IMAS 2014 — Upper Primary Grades 5–6 — Round 1

What is the value of 2015 + 1520 + 5201?

The three numbers in each of the following groups are multiplied together. Which group yields 2014 as the product?

A large bottle of apple juice costs 6.5 dollars while a small bottle of apple juice costs 2.8 dollars. How many dollars less is the cost of a large bottle compared to the total cost of three small bottles?

Which of the following differences has the smallest value?

The two stars in the diagram represent the same number. The sum of the three numbers in the second row is equal to twice the sum of the three numbers in the first row. What number does each star represent?

A sack of flour costs 800 dollars and a sack of rice costs 500 dollars. Anne buys several sacks of each kind and spends 3400 dollars. How many sacks of flour does she buy?

When two numbers are divided by 5, the respective remainders are 4 and 2. What is the remainder when the sum of the two numbers is divided by 5?

The numbers 38, 79, 17, 43, 74, 96 and 87 are rearranged so that starting from the second one, its tens digit is equal to the units digit of the preceding number. Which number is in the fourth place after the rearrangement?

To visit a friend, Rod must take the bus to the nearest Metro station, and this takes 15 minutes. He has to ride the Metro train for 20 stops, each taking 2.5 minutes. He also has to change trains twice, and it takes 3 minutes each time. Finally, after exiting the Metro, he still has to walk another 12 minutes before reaching his friends place. How many minutes does Rod have to spend traveling to his friend’s house?

A table has 3 rows and 3 columns. In each square, we put in the product of the row number and the column number of that square. For instance, the number in the third row and the second column is 3×2=6, as shown in the diagram. These nine numbers are then arranged in order of size, starting with the smallest. What is the fifth number in the arrangement?

Oliver arranges his duck toy and turtle toy in a row as shown in the diagram. He desires that all duck toys to be on the left and all turtle toys on the right. He may switch the positions of any two adjacent toys. What is the minimum number of switches does he require to achieve his desired arrangement?

The sum of one-fifth of a non-negative integer and one-third of another non-negative integer is 1. What is the maximum value of the sum of these two non-negative integers?

Max has a gray paper strip of width 5 cm. He cuts out some pieces and tapes them on the wall, to form a 50 cm by 35 cm window frame, as shown in the diagram, where each white area is 5 cm by 10 cm. What is the minimum length, in cm, of the paper strip required?

The tap is leaking at the rate of one drop per second. The volume of each drop is
0.05 mL. At 9 pm, Wendy puts an empty measuring cup under the tap. Some time during the night, she finds the cup partially filled, as shown in the diagram. No water is lost from the cup. At what time is the water level in the measuring cup closest to the time in the following?

The upper part of a glass is a cylinder of height 8cm and diameter 20 cm. The middle part is a cone of height 8 cm and diameter 20 cm. The bottom part is a solid stem. Correct to one decimal place, what is the capacity, in cm³ , of the cup? Take π=3.14.

A hall has four doors. Lea may enter the hall using any of them, and exit the hall using any of them. In how many different ways can she enter and exit the hall?

ABCD is a square of side length 10 cm. The segment BC is fixed. The segment AD moves in the plane to the segment A′D′ so that the lengths AB, DC and AD do not change. What is the area, in cm² , of the shaded region in the diagram when the segment A′D′ intersects the segment CD at its midpoint G?

On a table there is a ring, there are 12 equally spaced beads on the ring, 3 of which are black, as shown in the diagram. Which of the following five figures cannot be obtained from the given figure by rotating the ring on the table?

The figure in the diagram is formed from 20 equilateral triangles of equal sizes. How many equilateral triangles of any size does it contain? The triangles may overlap.

The sectors MAB and MCD are inside the square ABCD of side length 10 cm, as shown in the diagram. What is the total area, in cm² , of these two sectors, correct to 1 decimal place? Take π=3.14.