Real Numbers (IMO- Mathematics Olympiad Class 10): Questions 81 - 85 of 89

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Question number: 81

» Real Numbers

MCQ▾

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

MCQ▾

Question

Equation

Choices

Choice (4) Response

a.

2

b.

0

c.

3

d.

1

Question number: 83

» Real Numbers

MCQ▾

Question

a, b, c are real numbers such that Equation and Equation Prove that Equation . When does the equality hold?

Choices

Choice (4) Response

a.

Equality hold when Equation and Equation

b.

Equality hold when Equation and Equation

c.

Equality hold when Equation and Equation

d.

Equality hold when Equation and Equation

Question number: 84

» Real Numbers

MCQ▾

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

MCQ▾

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

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