tailieunhanh - Hanoi Open Mathematical Olympiad 2010 - Junior Section

Hanoi Mathematical Society Hanoi Open Mathematical Olympiad 2010 Junior Section Sunday, 28 March 2010 08h45-11h45 Important: Answer all 10 questions. Enter your answers on the answer sheet provided. For the multiple choice questions, enter only the letters (A, B, C, D or E) corresponding to the correct answers in the answer sheet. No calculators are allowed. | Hanoi Mathematical Society Hanoi Open Mathematical Olympiad 2010 Junior Section Sunday 28 March 2010 08h45-11h45 Important Answer all 10 questions. Enter your answers on the answer sheet provided. For the multiple choice questions enter only the letters A B C D or E corresponding to the correct answers in the answer sheet. No calculators are allowed. Q1. Compare the numbers P 888 . 888 X 333 . 333 and Q 444 . 444 X 666 . 667 2010 digits 2010 digits 2010 digits 2010 digits A P Q B P Q C P Q. Q2. The number of integer n from the set 2000 2001 . 2010g such that A 22n 2n 5 is divisible by 7 is A 0 B 1 C 2 D 3 E None of the above. Q3. The last 5 digits of the number M 52010 are A 65625 B 45625 C 25625 D 15625 E None of the above. 1 Q4. How many real numbers a 2 1 9 such that the corresponding number a is an integer. a A 0 B 1 C 8 D 9 E None of the above. Q5. Each box in a 2 X 2 table can be colored black or white. How many different colorings of the table are there A 4 B 8 C 16 D 32 E None of the above. Q6. The greatest integer less than 2 x 3 5 are A 721 B 722 C 723 D 724 E None of the above. Q7. Determine all positive integer a such that the equation 2x2 a 0 has two prime roots . both roots are prime numbers. Q8. If n and n3 2n2 2n 4 are both perfect squares hnd n. Q9. Let be given a triangle ABC and points D M N belong to BC AB AC respectively. Suppose that MD is parallel to AC and ND is parallel to AB. If S BMD 9cm2 S DNC 25cm2 compute S amn Q10. Find the maximum value of x y z M 2x y 2y z 2z x x y z 0