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If each student gets at least one pencil in the exam hall, w

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If each student gets at least one pencil in the exam hall, w [#permalink] New post 09 Aug 2013, 13:10
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If each student gets at least one pencil in the exam hall, what is the probability that a student gets exactly one pencil in the exam hall?

(1) 110 students are expected to get at least one pencil.
(2) 60 students are expected to get at least two pencils.

[Reveal] Spoiler:
st1 implies there are 110 students in the exam hall and everyone of them will get exactly one pencil.
but its not sufficient.
st2 tells, 60 students are expected to get at least two pencils. this not sufficient alone.
Now from both statements,
110 = exactly one + more than one
or 110 = exactly one + 60
or, exactly one = 50 .
so the probability of getting exactly one = 50/110 = 5/11 ,
so Answer (C)
[Reveal] Spoiler: OA

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Re: if each student gets at least one pencil in the exam hall [#permalink] New post 10 Aug 2013, 19:05
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x: Number of students get at least 1 pencil
a: Number of students get exactly 1 pencil
b: Number of students get more than 1 pencil
x= a + b

to find the probability that a student gets exactly one pencil, we need to know the number of student get exactly 1 pencil and the number of student get at least 1 pencil.
1. 110 students are expected to get at least one pencil: x=a + b = 110 --> insufficient

2. 60 students are expected to get at least two pencils or the number of student get more than 1 pencil b = 60 --> insufficient.

(1) + (2): we have: x = a + b = 110 and b = 60 => a=50

The probability that a student gets exactly 1 pencil is: 50/110 = 5/11 --> sufficient

The answer is C



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Re: if each student gets at least one pencil in the exam hall [#permalink] New post 11 Aug 2013, 00:12
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Asifpirlo wrote:
if each student gets at least one pencil in the exam hall, what is the probability that a student gets exactly one pencil in the exam hall?
(1) 110 students are expected to get at least one pencil
(2) 60 students are expected to get at least two pencils

[Reveal] Spoiler:
st1 implies there are 110 students in the exam hall and everyone of them will get exactly one pencil.
but its not sufficient.
st2 tells, 60 students are expected to get at least two pencils. this not sufficient alone.
Now from both statements,
110 = exactly one + more than one
or 110 = exactly one + 60
or, exactly one = 50 .
so the probability of getting exactly one = 50/110 = 5/11 ,
so Answer (C)


Each student gets one pencil . and 110 students got one pencil. There are 110 students in the exam hall.

Statement A:- 110 students gets atleast one pencil in the exam hall. With this we can only get the number of students in the exam hall.But not the number of students who got exactly one pencil. So A and D are out

Statement B:- 60 students are expected to get atleast two pencils in the exam hall. With this statement ALONE we will not be able to get the number of students who got exactly two pencils in the exam hall. So B is out.

Both statements combined. we get that 110 students get atleast one pencil. and 60 students get atleast two pencils. Refer to the diagram below

Attachment:
set.jpg
set.jpg [ 17.47 KiB | Viewed 1011 times ]


So the number of students who got exactly one pencil is the middle portion. ie 110 - 60 = 50. So the answer is C
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Re: if each student gets at least one pencil in the exam hall [#permalink] New post 03 Sep 2013, 04:34
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avohden wrote:
how does the fact that there may be other students that have three or more pencils effect the probability? Seems that more information is needed, thus E seems appropriate.


The point is that we only need the total # of students and the # of students with exactly one pencil to get the probability.

If each student gets at least one pencil in the exam hall, what is the probability that a student gets exactly one pencil in the exam hall?

(1) 110 students are expected to get at least one pencil. Stem says that each student gets at least one pencil, thus there are total of 110 students. We don't know how many students get exactly one pencil. Not sufficient.

(2) 60 students are expected to get at least two pencils. Not sufficient.

(1)+(2) 110 students get at least one pencil (1 or more) and 60 students get at least two pencils (2 or more), thus 110-60=50 get exactly one pencil (50 get exactly one pencil + 60 get 2 or more = 110 students get 1 or more). Therefore the probability is 50/110. Sufficient.

Answer: C.

Hope it's clear.
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Re: if each student gets at least one pencil in the exam hall [#permalink] New post 11 Aug 2013, 11:25
thutran wrote:
x: Number of students get at least 1 pencil
a: Number of students get exactly 1 pencil
b: Number of students get more than 1 pencil
x= a + b

to find the probability that a student gets exactly one pencil, we need to know the number of student get exactly 1 pencil and the number of student get at least 1 pencil.
1. 110 students are expected to get at least one pencil: x=a + b = 110 --> insufficient

2. 60 students are expected to get at least two pencils or the number of student get more than 1 pencil b = 60 --> insufficient.

(1) + (2): we have: x = a + b = 110 and b = 60 => a=50

The probability that a student gets exactly 1 pencil is: 50/110 = 5/11 --> sufficient

The answer is C



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yes......... pretty good work .............
really good work :)
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Re: if each student gets at least one pencil in the exam hall [#permalink] New post 11 Aug 2013, 11:26
clearwater wrote:
Asifpirlo wrote:
if each student gets at least one pencil in the exam hall, what is the probability that a student gets exactly one pencil in the exam hall?
(1) 110 students are expected to get at least one pencil
(2) 60 students are expected to get at least two pencils

[Reveal] Spoiler:
st1 implies there are 110 students in the exam hall and everyone of them will get exactly one pencil.
but its not sufficient.
st2 tells, 60 students are expected to get at least two pencils. this not sufficient alone.
Now from both statements,
110 = exactly one + more than one
or 110 = exactly one + 60
or, exactly one = 50 .
so the probability of getting exactly one = 50/110 = 5/11 ,
so Answer (C)


Each student gets one pencil . and 110 students got one pencil. There are 110 students in the exam hall.

Statement A:- 110 students gets atleast one pencil in the exam hall. With this we can only get the number of students in the exam hall.But not the number of students who got exactly one pencil. So A and D are out

Statement B:- 60 students are expected to get atleast two pencils in the exam hall. With this statement ALONE we will not be able to get the number of students who got exactly two pencils in the exam hall. So B is out.

Both statements combined. we get that 110 students get atleast one pencil. and 60 students get atleast two pencils. Refer to the diagram below

Attachment:
set.jpg


So the number of students who got exactly one pencil is the middle portion. ie 110 - 60 = 50. So the answer is C


yes......... pretty good work .............
really good work :) especially the diagram
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Re: if each student gets at least one pencil in the exam hall [#permalink] New post 31 Aug 2013, 22:56
how does the fact that there may be other students that have three or more pencils effect the probability? Seems that more information is needed, thus E seems appropriate.
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Re: if each student gets at least one pencil in the exam hall   [#permalink] 31 Aug 2013, 22:56
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