2011 JUNIOR DIVISION FIRST ROUND PAPER

What is 2011 + 1102 x (1 - 3)? 

Which number is the largest?

The temperature on the shady side of a certain planet is −253°C. The temperature on its sunny side is only −223°C. Which of the following statement is an accurate description of the relation between the temperatures on the shady side and on the sunny side?

The given diagram shows a rectangular piece of paper folded in quarters along two perpendicular folds. If a cut is made around the corner marked 1, which of the following cannot possibly be the shape of the resulting hole in the piece of paper?

Around 550 BC, the Greek mathematician Pythagoras discovered and proved a theorem which now bears his name. To celebrate this achievement, he had 100 cows killed for a feast. Thus the result is also known as the One Hundred Cows Theorem. What is the anniversary of this result in 2011? (There is no Year 0.)

A rectangle is 6 cm by 8 cm. It is revolved about an axis on the rectangle itself. What is the number of different cylinders that may be obtained in this way ? 

There is a pattern to the given sequence of figures:

Which of the following will be the 2011-th figure of the sequence?

The given diagram shows two overlapping right triangles having a common vertex O. If ∠AOD = 123°, what is the measure, in degrees, of ∠BOC ?

A greengrocer is having an apple sale. The price is $6 per kilogram. If the total purchase exceeds 3 kilograms, a 20% discount is applied to the portion over 3 kilograms. There is no discount if the total purchase does not exceed 3 kilograms. If Leith buys 8 kilograms of apples from this greengrocer, how much does he pay?  

The given diagram shows a pocket knife. The shaded part is a rectangle with a small semicircular indentation. The two edges of the blade are parallel, forming angles 1 and 2 with the shaft as shown. What is the measure, in degrees, of ∠1 + ∠2 ?  

The given diagram shows the projected sale and actual sale of a certain toy company for the fourth quarter of the year. The achievement percentage is equal to ×100% . What is this achievement percentage?

Leon is given five wooden blocks:

Which of the following blocks should be added so that he can make a 4 × 4 × 4 cube? (None of the blocks can be dissected)

The given diagram shows how a square ABCD with side length 40 may be dissected into six pieces by three straight cuts AC, BD and EF, where E and F are the respective midpoints of AB and BC. The pieces are then rearranged to form the given shape. What is the total area, in square centimetres, of the shaded part of the given shape?

The given diagram shows the calendar for the month of November, 2011. Three numbers from the same column are chosen. Of the following number, which can be the sum of three such numbers?

The given diagram shows a large cube formed of eight identical small cubes.The surface area of the large cube is 216 square centimetres less than the total surface areas of the eight small cubes. What is the length, in centimetres, of a side of a small cube? 

In an NBA basketball game, a player scores 44 points, 5 of which come from 5 foul shots (each shot scores 1 point). He makes more 2-point shots than 3-point shots. Of the following number, which cannot possibly be the total number of 2-point and 3-point shots made by this player?

The given diagram shows a rectangle ABCD being folded along a straight segment AE with E on CD, so that the new position of D is on AB. Triangle ADE is then folded along DE so that the new position of A is on the extension of DB. The new position of AE intersects BC at F. If AB = 10 centimetres and AD = 6 centimetres, what is the area, in square centimetres, of triangle ABF? 

A child is operating a remote-controlled car on a flat surface. Starting from the child’s feet, the car moves forward 1 metre, makes a 30° turn counterclockwise, moves forward 1 metre, makes a 30° turn counterclockwise, and so on. When the car first time returns to its starting point for the first time, what is the total distance, in metres, that it has covered?

Each interior angle of a regular convex polygon is greater than 100° and less than 140°. Of the following numbers, which cannot possibly be the number of sides of this polygon?

In the given diagram, each vertex of the hexagon PQRSTU is labeled with 0 or 1. Starting counterclockwise from a vertex, he multiplies the labels by 3, 7, 15, 31, 63 and 127 respectively and add the six products. If the starting point is P, the final sum is 1 x 3 + 1 x 7 + 0 x 15 + 1 x 31 + 0 x 63 + 1 x 127 = 168. What is the starting point if the final sum is 180? 

A drunk walks 1 metre east. Then he stops, makes a 90° turn clockwise or counterclockwise and walks 2 metres. Then he stops, makes a 90° turn clockwise or counterclockwise and walks 3 metres. He continues in this pattern, stopping, making 90° turn clockwise or counterclockwise and walks 1 metre more than the preceding segment. What would be the longest distance, in metres, between his initial position and his position when he makes his seventh stop?

Answer:

In the given diagram, ABCD is a rectangle with AB = 25 cm and BC = 20 cm. F is a point on CD and G is a point on the extension of AB such that FG passes through the midpoint E of BC. If ∠AFE  = ∠CFE, what is the length, in cm, of CF?

Answer:

Consider all five-digit numbers using each of the digits 1, 2, 3, 4 and 5 exactly once, possibly with a decimal point somewhere. Starting with the smallest such number, namely, 1.2345, they are listed in ascending order. What is 1000 times the difference of the 150th and the 145th numbers?  

Answer:  

In a row are six counters, each either black or white. Between every two adjacent counters, we place a new counter. If the two adjacent counters are of the same colour, we place a white counter. If they are of different colours, we place a black counter. Then we remove the original six counters, leaving behind a row of five counters. We now repeat this operation two more times, reducing the number of counters in the row to four and then to three. If the last three counters are all white, how many different colour patterns for the original six counters are there? An example is attached.

Answer:

Mickey lives in a city with six subway lines. Every two lines have exactly one common stop for changing lines, and no three lines meet at a common stop. His home is not at one of the common stops. One day, Mickey suddenly decides to leave home and travel on the subway, changing trains at least once at each stop before returning home. What is the minimum number of changes he has to make to accomplish this task?
Answer: