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Arithmetic with numbers

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by danjuma » Sat Oct 02, 2010 8:41 pm
1. Of the students who eat in a certain cafeteria, each student either likes or dislikes lima beans and each student either likes or dislikes brussel sprouts. Of these students, 2/3 dislikes lima beans, and of those who dislike lima beans, 3/5 dislike brussel sprouts. How many of the students like brussel sprouts but dislike lima beans?

a. 120 students eat in the cafe
b. 40 of te students like lima beans


Thanks.
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Source: — Data Sufficiency |

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by Rahul@gurome » Sat Oct 02, 2010 9:42 pm
Solution:
Let the total number of students be x.
So number of students who dislike lima beans is (2/3)x.
Also number of students who dislike both lima beans and brussel sprouts is (3/5) * (2/3)x = (2/5)x.
So number of students who like brussel sprouts but dislike lima beans is (2/3)x - (2/5)x = 4x/15.
We need this value 4x/15.

Consider first (1) alone.
x is 120.
So 4x/15 is 4/15 * 120 = 32.
Or (1) alone is sufficient.
Next consider (2) alone.
Since (2/3)x students dislike lima beans, x - (2/3)x = x/3 students like lima beans.
Or x/3 = 40.
So x = 120.
Or 4x/15 = 32.
So (2) alone is also sufficient.

The correct answer is (D).
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by narik11 » Sun Oct 03, 2010 10:56 am
Rahul@gurome wrote: So number of students who like brussel sprouts but dislike lima beans is (2/3)x - (2/5)x = 4x/15.
We need this value 4x/15.
Hi Rahul,
I am unable to get this part, can u explain it in detail.
Thanks in advance
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by GMATMadeEasy » Sun Oct 03, 2010 2:26 pm
I am also not very clear.

Answer from Manhattan is different :
https://www.manhattangmat.com/forums/of- ... t1967.html

Also, Can't we apply here two by two grid ?
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by Rahul@gurome » Sun Oct 03, 2010 7:32 pm
So number of students who like brussel sprouts but dislike lima beans is (2/3)x - (2/5)x = 4x/15.
We need this value 4x/15.
Hi Rahul,
I am unable to get this part, can u explain it in detail.
Thanks in advance
In set theory if n(S) is defined as the number of elements in set S, then
n(A - B) = n(A) - n(A intersection B).
Take A as the set of people who dislike lima beans and B as the set of people who dislike brussel sprouts.
So (A - B) is the set of people who dislike lima beans but who like brussel sprouts.
Also (A intersection B) is the set of people who dislike lima beans and who also dislike brussel sprouts.
Now n(A) = (2/3)x.
n(A intersection B) = (2/5)x.
Or n(A-B) = (2/3)x - (2/5)x = 4x/15.
The question is asking for this value n(A - B).
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by [email protected] » Fri Oct 22, 2010 12:44 am
I am also not very clear.

Answer from Manhattan is different :
https://www.manhattangmat.com/forums/of- ... t1967.html

Also, Can't we apply here two by two grid ?
yes v can apply 2grid here..
ppl who like lima beans.. LMY who don like LYN
ppl who like Brussels sprouts.. BY who don like BN

Statement 1: total students =120

LMY LMN total

BY 64

BN 16

Total 40 80 120


Statement 2: LMY total =40
so let t total be x
given 2/3 don lik lima beans
so from t grid.. 2/3x=40=x

So LMN =80

repeat the same/.. so ans d

am i clear to u??
hope it helps..
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