# 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)