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sanjay
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Post subject: DS problem  Posted: Sun Nov 01, 2009 1:50 pm |
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GMAT prep problem. Test-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 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?
A. 120 students eat in the cafeteria.
B. 40 of the students like lima beans.
OA is C.
I would appreciate if someone can explain me how to solve it.
Sanjay
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alok.sarsidharan
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Post subject: Re: DS problem Posted: Mon Nov 02, 2009 9:14 am |
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Are you sure the answer is C ??? I was getting D as the answer, each statement alone is sufficient.
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sanjay
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Post subject: Re: DS problem Posted: Tue Nov 03, 2009 8:11 am |
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I am so so sorry!!!
Yes, the answer is "D".
I'd appreciate your effort, it you please explain me how to solve it.
Sanjay
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lalitkc
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Post subject: Re: DS problem Posted: Fri Nov 06, 2009 3:29 am |
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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?
A. 120 students eat in the cafeteria.
B. 40 of the students like lima beans.
Let the total students who eat in the cafeteria be 'x'.
therefore we can say that 2x/3 dislike lima beans
and 3/5 (2x/3) = 2x/5 dislike both lima beans and brussels sprouts.
So students who dislike only lima beans (and like brussels sprouts) = 2x/3 - 2x/5 = 4x/15 ---- (i)
Statement 1 => x = 120
From (i) => Students who like brussel sprouts but dislike Lima beans = 4x/15 = 32
Hence Statement 1 is sufficient.
Statement 2 => 40 students like Lima beans = (x-40) students dislike Lima Beans = 2x/3 ==> x = 120 which is statement 1. Hence Statement 2 is sufficient
Answer : D
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sanjay
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Post subject: Re: DS problem Posted: Fri Nov 06, 2009 8:24 am |
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Makes sense now! Seems so easy once you get to know it.
Thanks for helping me out, Lalit.
Sanjay
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lalitkc
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Post subject: Re: DS problem Posted: Mon Nov 16, 2009 2:15 pm |
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Let L = students who like Lima beans ; L’ = students who dont like Lima beans
B = students who like Brussel beans B’ = students who don’t like Brussel beans
S = total number of students who eat in the cafeteria
Given: L’ = 2/3 S ==> L = 1/3 S -- eqn 1
Students who dislike both L & B = B’L’= 3/5 L’ ==> students who like B but dislike L = BL’ = 2/5 L’ –- eqn 2
Question is: Find BL’
St 1 ==> S = 120 ==> From eqn 1 & 2, we can find BL’. So Stmt 1 is sufficient
St 2 ==> L = 40 ==> L’ = 80 ==> From eqn 2 we can find BL’. So Stmt 2 is sufficient
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Ben Ku
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Post subject: Re: DS problem Posted: Thu Dec 24, 2009 6:29 pm |
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lalitkc offers two good solutions. I will only add that setting up a double-set matrix as described in our classes and Strategy Guides is a helpful approach to this problem. Let me know if there are additional questions. Thanks!
_________________
Ben Ku
Instructor
ManhattanGMAT
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