Real Numbers (IMO Mathematics Olympiad Class 10): Questions 81  85 of 89
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Question number: 81
» Real Numbers
Question
28 integers are chosen from the interval [104, 208]. Show that there exit two of them having a common prime divisor.
Choices
Choice (4)  Response  

a.  2 

b.  0 

c.  3 

d.  1 

Question number: 82
» Real Numbers
Question
Choices
Choice (4)  Response  

a.  2 

b.  0 

c.  3 

d.  1 

Question number: 83
» Real Numbers
Question
a, b, c are real numbers such that and Prove that . When does the equality hold?
Choices
Choice (4)  Response  

a.  Equality hold when and 

b.  Equality hold when and 

c.  Equality hold when and 

d.  Equality hold when and 

Question number: 84
» Real Numbers
Question
Three men, four women and six children can complete a work in seven days. A women does double the work a man does and a child does half the work a man does. How many women alone can complete the work in 7 days?
Choices
Choice (4)  Response  

a.  8 

b.  14 

c.  7 

d.  12 

Question number: 85
» Real Numbers
Question
There are two examination rooms P and Q. If 10 candidates are sent from P to Q, the number of students in each room is the same. If 20 candidates are sent from Q to P, the number of students in P is double the number of students in Q. Find the number of students in each room.
Choices
Choice (4)  Response  

a.  P = 95, Q = 70 

b.  P = 100, Q = 80 

c.  P = 110, Q = 60 

d.  P = 60, Q = 40 
