Difference between revisions of "Olimpiada de Mayo"
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* Venezuela | * Venezuela | ||
==Past Tests/Results== | ==Past Tests/Results== | ||
− | * The [http://www.oma.org.ar/enunciados/may3.htm 1997 test | + | * The [http://www.oma.org.ar/enunciados/may3.htm 1997 test] |
* The [http://www.oma.org.ar/enunciados/may4.htm 1998 test], [http://www.oma.org.ar/internacional/resultados-may4.htm 1998 test results] | * The [http://www.oma.org.ar/enunciados/may4.htm 1998 test], [http://www.oma.org.ar/internacional/resultados-may4.htm 1998 test results] | ||
− | * The [http://www.oma.org.ar/enunciados/may5.htm 1999 test | + | * The [http://www.oma.org.ar/enunciados/may5.htm 1999 test] |
− | * The [http://www.oma.org.ar/enunciados/may6.htm 2000 test | + | * The [http://www.oma.org.ar/enunciados/may6.htm 2000 test] |
− | * The [http://www.oma.org.ar/enunciados/may7.htm 2001 test | + | * The [http://www.oma.org.ar/enunciados/may7.htm 2001 test] |
− | * The [http://www.oma.org.ar/enunciados/may8.htm 2002 test | + | * The [http://www.oma.org.ar/enunciados/may8.htm 2002 test] |
− | * The [http://www.oma.org.ar/enunciados/may9.htm 2003 test | + | * The [http://www.oma.org.ar/enunciados/may9.htm 2003 test] |
− | * The [http://www.oma.org.ar/enunciados/may10.htm 2004 test | + | * The [http://www.oma.org.ar/enunciados/may10.htm 2004 test] |
− | * The [http://www.oma.org.ar/enunciados/may11.htm 2005 test | + | * The [http://www.oma.org.ar/enunciados/may11.htm 2005 test] |
* The [http://www.oma.org.ar/enunciados/may12.htm 2006 test], [http://www.oma.org.ar/internacional/resultados-may12.htm 2006 test results] | * The [http://www.oma.org.ar/enunciados/may12.htm 2006 test], [http://www.oma.org.ar/internacional/resultados-may12.htm 2006 test results] | ||
* The [http://www.oma.org.ar/enunciados/may13.htm 2007 test], [http://www.oma.org.ar/internacional/resultados-may13.htm 2007 test results] | * The [http://www.oma.org.ar/enunciados/may13.htm 2007 test], [http://www.oma.org.ar/internacional/resultados-may13.htm 2007 test results] | ||
* The [http://www.oma.org.ar/enunciados/may14.htm 2008 test], [http://www.oma.org.ar/internacional/resultados-may14.htm 2008 test results] | * The [http://www.oma.org.ar/enunciados/may14.htm 2008 test], [http://www.oma.org.ar/internacional/resultados-may14.htm 2008 test results] | ||
+ | |||
==Problems== | ==Problems== | ||
Some problems from previous Olimpiada de Mayo tests. | Some problems from previous Olimpiada de Mayo tests. |
Revision as of 19:00, 20 May 2009
Olimpiada de Mayo(May Olympiad) is an annual test that has two levels, level one is for students that have not reached the age of years the year before, and level two is for students that have not reached the age of
years the year before. The test is taken by
latinamerican countries.
Contents
Member Countries
- Argentina
- Brasil
- Bolivia
- Colombia
- Ecuador
- El Salvador
- México
- Panamá
- Paraguay
- Perú
- Puerto Rico
- Venezuela
Past Tests/Results
- The 1997 test
- The 1998 test, 1998 test results
- The 1999 test
- The 2000 test
- The 2001 test
- The 2002 test
- The 2003 test
- The 2004 test
- The 2005 test
- The 2006 test, 2006 test results
- The 2007 test, 2007 test results
- The 2008 test, 2008 test results
Problems
Some problems from previous Olimpiada de Mayo tests.
Problem 1
We choose 2 numbers in between 1 and 100, inclusive, such that their difference is 7 and their product is a multiple of 5. How many ways can we do this? 1st level, 5th olympiad test
Problem 2
How many 7-digit numbers are multiples of and end in
? 2nd level, 3rd olympiad test
Solutions
Solution to Problem #1
Let the two numbers be and
such that
.
We know that and
, since only one of the two numbers can be a multiple of
we can start with cases, one in which
is a multiple of
and the other where
is a multiple of
.
Case 1: ( is a multiple of
)
The lowest value forthat satisfies the conditions is
.
The highest value forthat satisfies the conditions is
.
So there are a total of cases that work.
Case 2: ( is a multiple of
)
The lowest value forthat satisfies the conditions is
.
The highest value forthat satisfies the conditions is
.
So there are a total of cases that work.
In total there are cases that work.
Solution to Problem #2
First we look for the Least common multiple of that ends in
zeros so that when added to a number that ends in
it will still be a multiple of
and end in
, and this number is
.
So any number in the form of ends in
and is a multiple of
.
We want to find
Since we are only dealing with the thousands we don't need to worry about the :
$\begin{eqnarray*} 1000 & < & 3880 + 97k < 100000 \\ 1000 & < & 97(40 + k) < 10000 \\ 10 & < & 40 + k < 103 \\ - 30 & < & k < 63 \end{eqnarray*}$ (Error compiling LaTeX. Unknown error_msg)
From this we see that there are solutions.