# 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▾

### 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 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

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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