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Senior Manager  Joined: 10 Jul 2013
Posts: 282
If each student gets at least one pencil in the exam hall, w  [#permalink]

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Difficulty:   65% (hard)

Question Stats: 53% (01:18) correct 47% (00:58) wrong based on 245 sessions

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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.

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 ,
Intern  Joined: 16 Jun 2010
Posts: 17
Re: if each student gets at least one pencil in the exam hall  [#permalink]

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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

1.
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Re: if each student gets at least one pencil in the exam hall  [#permalink]

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1
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

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 ,

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 [ 17.47 KiB | Viewed 2735 times ]

So the number of students who got exactly one pencil is the middle portion. ie 110 - 60 = 50. So the answer is C
Senior Manager  Joined: 10 Jul 2013
Posts: 282
Re: if each student gets at least one pencil in the exam hall  [#permalink]

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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

1.

yes......... pretty good work .............
really good work Senior Manager  Joined: 10 Jul 2013
Posts: 282
Re: if each student gets at least one pencil in the exam hall  [#permalink]

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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

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 ,

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
Senior Manager  Status: 1,750 Q's attempted and counting
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Re: if each student gets at least one pencil in the exam hall  [#permalink]

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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.
Math Expert V
Joined: 02 Sep 2009
Posts: 59590
Re: if each student gets at least one pencil in the exam hall  [#permalink]

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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.

Hope it's clear.
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Re: If each student gets at least one pencil in the exam hall, w  [#permalink]

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_________________ Re: If each student gets at least one pencil in the exam hall, w   [#permalink] 29 Jul 2017, 07:40
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