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A certain high school with a total enrollment of 900

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A certain high school with a total enrollment of 900 [#permalink] New post 12 Nov 2009, 12:41
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A certain high school with a total enrollment of 900 students held a science fair for three days last week. How many of the students enrolled in the high school attended the science fair on all three days?

(1) Of the students enrolled in the school, 30 percent attended the science fair on two or more days.
(2) Of the students enrolled in the school, 10 percent of those that attended the science fair on at least one day attended on all three days.

Friends, I would really appreciate your help.
OA after some discussion.
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Re: Tough one : Please help with this old paper test problem. [#permalink] New post 12 Nov 2009, 13:23
gmat620 wrote:
A certain high school with a total enrollment of 900 students held a science fair for three days last week. How many of the students enrolled in the high school attended the science fair on all three days?

(1) Of the students enrolled in the school, 30 percent attended the science fair on two or more days.
(2) Of the students enrolled in the school, 10 percent of those that attended the science fair on at least one day attended on all three days.

Friends, I would really appreciate your help.
OA after some discussion.


IMO, the answer is C.

I can't place a picture of overlapping sections here, but in words it would look like:
Let's say students who attend a fair only on the first day = A, only on the 2nd day = B, only on the 3rd day = C; 1 and 2 day = d; 2 and 3 day = e; 1 and 3 day = f; and X is the number of students who attended the science fair on all three days.
So, we have A+B+C+d+e+f+X=900. We need to find out X.

(1) we are only told that
d+e+f+X=0.3*900 ---> d+e+f+X=270. Not sufficient

(2) we are told that (A+B+C)*10%=X. Not sufficient.

(1)+(2)
A+B+C+d+e+f+X=900
d+e+f+X=270
(A+B+C)*10%=X
solving these three equations, we get that X=53. So, C is the answer.
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Re: Tough one : Please help with this old paper test problem. [#permalink] New post 12 Nov 2009, 13:45
Shelen wrote:
gmat620 wrote:
A certain high school with a total enrollment of 900 students held a science fair for three days last week. How many of the students enrolled in the high school attended the science fair on all three days?

(1) Of the students enrolled in the school, 30 percent attended the science fair on two or more days.
(2) Of the students enrolled in the school, 10 percent of those that attended the science fair on at least one day attended on all three days.

Friends, I would really appreciate your help.
OA after some discussion.


IMO, the answer is C.

I can't place a picture of overlapping sections here, but in words it would look like:
Let's say students who attend a fair only on the first day = A, only on the 2nd day = B, only on the 3rd day = C; 1 and 2 day = d; 2 and 3 day = e; 1 and 3 day = f; and X is the number of students who attended the science fair on all three days.
So, we have A+B+C+d+e+f+X=900. We need to find out X.

(1) we are only told that
d+e+f+X=0.3*900 ---> d+e+f+X=270. Not sufficient

(2) we are told that (A+B+C)*10%=X. Not sufficient.

(1)+(2)
A+B+C+d+e+f+X=900
d+e+f+X=270
(A+B+C)*10%=X
solving these three equations, we get that X=53. So, C is the answer.


yes even I did the same but OA is
[Reveal] Spoiler:
E
. I think there's something missing. The sheer simplicity of this question is the trap. Let us see if any one of us can find that out or else we would conclude that the OA is wrong. Anyways, thanx for your precious time. It boosted my confidence to some extent.
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Re: Tough one : Please help with this old paper test problem. [#permalink] New post 12 Nov 2009, 14:11
gmat620 wrote:
A certain high school with a total enrollment of 900 students held a science fair for three days last week. How many of the students enrolled in the high school attended the science fair on all three days?

(1) Of the students enrolled in the school, 30 percent attended the science fair on two or more days.
(2) Of the students enrolled in the school, 10 percent of those that attended the science fair on at least one day attended on all three days.

Friends, I would really appreciate your help.
OA after some discussion.


The trick here is that we don't know whether all of 900 students attended on at least one day. Meaning that there can be # of students which didn't took part in the fair.

So we have following groups:
A. Attended on only one day
B. Attended on two days exactly
C. Attended on all three days
D. Not attended.
And the sum of these groups is A+B+C+D=900. We want to determine value of C.

(1) 30% of 900 attended 2 or more days. --> 270 attended 2 or more days. --> B+C=270. B? Not insufficient.

(2) 10 percent of those that attended the science fair on at least one day attended on all three days. --> 10%*(A+B+C)=C --> A+B=9C. A, B? Not sufficient.

(1)+(2) B+C=270, A+B=9C and A+B+C+D=900. Three equations four unknowns. Not sufficient.

Answer: E.
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Re: Tough one : Please help with this old paper test problem. [#permalink] New post 12 Nov 2009, 14:19
'So, we have A+B+C+d+e+f+X=900. We need to find out X.'
You make an assumption here that everyone attends atleast one science fair.There could be students not attending on any given day as well. We do not know that count therefore you cannot take the total as 900- if 40 did NOT attend on any days -it would be 860
i hope that helps!!!
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Re: Tough one : Please help with this old paper test problem. [#permalink] New post 12 Nov 2009, 14:27
Thanks Bunuel for your wonderful explanation. I got it now.
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Re: Tough one : Please help with this old paper test problem. [#permalink] New post 12 Nov 2009, 23:34
Thank you, guys, now I see what the trick was :)
Re: Tough one : Please help with this old paper test problem.   [#permalink] 12 Nov 2009, 23:34
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