

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

(A) Statement (1) alone is sufficient, but statement (2) alone is not sufficient.
(B) Statement (2) alone is sufficient, but statement (1) alone is not sufficient.
(C) BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
(D) Each statement ALONE is sufficient.
(E) Statements (1) and (2) TOGETHER are NOT sufficient.
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Re: Of the students who eat in a certain cafeteria, each student [#permalink]

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27 Jul 2015, 04:49
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Priyanka402 wrote:
Hi,
Pls answer this question with explanation as I was unable to solve correctly.

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

(A) Statement (1) alone is sufficient, but statement (2) alone is not sufficient.
(B) Statement (2) alone is sufficient, but statement (1) alone is not sufficient.
(C) BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
(D) Each statement ALONE is sufficient.
(E) Statements (1) and (2) TOGETHER are NOT sufficient.

1. You did not choose the correct forum for your question. You had it filed under verbal section while this was a DS question.
2. Search for the question before posting it as there is a high probability of the same question to have been discussed before.
3. Format the question properly by following the posting guidelines.
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Re: Of the students who eat in a certain cafeteria, each student [#permalink]

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05 Dec 2015, 21:05
Bingo, I got it at my first attempt. its D.
One rule: If Answer is D, both statements will never conflict.
So, 2/3 dislikes lima beans; it means 1/3 likes lima beans. The number is then (1/3*120) 40.
And statement 2 provides us same number.
So answer is D even without much calculation.
Kudos...........
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Re: Of the students who eat in a certain cafeteria, each student [#permalink]

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09 Dec 2015, 11:32
moinbdusa wrote:
Bingo, I got it at my first attempt. its D.
One rule: If Answer is D, both statements will never conflict.
So, 2/3 dislikes lima beans; it means 1/3 likes lima beans. The number is then (1/3*120) 40.
And statement 2 provides us same number.
So answer is D even without much calculation.
Kudos...........

There are going to be cases where for value questions:
Stmnt 1 gives x=10
Stmnt 2 gives x=20
But still the answer is D.
@Bunuel...please correct me if i am wrong.
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Re: Of the students who eat in a certain cafeteria, each student [#permalink]

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29 Dec 2015, 23:49
Bunuel wrote:
dimitri92 wrote:
What is the best approach to tackle questions like these ?

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?

I'd advise to make a table:
Attachment:
The attachment Lima-Sprouts.JPG is no longer available

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.

I think drawing a correct table here is key. The table I drew was not wrong but it wasn't right for the question asked. So how to ensure that you make the right table?
Attachments

lima beans.JPG [ 17.25 KiB | Viewed 13751 times ]

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

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05 Apr 2016, 22:34
Attached is a visual that should help.
Attachments

Screen Shot 2016-04-05 at 10.33.10 PM.png [ 127.86 KiB | Viewed 10222 times ]

Re: Of the students who eat in a certain cafeteria, each student   [#permalink] 05 Apr 2016, 22:34

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