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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, 11:41
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B
C
D
E

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Question Stats:

81% (01:48) correct 19% (01:02) wrong based on 56 sessions
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.

OPEN DISCUSSION OF THIS QUESTION IS HERE: a-certain-high-school-with-a-total-enrollment-of-900-student-138300.html
[Reveal] Spoiler: OA

Last edited by Bunuel on 29 May 2015, 04:15, edited 1 time in total.
Added the OA.
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Re: A certain high school with a total enrollment of 900 [#permalink] New post 12 Nov 2009, 12:23
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: A certain high school with a total enrollment of 900 [#permalink] New post 12 Nov 2009, 12:45
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: A certain high school with a total enrollment of 900 [#permalink] New post 12 Nov 2009, 13:11
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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: A certain high school with a total enrollment of 900 [#permalink] New post 12 Nov 2009, 13:19
'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: A certain high school with a total enrollment of 900 [#permalink] New post 12 Nov 2009, 13:27
Thanks Bunuel for your wonderful explanation. I got it now.
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Re: A certain high school with a total enrollment of 900 [#permalink] New post 12 Nov 2009, 22:34
Thank you, guys, now I see what the trick was :)
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Re: A certain high school with a total enrollment of 900 [#permalink] New post 22 Oct 2014, 09:43
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Re: A certain high school with a total enrollment of 900 [#permalink] New post 29 May 2015, 04:05
Can somebody pls add OA to the timing module?
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Re: A certain high school with a total enrollment of 900 [#permalink] New post 29 May 2015, 04:16
Expert's post
Bunuel 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.


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.


OPEN DISCUSSION OF THIS QUESTION IS HERE: a-certain-high-school-with-a-total-enrollment-of-900-student-138300.html
_________________

NEW TO MATH FORUM? PLEASE READ THIS: ALL YOU NEED FOR QUANT!!!

PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

RESOURCES: [GMAT MATH BOOK]; 1. Triangles; 2. Polygons; 3. Coordinate Geometry; 4. Factorials; 5. Circles; 6. Number Theory; 7. Remainders; 8. Overlapping Sets; 9. PDF of Math Book; 10. Remainders; 11. GMAT Prep Software Analysis ; 12. SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) ; 12. Tricky questions from previous years.

COLLECTION OF QUESTIONS:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS ; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


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Re: A certain high school with a total enrollment of 900   [#permalink] 29 May 2015, 04:16
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