Matematika :

Oct 24, 2011

Soal Matematika : 2010 NORDIC

1. Three boys, A, B, and C, can work separately or together on a job. If working together, their efforts combine eficiently. It takes A working alone twice as long as it takes B working alone. It takes A four times as long as B and C working together to do the job. Also, it takes A two hours longer to do the job than it takes all three boys working together. How many hours does it take B to do the job?

2. We call a number ascending if each digit is greater than the digit that precedes it. For example, 457 is ascending, but 447 is not. How many ascending numbers are there between 400 and 5000?

3. Out of all polynomials with integer coe±cients which have both ½√2 and ½√3 as roots, consider those of smallest possible degree. Among all of these, what is the smallest positive coe±cient which occurs in any of them?

4. A triangle has vertices at (0, 0), (4, 2), and (5, 1). What is the tangent of its angle at the vertex (4, 2)?

5. What is the smallest positive integer n such that the product 19999 × n ends in the four digits 2010?

6. A parallelogram has area 36 and diagonals of length 10 and 12. What is the length of its longest side?

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