2014 Upper Primary Division Round 2

What is the simplified value of 32 × 37 × 75?

In a gymnastics competition, an athlete receives a score from each of the seven judges. After the highest score and the lowest score have been removed, the average of the remaining five scores is the actual score for that athlete. If the seven judges give scores of 9.2, 9.5, 9.3, 9.6, 9.1, 9.6 and 9.4 to an athlete, what is the actual score for this athlete?

There are 4 children in the first row, and each subsequent row has one more child than the preceding row. If there are 39 children altogether, how many children are in the last row?

When 200 is subtracted from the square of a positive integer n, the difference is a three-digit multiple of 4. How many different values can n take?

From a cubical box without the top, a circle is removed from each of two opposite faces. Which of the following shapes can be folded to form such a box? 

If a computer printer is sold at a 10% off discount, a profit of $220 can still be made. However, if it is sold at a 20% off discount, there will be a loss of $100. What is the list price of this computer printer?

Answer:

There are three storage compartments in an airplane. The maximum weight which can be stored in them are 10, 16 and 8 tons respectively. The maximum volume which can be stored in them are 66, 84 and 51 respectively. The airplane is used to transport grain, each ton of which has volume 6. If the actual weight of grain in each compartment must be in the same proportion to the maximum weight allowed in that compartment, what is the maximum weight of grain the airplane can transport at a time? 

Answer:

In triangle ABC, D is the midpoint of BC. E is an arbitrary point on CA, and F is the midpoint of BE. If the area of triangle ABC is 120 and the area of the quadrilateral AFDC is 80, what is the area, in , of triangle BDF?

Answer:

The number sentences 1000 - 991 = 9 and 1001 - 994 = 7 are examples in which the difference between a four-digit number and a three-digit number is a one-digit number. How many such number sentences are there, including these two examples?

Answer:

An ant starts from the top left corner square of a 3 × 5 chessboard. It moves from a square to the adjacent square in the same row or column. After visiting every square exactly once, it ends up at the square in the middle row second column from the right. How many different paths can the ant follow?

Answer: paths

Lily’s eight-digit telephone number is divisible by 3 and 5. Micky can only remember its first six digits, which are 8, 9, 2, 0, 1 and 5 in that order. What is the maximum number of times Micky has to dial before connecting to the correct telephone number?

Answer: times

ABCD, CEFG and DGMN are squares, with G on CD and F on MN. If AB = 10cm and MN = 6cm, what is the area of triangle AME, in ?

Answer:

The numbers 1, 2, 3, 4, 5, 6, 7, 8, 9 and 10 are divided into two groups. The sum of all the numbers in one group is n, while the product of all the numbers in the other group is also n. What is the maximum value of n?

Answer:

We increase by 1 each of three prime numbers, not necessarily distinct. Then we form the product of these three sums. How many numbers between 1999 to 2021 can appear as such a product?

Answer:

Each side of an equilateral triangle is divided into 6 equal parts by 5 points, and these points are joined by lines parallel to the sides of the triangle, dividing into 36 small equilateral triangles. A regular hexagon is the same size as 6 of the small equilateral triangles put together. What is the maximum number of such hexagons that can along the grid line fit inside the large equilateral triangle without overlap?

Answer: regular hexagons