Difference between revisions of "2007 Cyprus MO/Lyceum/Problems"
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== Problem 11 == | == Problem 11 == | ||
+ | If <math>X=\frac{1}{2007 \sqrt{2006}+2006 \sqrt{2007}}</math> and <math>Y=\frac{1}{\sqrt{2006}}-\frac{1}{\sqrt{2007}}</math>, which of the following is correct? | ||
+ | A. <math>X=2Y</math> | ||
+ | |||
+ | B. <math>Y=2X</math> | ||
+ | |||
+ | C. <math>x=Y</math> | ||
+ | |||
+ | D. <math>x=D^2</math> | ||
+ | |||
+ | E. <math>Y=X^2</math> | ||
[[2007 Cyprus MO/Lyceum/Problem 11|Solution]] | [[2007 Cyprus MO/Lyceum/Problem 11|Solution]] |
Revision as of 13:03, 6 May 2007
Contents
Problem 1
If ,then the value of the expression
is
A.
B.
C.
D.
E.
Problem 2
Given the formula , then
equals to
A.
B.
C.
D.
E.
Problem 3
A cyclist drives form town A to town B with velocity and comes back with velocity
. The mean velocity in
for the total distance is
A.
B.
C.
D.
E.
Problem 4
We define the operation ,
.
The value of is
A.
B.
C.
D.
E.
Problem 5
If the remainder of the division of with
is
, then the remainder of the division of
with
is
A.
B.
C.
D.
E.
Problem 6
An image is supposed to go here. You can help us out by creating one and editing it in. Thanks.
is a square of side 2 and
is an arc of the circle with centre the midpoint
os the side
and radius 2. The length of the segments
is
A.
B.
C.
D.
E.
Problem 7
If the angle of the diagonal d of a rectangle forms an angle with one of its sides, then the area of the recangle is
A.
B.
C.
D.
E. None of these
Problem 8
If we substract from 2 the inverse number of , we get the inverse of
. Then the number
equals to
A.
B.
C.
D.
E.
Problem 9
We consider the sequence of real numbers such that
,
and
,
. The value of the term
is
A.
B.
C.
D.
E.
Problem 10
The volume of an orthogonal parallelepiped is and its dimensions are integer numbres. The minimum sum of the dimensions is
A.
B.
C.
D.
E. None of these
Problem 11
If and
, which of the following is correct?
A.
B.
C.
D.
E.