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Test Report: Math for Olympiad from SAPMOPS 1

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

  1. 1/7 of a group of pupils score A for Mathematics; 1/3 of the pupils
    score B; 1/2 of the pupils score C; and the rest score D.
    If a total of 100 pupils score A or B, how many pupils score D?
    1. 1
    2. 2
    3. 3
    4. 4
    5. 5

  2. 10 years ago, the ratio of John's age to Peter's age was 5 : 2. The ratio is 5 : 3 now. What will be the ratio 10 years later?

    1. 10:7
    2. 7:10
    3. 8:11
    4. 10:8
    5. 9:11

  3. 1000 kg of a chemical is stored in a container.
    The chemical is made up of 99% water and 1% oil.
    Some water is evaporated from the chemical until the water content is reduced to 96 %.
    How much does the chemical weigh now?
    1. 250 kg
    2. 260 kg
    3. 270 kg
    4. 280 kg
    5. 290 kg

  4. A bag contains identical sized balls of different colours: 10 red, 9 white, 7 yellow, 2 blue and 1 black.
    Without looking into the bag, Peter takes out the balls one by one from it.
    What is the least number of balls Peter must take out to ensure that at least
    3 balls have the same colour?
    1. 8
    2. 9
    3. 10
    4. 11
    5. 12

  5. A box of chocolate has gone missing from the refrigerator.
    The suspects have been reduced to 4 children.
    Only one of them is telling the truth.
    John : " I did not take the chocolate."
    Wendy : " John is lying."
    Charles: " Wendy is lying."
    Sally : " Wendy took the chocolate."
    Who took the chocolate ?
    1. Wendy
    2. Charles
    3. John
    4. Sally
    5. No one

  6. A bus was scheduled to travel from Town X to Town Y at constant speed V km/hour If the speed of the bus was increased by 20%, it could arrive at Town Y 1 hour ahead of schedule. Instead, if the bus travelled the first 120 km at V km/hour and then the speed was increased by 25%, it could arrive at Town Y 4/5 hours ahead of schedule. Find the distance between the two towns.
    1. 350 km
    2. 360 km
    3. 370 km
    4. 380 km
    5. 390 km

  7. A car travels from town P to town Q at a constant speed.
    When it increases its speed by 20%, the journey from P to Q takes 1 hour less than its usual time.
    When it travels at its usual speed for 100 km before increasing its speed by 30%, the journey also takes 1 hour less than usual.
    Find the distance between the two towns.
    1. 350 km
    2. 360 km
    3. 370 km
    4. 380 km
    5. 390 km

  8. A particular month has 5 Tuesdays.
    The first and the last day of the month are not Tuesday.
    What day is the last day of the month?
    1. Monday
    2. Tuesday
    3. Wednesday
    4. Thursday
    5. Friday

  9. A piece of pasture grows at a constant rate everyday.
    200 sheep will eat up the grass in 100 days.
    150 sheep will eat up the grass in 150 days.
    How many days does it take for 100 sheep to eat up the grass?
    1. 300 days
    2. 310 days
    3. 315 days
    4. 325 days
    5. 335 days

  10. A student multiplies the month and the day in which he was born by 31 and 12 respectively. The sum of the two resulting products is 170.
    Find the month and the date in which he was born.
    1. February 8th
    2. February 9th
    3. February 11th
    4. February 12th
    5. February 14th
  11. A three digit number 5ab is written 99 times as 5ab5ab5ab……..5ab.
    The resultant number is a multiple of 91.
    What is the three digit number?
    1. 526
    2. 536
    3. 546
    4. 556
    5. 566

 
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