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# If 20 percent of the students at a certain school went to a camping tr

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Manager
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If 20 percent of the students at a certain school went to a camping tr  [#permalink]

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20 Mar 2011, 21:13
4
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Difficulty:

65% (hard)

Question Stats:

64% (02:12) correct 36% (02:11) wrong based on 161 sessions

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If 20 percent of the students at a certain school went to a camping trip and took more than \$100, and 75 percent of the students who went to the camping trip did not take more than \$100, what percentage of the students at the school went to the camping trip?

(A) 95
(B) 90
(C) 85
(D) 80
(E) 75
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Re: If 20 percent of the students at a certain school went to a camping tr  [#permalink]

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20 Mar 2011, 23:54
1
Let x be the number of students in the school. 0.2x students went to the trip and took more than 100\$. They compose (100-75)=25% of all students who went to the trip. Therefore the toal of 0.2x/0.25=0.8x students went to the camping which is 80%.

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Re: If 20 percent of the students at a certain school went to a camping tr  [#permalink]

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21 Mar 2011, 00:09
2
X -> Total # of students

Y -> went to camp

0.2x -> Camp with > \$100

0.75 * y -> Camp with < 100

So 0.25 of y took > \$100

0.25y = 0.2x

=> y/x = 20/25 * 100 = 80%

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Re: If 20 percent of the students at a certain school went to a camping tr  [#permalink]

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07 Jun 2011, 08:37
1
dreambeliever wrote:
If 20 percent of the students at a certain school went to a camping trip and took more than \$100, and 75 percent of the students who went to the camping trip did not take more than \$100, what percentage of the students at the school went to the camping trip?

(A) 95
(B) 90
(C) 85
(D) 80
(E) 75

Better way to approach these kind of problems are pick a simple number (total) say we have a total 100 students. Now read the bolded part carefully- it prompts you immediately that (X-0.75X)= 0.25X (where x is the % students going for the camping) is the % total students (which is same as 20% of total students).

So 0.25X = 20% of 100 -> X= 80 so D
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Re: If 20 percent of the students at a certain school went to a camping tr  [#permalink]

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14 Jun 2011, 09:16
Can someone help me understand the question?
I must be sounding silly however my doubt is,
If 20% of students at a certain school went to a camping trip, then what is the point in asking the percentage of students at school who went to the camping trip?
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Re: If 20 percent of the students at a certain school went to a camping tr  [#permalink]

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14 Jun 2011, 11:15
1
shm0401 wrote:
Can someone help me understand the question?
I must be sounding silly however my doubt is,
If 20% of students at a certain school went to a camping trip, then what is the point in asking the percentage of students at school who went to the camping trip?

Genuine doubt:

[highlight]If 20 percent of the students at a certain school went to a camping trip AND took more than \$100[/highlight], and 75 percent of the students who went to the camping trip did not take more than \$100, what percentage of the students at the school went to the camping trip?

The highlighted part is one giant sentence and should be read together.

e.g.
100- Students
20- Students went to the trip AND also took more than \$100

Say, x students went to the trip.
So, x-20 will be the percent of student who took less than or equal to \$100 with them.

And it is given that this x-20=75% who went to the picnic
OR
x-20=0.75x
x=80
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Re: If 20 percent of the students at a certain school went to a camping tr  [#permalink]

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06 Sep 2017, 19:08
Solved this one in another way, as in, by using the conditional probability formula.

Let there be 2 events:
S -> student went to the camping trip
C -> student took more than 100 bucks

So, it is a given fact that:

1) P (S and C) = 0,2
2) P (not C | S) = 0,75 -> 1 - P (C | S) = P (not C | S) -> P (C | S) = 0,25

According to the mentioned formula: P (C | S) = P(C and S) / P(S)

P(S) = P( C and S )/ P (C | S) -> 0,2/0,25 -> 80% -> answer D
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Re: If 20 percent of the students at a certain school went to a camping tr  [#permalink]

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07 Sep 2017, 01:02
Let the total number of students be 100 .
The number of students who went to camping trip with more than \$100 =20
Let the number of students who went to shopping = x
Now we have from the information given
X-0.75X=20
X=80
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Re: If 20 percent of the students at a certain school went to a camping tr  [#permalink]

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13 Jan 2018, 09:49
Number of students must be an integer. So, 75% of the students must be an integer. Only option D satisfies.
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Re: If 20 percent of the students at a certain school went to a camping tr   [#permalink] 13 Jan 2018, 09:49
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