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Difference between revisions of "2006 Cyprus MO/Lyceum/Problems"

(→‎Problem 1)
(→‎Problem 2)
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== Problem 2 ==
 
== Problem 2 ==
 +
The operation <math>\alpha * \beta</math> is defined by <math>\alpha * \beta = \alpha^2 - \beta^2</math>  <math>\forall \alpha , \beta \in R</math>.
 +
The value of the expression <math>K = \left[\left(1+\sqrt{3}\right) * 2\right]*\sqrt{2} </math> is
  
 +
A. <math>3</math>
 +
 +
B. <math>0</math>
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 +
C.  <math>\sqrt{3}</math>
 +
 +
D. <math>9</math>
 +
 +
E. <math>1</math>
  
 
[[2006 Cyprus MO/Lyceum/Problem 2|Solution]]
 
[[2006 Cyprus MO/Lyceum/Problem 2|Solution]]

Revision as of 08:15, 31 May 2007

Problem 1

A diary industry, in a quantity of milk with $4%$ (Error compiling LaTeX. Unknown error_msg) fat adds a quantity of milk with $1%$ (Error compiling LaTeX. Unknown error_msg) fat and produces $1200$kg of milk with $2%$ (Error compiling LaTeX. Unknown error_msg) fat. The quantity of milk with $1%$ (Error compiling LaTeX. Unknown error_msg) fat, that was added is (in kg)

A. $1000$

B. $600$

C. $800$

D. $120$

E. $480$

Solution

Problem 2

The operation $\alpha * \beta$ is defined by $\alpha * \beta = \alpha^2 - \beta^2$ $\forall \alpha , \beta \in R$. The value of the expression $K = \left[\left(1+\sqrt{3}\right) * 2\right]*\sqrt{2}$ is

A. $3$

B. $0$

C. $\sqrt{3}$

D. $9$

E. $1$

Solution

Problem 3

Solution

Problem 4

Solution

Problem 5

Solution

Problem 6

Solution

Problem 7

2006 CyMO-7.PNG

Solution

Problem 8

2006 CyMO-8.PNG

Solution

Problem 9

Solution

Problem 10

Solution

Problem 11

2006 CyMO-11.PNG


Solution

Problem 12

Solution

Problem 13

Solution

Problem 14

2006 CyMO-17.PNG


Solution

Problem 15

Solution

Problem 16

Solution

Problem 17

2006 CyMO-17.PNG


Solution

Problem 18

2006 CyMO-18.PNG


Solution

Problem 19

2006 CyMO-19.PNG


Solution

Problem 20

Solution

Problem 21

Solution

Problem 22

2006 CyMO-22.PNG


Solution

Problem 23

Solution

Problem 24

Solution

Problem 25

Solution

Problem 26

Solution

Problem 27

Solution

Problem 28

Solution

Problem 29

Solution

Problem 30

Solution

See also

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