Search found 134 matches
- Fri Jan 10, 2014 1:29 am
- Forum: National Math Olympiad (BdMO)
- Topic: BdMO National 2013: Junior 9
- Replies: 7
- Views: 14513
BdMO National 2013: Junior 9
The ratio of GCD and LCM of two integers is $1: 36$ and sum of the integers is $5460$. What is the difference between these two integers?
- Fri Jan 10, 2014 1:27 am
- Forum: National Math Olympiad (BdMO)
- Topic: BdMO National 2013: Junior 8
- Replies: 3
- Views: 3957
BdMO National 2013: Junior 8
$ABCD$ is a rectangle where $AB= \sqrt{2}$ and $BC= \sqrt6$ . $P$ and $Q$ are two points on $AC$ such that $AP=CQ$. From $P$ and $Q$, two perpendicular $PR$ and $QS$ are drawn on $BC$ and $AD$ respectively. If $PRQS$ is a rhombus and $PR=CQ$, then find the length of $PQ$.
- Fri Jan 10, 2014 1:26 am
- Forum: National Math Olympiad (BdMO)
- Topic: BdMO National 2013: Junior 7
- Replies: 1
- Views: 3101
BdMO National 2013: Junior 7
A positive integer is called “Fantabulous” if there is another fantabulous positive integer smaller than it. Find the number of fantabulous integers.
- Fri Jan 10, 2014 1:25 am
- Forum: National Math Olympiad (BdMO)
- Topic: BdMO National 2013: Junior 6
- Replies: 12
- Views: 8901
BdMO National 2013: Junior 6
You have $1, 2, 3, 4, 5, 6, 7, 8, 9$ kg weights in your home. You have only one piece of each of the weights. You also have a balance. If you put a weight on the left side of that balance, its weight becomes twice. Every time you choose three weights to put on the balance in such a manner that the b...
- Fri Jan 10, 2014 1:24 am
- Forum: National Math Olympiad (BdMO)
- Topic: BdMO National 2013: Junior 4
- Replies: 1
- Views: 3132
BdMO National 2013: Junior 4
Let $a$ be an integer divisible by $2$ but not divisible by $4$. What is the largest positive integer $n$ such that $2^n$ divides $a^{2012} + a^{2013} + \cdots + a^{3012}$?
- Fri Jan 10, 2014 1:23 am
- Forum: National Math Olympiad (BdMO)
- Topic: BdMO National 2013: Junior 3
- Replies: 1
- Views: 2944
BdMO National 2013: Junior 3
$ABC$ is a triangle where $AN$ is perpendicular to $CB$ and $BM$ perpendicular to $AC$. The length of $BC$ is $10$, that of $AC$ is $12$ and that of $AN$ is $6$. Find the length of $BM$.
- Fri Jan 10, 2014 1:22 am
- Forum: National Math Olympiad (BdMO)
- Topic: BdMO National 2013: Junior 2
- Replies: 2
- Views: 3693
BdMO National 2013: Junior 2
Two isosceles triangles are possible with area of 120 square unit and length of edges integers. One of these two triangles has sides of lengths $17,17$ and $16$. Determine the length of edges of second one.
[Hint: In $\Delta ABC$ if $AB=AC$ and $AD$ is perpendicular to $BC$ then $BD=CD$.]
[Hint: In $\Delta ABC$ if $AB=AC$ and $AD$ is perpendicular to $BC$ then $BD=CD$.]
- Fri Jan 10, 2014 1:21 am
- Forum: National Math Olympiad (BdMO)
- Topic: BdMO National 2013: Primary 8, Junior 5
- Replies: 1
- Views: 3333
BdMO National 2013: Primary 8, Junior 5
There are some boys and girls in a class. Every boy is friends with exactly three girls, and every girl is friends with exactly three boys. If there are $13$ boys in the class, how many girls are there? (Assume that friendship is mutual, i.e. if $A$ is friend of $B$ then $B$ is also friend of $A$.)
- Fri Jan 10, 2014 1:20 am
- Forum: National Math Olympiad (BdMO)
- Topic: BdMO National 2013: Primary 7
- Replies: 2
- Views: 4043
BdMO National 2013: Primary 7
Arefin, Farhad, Himu, Mahdi, Rachi, Sadia and Tusher are seven friends who live in Gulshan by the side of same linear road. Distances of others home from Tusher home are given below. Tusher’s home is at the starting point of that road. They want to meet at the same place on that road every evening f...
- Fri Jan 10, 2014 1:18 am
- Forum: National Math Olympiad (BdMO)
- Topic: BdMO National 2013: Primary 6
- Replies: 3
- Views: 4589
BdMO National 2013: Primary 6
A polygon is an area bounded by three or more edges in a plane. For example a triangle has three edges, a quadrilateral has four edges, a pentagon has five edges and in this way they are given names according to their number of edges. A regular polygon is a polygon that has edges of equal lengths an...