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# A certain high school with a total enrollment of 900 student

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Math Expert
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A certain high school with a total enrollment of 900 student [#permalink]

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03 Sep 2012, 06:10
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Question Stats:

70% (01:34) correct 30% (01:31) wrong based on 1281 sessions

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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.

Practice Questions
Question: 34
Page: 277
Difficulty: 650
[Reveal] Spoiler: OA

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Math Expert
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Re: A certain high school with a total enrollment of 900 student [#permalink]

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03 Sep 2012, 06:11
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SOLUTION

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?

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 take part in the fair.

So we have the 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 the value of C.

(1) Of the students enrolled in the school, 30 percent attended the science fair on two or more days. So, 900*0.3=270 attended 2 or more days --> B+C=270. Not sufficient.

(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 --> 10%*(A+B+C)=C --> A+B=9C. Not sufficient.

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

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Re: A certain high school with a total enrollment of 900 student [#permalink]

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03 Sep 2012, 06:37
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Each statement alone is clearly not sufficient.

Statement (1) + (2) together:
900 * 0.3 = 270 students attended the fair on two or more days.
Since we don't know the number of students that didn't attend the fair at all or on one day, we don't know, how many students attended the fair on all three days.

It could be: 30 students on all three days, 240 students on two days, 30 students on one day, 600 students never.
It could be: 60 students on all three days, 210 students on two days, 330 students on one day, 300 students never.

Answer is E, both statements together not sufficient.

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Re: A certain high school with a total enrollment of 900 student [#permalink]

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19 Dec 2013, 05:06
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Bunuel 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.

Practice Questions
Question: 34
Page: 277
Difficulty: 650

Stmt 1: 30 % attended on two or more days. so 270 students attended at least two days, but you get nothing about three days. IS

Stmt 2: 10 % of those that attended 1 day attended all three days. Since you don't know whether all 900 students attented once, this doesn't help. IS

Together: I still don't know nothing about the number of students in stmt 2 and stmt 1 doesn't help here. So still IS. Hence E.

Looks more complicated than it actually was. some logic thinking and the answer was there

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A certain high school with a total enrollment of 900 student [#permalink]

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20 Dec 2015, 07:07
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Bunuel wrote:
SOLUTION

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?

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 take part in the fair.

So we have the 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 the value of C.

(1) Of the students enrolled in the school, 30 percent attended the science fair on two or more days. So, 900*0.3=270 attended 2 or more days --> B+C=270. Not sufficient.

(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 --> 10%*(A+B+C)=C --> A+B=9C. Not sufficient.

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

Dear Bunuel,

Could you be so kind to help me to puzzle out?

(1) Of the students enrolled in the school, 30 percent attended the science fair on two or more days.

as i understand if 30% of students attended on two or more days, then more days=3 days,
so why it is not sufficient?
OR
maybe i'm having problem with wording
and
INSTEAD OF "on two days" it must to be "on the 2nd day"?

(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.

even if 10% of 900 students attended all three days, there are may be some other students who attended only one day or two days, i.e. there are might be additional number of students except 10%; for instance: 25% of 900 students may attend on 3rd day, so 10%+25%

Thanks!

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Re: A certain high school with a total enrollment of 900 student [#permalink]

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20 Dec 2015, 11:34
studentsensual wrote:
Bunuel wrote:
SOLUTION

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?

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 take part in the fair.

So we have the 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 the value of C.

(1) Of the students enrolled in the school, 30 percent attended the science fair on two or more days. So, 900*0.3=270 attended 2 or more days --> B+C=270. Not sufficient.

(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 --> 10%*(A+B+C)=C --> A+B=9C. Not sufficient.

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

Dear Bunuel,

Could you be so kind to help me to puzzle out?

(1) Of the students enrolled in the school, 30 percent attended the science fair on two or more days.

as i understand if 30% of students attended on two or more days, then more days=3 days,
so why it is not sufficient?
OR
maybe i'm having problem with wording
and
INSTEAD OF "on two days" it must to be "on the 2nd day"?

(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.

even if 10% of 900 students attended all three days, there are may be some other students who attended only one day or two days, i.e. there are might be additional number of students except 10%; for instance: 25% of 900 students may attend on 3rd day, so 10%+25%

Thanks!

Of the students enrolled in the school, 30 percent, attended the science fair on two or more days. This means that 270 people attended the science fair on two days exactly or on all three days. For example, 100 people could have attended on 2 days exactly out of 3 and 170 on all 3 days.
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Re: A certain high school with a total enrollment of 900 student [#permalink]

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09 Oct 2017, 12:21
Hi- I have a question: If it was given that everyone attended at least 1 day, would the answer be C?

My work in such a scenario:
1) 270 students attended 2 or 3 days = 630 students attended 1 day only. Not sufficient.
2) Not sufficient.

1 and 2) 10% of the 630 students that attended 1 day = 63 students attended all 3 days. Sufficient.

Is my math in this scenario correct?
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Re: A certain high school with a total enrollment of 900 student   [#permalink] 09 Oct 2017, 12:21
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