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

Question

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.

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GMATinsight · Answer

Question: Probability of 1 pencil students = ?

Statement 1  : 110 students are expected to get at least one pencil.
i.e. Total Students = 110 but the students with exactly 1 pencil is unknown hence
  NOT SUFFICIENT

Statement 2  : 60 students are expected to get at least two pencils.

i.e Students with 2 pencils or more = 60
But total students are unknown hence
  NOT SUFFICIENT

COmbining the statements
  We get, 
Total = 110
Two or more pencils = 60
1 pencil Students = 110-60 = 50
  SUFFICIENT

Answer: Option C

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ajay0520 · Answer

statement: each student gets at least one pencil in exam hall
Question is asking probability for student getting exactly 1 pencil.
 here answer will be P= student getting exactly 1 pencil/ total no of student
Statement1: 110 students are expected to get  at least one pencil .
this tells us no of students=110 as all the students are supposed to get at least one pencil as said in question

Statement 2:60 students are expected to get   at least two pencils.

this gives us number of students getting 2 or more pencil but no information about total no of students hence not sufficient.

ST1+ST2: no of students getting exactly 1 pencil= students getting at least one pencil- students that get at least two pencils.
= 50

hence probability=50/110
=5/11
hence  answer c

NextstopISB · Answer

Step 1: Define variables 
Let N be the total number of students. 
Let X be the number of students who receive exactly one pencil. 
Let Y be the number of students who receive at least two pencils.

Step 2: Translate given statements

(1) 110 students are expected to get at least one pencil. 
- This means N = 110.

(2) 60 students are expected to get at least two pencils. 
- This means Y = 60.

Step 3: Find X 
Since every student gets at least one pencil, the number of students who get exactly one pencil is: 
X = N - Y 
X = 110 - 60 
X = 50

Step 4: Compute probability 
The probability that a randomly chosen student gets exactly one pencil is: 
P(X) = X / N = 50 / 110 = 5/11

Final Answer: 5/11

Missinga · Answer

To find: probability that a student gets exactly one pencil in the exam hall

(1) 110 students are expected to get at least one pencil...
 Students getting 1 or more than 1 pencil= 110 
Insufficient

(2) 60 students are expected to get at least two pencils...
Students getting 2 or more pencils= 60 
Insufficient

Taking (1)&(2) together 
Students getting exactly 1 pencil= (Students getting 1 or more than 1 pencil)-(Students getting 2 or more than 2 pencils) 
= (110)-(60)= 50

Probability= 50/110= 5/11

Answer: C

ManifestDreamMBA · Answer

If each student gets at least one pencil in the exam hall, then Total number of students is same as students who get atleast one pencil
 P = \frac{{Student gets exactly 1 Pencil}}{{All students} }  OR  \frac{{Student gets exactly 1 Pencil}}{{Students get atleast one pencil} }

Statement 1
Given 110 students are expected to get at least one pencil, All students = 110
 P = \frac{{Student gets exactly 1 Pencil}}{{All students} } 
 P = \frac{{Student gets exactly 1 Pencil}}{110 } 
We don't know the numerator
Insufficient

Statement 2
Given 60 students are expected to get at least two pencils
We don't know anything about students who gets exactly one pencil
Insufficient

Combined, we have students who get at least one pencil = 110 and students who get at least two pencil = 60. 
This means exactly students who get exactly one pencil = 110-60 = 50
Using 1, we know 
 P = \frac{{Student gets exactly 1 Pencil}}{110 } 
P = 50/110
Answer C

phil2804 · Answer

Hello  Bunuel

How can we be sure that the numbers in 1 & 2 are correct. I'd translate "expect" (= could be) but not is 100% sure.
If the Question would not be stating expect, I would say this question is really easy and not 655-705 material.
Please help here!

KR

anmolagarwal900 · Answer

Students are expected to get atleast 1 pencil - they could get 2/3/4, so remainder 50 maynot just get 1 pencil hence IMO answer could be E.

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

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GMAT Data Sufficiency (DS) Questions

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

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