**Bangladesh National Mathematical Olympiad 2015:**

Primary

Primary

Problem 1

Write down all the prime numbers in the range of $1$ to $50$.

Problem 2

Four people $A, B, C$ and $D$ have an average monthly income of $10000$ taka. First three of them have an average monthly income of $12000$ taka. Average income of first two of them is $15000$ taka. Find the monthly income of $B, C$ and $D$ if $A$ has a monthly income of $20000$ taka?

Problem 3

In the following figures a rectangular piece of paper $ABCD$ has been folded several times. First, the side $CD$ was made to fall on the line $AD$. Point $E$ in figure $(ii)$ represents the point $C$ after folding. In the next figure the portion $BF$ was made to fall on $EF$. Lastly, the side $AG$ was made to fall on $GH$. Find the lengths of $GJ, IJ, IE, ED, EH$ and $HF$. It is given that$ AB = 8$ and $BC = 15$.

Problem 4

A circus party has the same number of lions as tigers. You asked to the owner of the circus the number of lions and tigers. He gave you the following information:

(i) An elephant is enough to feed all the tigers and lions in the circus.

(ii) Eighteen deers produce the same amount of meat as an elephant does.

(iii) A lion eats twice as much as a tiger.

(iv) One buffalo is enough to feed a lion and a tiger.

(v) A tiger will eat exactly the same amount of meat a deer has.

Find the number of tigers and lions in that circus party.

Problem 5 .

Surjo is four years old and he is learning to write numbers. His math notebook looks like a square grid with $20$ rows and $20$ columns. He usually writes the numbers from top to bottom and when one column is finished he starts writing along the next column. One day he starts writing the numbers from left to right (along the rows). How many of the numbers will be placed in exactly the same place where it would have appeared if he had written along the columns?

Problem 6

In the following figure $BKLGNM$, $CMNHPO$ and $DOPIRQ$ are regular hexagons (all six sides of each hexagon are equal and so are the angles). $ BKLGNM$ has an area of $24$ square units. What is the area of the rectangle $AFJE$?