Test Report: Math for Olympiad from SAPMOPS 2

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These Math Problems were collected from SAPMOPS Asia Pacific Mathematical Olympiad for Primary Schools
http://www.hwachong.edu.sg

1. At 7.00 am, a vessel contained 4000 cm3 of water. Water was removed from the vessel at a constant rate of 5 cm3 per minute. At 8.00 am, 80 cm3 of water was added. A further 80 cm3 was added at the end of each hour after that. Find the time when the vessel was empty for the first time.
   
   1. 00.50 am
   2. 00.52 am
   3. 00.54 am
   4. 00.56 am
   5. 00.58 am


2. At 8.00 a.m., car A leaves Town P and travels along an expressway.
   After some time, car B leaves Town P and travels along the same
   expressway. The two cars meet at 9.00 a.m. If the ratio of A's speed to
   B's speed is 4 : 5 , what time does B leave Town P ?
   
   
   1. 8.07 am
   2. 8.08 am
   3. 8.10 am
   4. 8.12 am
   5. 8.14 am


3. Between 12 o'clock and 1 o'clock, at what time will the hour
   hand and minute hand make an angle of 110^o?
   
   1. 12.20
   2. 12.30
   3. 12.40
   4. 12.50
   5. 12.55


4. David had $100 more than Allen at first. After David's money had decreased by $120 and Allen's money had increased by $200, Allen had 3 times as much money as David.
   What was the total amount of money they had at first ?
   
   1. $340
   2. $350
   3. $360
   4. $370
   5. $380


5. Find the missing number ...
   5 x .... : 3 x 4 – 299 = 2001
   
   1. 315
   2. 325
   3. 345
   4. 355
   5. 365


6. Find the missing number in the following number sequence.
   1, 4, 10, 22, 46, _____, 190 , . . .
   
   1. 94
   2. 95
   3. 96
   4. 97
   5. 98


7. Find the smallest number such that
   (i) it leaves a remainder 2 when divided by 3;
   (ii) it leaves a remainder 3 when divided by 5;
   (iii) it leaves a remainder 5 when divided by 7.
   
   1. 63
   2. 65
   3. 67
   4. 68
   5. 70


8. Find the sum of the first 100 numbers in the following number
   sequence.
   1, 2, 3, 4, 5, 6, 7, 8, 9, 1, 0, 1, 1, 1, 2, 1, 3, 1, 4, 1, 5, . . .
   
   1. 266
   2. 289
   3. 295
   4. 365
   5. 455


9. Find the value of .
   
   1. 3
   2. 3 1/3
   3. 3 2/3
   4. 4
   5. 4 1/3


10. Find the value of
    1/2002 + 2/2002 + 3/2002 + ...... + 2000/2002 + 2001/2002
    
    1. 785
    2. 880
    3. 895
    4. 990 1/2
    5. 1000 1/2


11. Find the value of
    0.1+ 0.11 + 0.111 + . . . . + 0.1111111111 .
    
    1. 109
    2. 11
    3. 1.0987654321
    4. 1.8987654321
    5. 1.9987654321


12. Given that five whole numbers a, b, c, d and e are the ages of 5 people and that a is 2 times of b, 3 times of c, 4 times of d and 6 times of e, find the smallest possible value of a + b + c + d + e.
    
    1. 23
    2. 25
    3. 27
    4. 29
    5. 30


13. How many 5-digit numbers are multiples of 5 and 8 ?
    
    1. 2250
    2. 2150
    3. 2350
    4. 2450
    5. 2550


14. How many digits are there before the hundredth 9 in the following number
    9797797779777797777797777779…….?
    
    1. 5000
    2. 5029
    3. 5039
    4. 5049
    5. 5059


15. How many numbers are there in the following number sequence
    1.11, 1.12, 1.13, . . . , 9.98, 9.99.
    
    1. 887
    2. 888
    3. 889
    4. 890
    5. 891