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  • AMO 2015 Secondary 1 Question 25 Geometry Area – Right Triangle Configuration – MIMO 2017 – Upper Primary – Money Same Amount Problem – MIMO 2017 – Upper Primary – Geometrical Construction Proof

    Anonymous Christian
    Oct 11, 2018
    AMO, Math Olympiad, MIMO
    Comments Off on AMO 2015 Secondary 1 Question 25 Geometry Area – Right Triangle Configuration – MIMO 2017 – Upper Primary – Money Same Amount Problem – MIMO 2017 – Upper Primary – Geometrical Construction Proof

    AMO 2015 Secondary 1 Question 25 Geometry Area – Right Triangle Configuration

     

    Question (Sample)

     

     

    Solution

     

     

     

     

     

     

     

     

     

     

     

     

     

     

    MIMO 2017 – Upper Primary – Money Same Amount Problem

     

    Question 10

    Five persons A, B, C, D and E raised the same amount of money to buy the same gifts together. Four of them A, B, C and D bought 8 gifts, 6 gifts, 12 gifts and 9 gifts more than E respectively. When they settled the bill, A paid $7 to B. How much did C and D pay to E respectively?

     

     

     

     

    Solution

     

    (Shown in Image).

     

    I think that the answer is E gets a total of $49 back where $35 is from C while $14 is from D respectively.

     

     

     

     

     

     

     

     

     

     

     

    MIMO 2017 – Upper Primary – Geometrical Construction Proof

     

    Question 11.

     

    Both Question and two solutions are in images below.

     

     

     

     

     

     

     

     

     

     

     

     

     

     

     

    Bonus Questions (Additional Questions):

    1) Tangent Circles in Pentagon Sides KMC 2016

     

    Question

    Please refer to the first Image

     

     

     

     

    Solution

     

    In Second Image

     

     

     

     

     

     

     

     

     

     

     

     

     

    2) Maximizing Addends in Pyramid Layers KMC 2016 Cadet

     

    Question

    In Image

     

     

     

     

     

    Solution

     

    Since we are going to use 8 numbers and the ninth number at the center,

     

    for maximum

     

    Since the center is MOST repeated in layer calculations,

     

    (i) we minimize the 8 different positive integers

     

    hence choose —> 1 + 2 + 3 + … + 8 = (8 x 9)/2 = 36

     

    (ii) we calculate the remaining center number

     

    Total sum fixed at 50 means,

     

    Center number = 50 – 36 = 14

     

    Cube at bottom configuration

    3 7 2

    8 (14) 6

    4 5 1

     

    Giving the 2nd layer for optimum as

    32 29

    31 26

     

    Total = 32 + 31 + 29 + 26 = 118 (Answer)

     

     

     

     

     

     

    Additive Rates of Decrease

     

    Question (MIMO 2017, Upper Primary, No. 12)

     

    The weather is getting colder, the grass on the field is decreasing at a constant rate every day. Mr McDonald told that the grass on the field could feed 20 goats for 5 days or 16 goats for 6 days. If Mr McDonald has 11 goats, the grass could last for how many days?

     

    Answer: 8 Days.

     

    Solution (Please refer to attached Image).

     

    Number Patterns – International Olympiad of Science

    Question – International Olympiad of Science

     

    No. 13 & No. 39 in Image

     

     

     

     

     

     

    Possible Solution

     

    No. 39 (in Image too – a possibility).

     

     

     

     

     

     

     

     

     

     

    Perhaps Q13 is like this:

     

    Number Arrangement:

     

    a b

    c d

     

    Pattern

     

    (a + b) – (c + d) = d

     

    Example:

     

    (i) First Picture

     

    a = 9, b = 17, c = 8 and d = 9

     

    So,

     

    (9 + 17) – (8 + 9) = 9

     

    (ii) Second Picture

     

    a = 18, b = 37, c = 15 and d = 20

     

    So,

     

    (18 + 37) – (15 + 20) = 20

     

    (iii) Third Picture

     

    a = 26, b = 28, c = 18 and d = y

     

    (26 + 28) – (18 + y) = y

     

    54 – 18 – y = y

     

    36 = 2y

     

    y = 18 (answer)

     

     

anonymous-christian

Jonathan Ramachandran is founder at AnonymousChristian.org which serves as a Christian Blog discussing the Greater Hope of Biblical Christian in Christ Alone. He is also an IMO (International Math Coach) and a featuring Guitarist for many bands.

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