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IMAS 2015 — Upper Primary Grades 5–6 — Round 1

Question 1

Which of the following expression is incorrect?
  1. $29+92=(2+9)\times(9+2)$
  2. $47+74=(4+7)\times(7+4)$
  3. $36+63=(3+6)\times(6+3)$
  4. $56+65=(5+6)\times(6+5)$
  5. $38+83=(3+8)\times(8+3)$

Question 2

Each of P, Q and R writes down an integer greater than 2015. When 2013 is subtracted from P’s number, 2014 is subtracted from Q’s number and 2015 is subtracted from R’s number, the product of the differences is 88407. Which of the following statements is correct?
  1. P’s and Q’s numbers are odd and R’s is even.
  2. Q’s and R’s numbers are odd and P’s is even.
  3. R’s and P’s numbers are odd and Q’s is even.
  4. All three numbers are odd.
  5. Q’s number is odd and R’s and P’s numbers are even.

Question 3

Which of the following figures has area closest to 1?
  1. Question illustration
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Question 4

The numerator of a fraction is reduced by 25% and the denominator is increased by 25%. By which of the following numbers can we multiply the original fraction to obtain the new fraction?
  1. $\frac12$
  2. $\frac14$
  3. $\frac34$
  4. $\frac35$
  5. 1

Question 5

Sixteen points are arranged in a 3 cm by 3 cm formation. Four of them are removed, leaving behind twelve points as shown in the diagram. If we choose three of these twelve points as vertices of a triangle, what is the largest possible area of this triangle, in cm² ?

Question illustration
  1. 9
  2. $\frac92$
  3. 3
  4. 2
  5. $\frac32$

Question 6

From one-third of a positive integer, one-quarter of the next integer is subtracted. If the difference is 2, what is the sum of the two integers?
  1. 31
  2. 45
  3. 55
  4. 79
  5. 103

Question 7

The diagram below is the seating plan of a cinema. How many blocks of three adjacent seats are unshaded, not counting those in the first row?

Question illustration
  1. 15
  2. 16
  3. 17
  4. 18
  5. 19

Question 8

In an amusement park, each ride on the Bumper Cars costs 10 dollars, each ride on the Pirate Boat costs 15 dollars and each ride on the Roller Coaster costs 20 dollars. If Waldo spends 110 dollars in total on at least one ride of each kind, how many times has he taken a ride on the Roller Coaster?
  1. 1
  2. 2
  3. 3
  4. 4
  5. 5

Question 9

The first term of a sequence is 2. Each subsequent term is the remainder when 3 times the preceding term is divided by 5. Thus the second term is 1, the remainder when $3\times2=6$ is divided by 5. How many of the first 2015 terms of this sequence are equal to 1?
  1. 403
  2. 504
  3. 672
  4. 1008
  5. 2014

Question 10

A cubic box of side length 15 cm has two holes. One of them is 5 cm above and 5 cm to the left of the bottom right corner of the front face. The other is 5 cm below and 5 cm to the left of the top right corner of the right face. The size of the holes and the thickness of the box are negligible. If the box is filled with water and one of its faces rests on a horizontal surface, some water will leak out through the holes. What is the maximum amount, in cm³ , of water that can remain inside the box?

Question illustration
  1. 1000
  2. 1125
  3. 1500
  4. 2250
  5. 3375

Question 11

How many prime numbers less than 50 is 1 more than the product of two distinct prime numbers each less than 50?
  1. 2
  2. 3
  3. 4
  4. 5
  5. 6

Question 12

Goldie has two identical gold coins and Sylvia has three identical silver coins. The total weight of Goldie’s coins is equal to the total weight of Sylvia’s coins. If they trade one coin with each other, then the total weight of Goldie’s coins is 12 grams less than the total weight of Sylvia’s coins. What is the weight, in grams, of each gold coin?
  1. 12
  2. 15
  3. 18
  4. 21
  5. 24

Question 13

Jasmine tea sells for 320 dollars per kg while Oolong tea sells for 480 dollars per kg. A mixture consisting of 3 parts of Jasmine tea to 5 parts of Oolong tea sells for 450 dollars per kg. What is the maximum amount, in dollars, for which 10 kg of each of Jasmine tea and Oolong tea may be sold?
  1. 8000
  2. 8080
  3. 8400
  4. 8480
  5. 9000

Question 14

Which of the following boxes has a net as shown in the diagram below?



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Question 15

The greatest common divisor of a certain positive integer and 315 is 3, and the least common multiple of the same integer and 45 is 360. What is this integer?
  1. 12
  2. 24
  3. 30
  4. 36
  5. 48

Question 16

After the fourth test, Kenny’s average mark rises by 5 points, but after the fifth test, it drops by 9 points. If his total score in the last two tests is 122 points, how many points does he score in the last test?
  1. 91
  2. 71
  3. 61
  4. 41
  5. 31

Question 17

Two paths are to be constructed in a garden 5 m by 5 m and three plans have been submitted. If the amount of space not taken up by the paths is to be as large as possible, which of the following statements is correct? Plan I Plan II Plan III

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  1. The non-path area in Plan I is the largest.
  2. The non-path area in Plan II is the largest.
  3. The non-path area in Plan III is the largest.
  4. The non-path areas in all three plans are the same.
  5. The non-path areas in Plan I and Plan III are the same.

Question 18

City B is between City A and City C. William is riding a bike from B to C, a distance of 16 km. After he has gone 6 km, Mary begins to drive a car at 60 km per hour from A to C. If William continues onward, he will reach C at the same time as Mary. If he turns back, he will reach B at the same time as Mary. What is his riding speed, in km per hour?
  1. 15
  2. 16
  3. 18
  4. 20
  5. 24

Question 19

The eight symbols 2, 0, 1, 5, I, M, A and S are to be arranged in a row. The digits must precede the letters, and 0 cannot be in the first place. How many such arrangements are there?
  1. 100
  2. 232
  3. 400
  4. 432
  5. 576

Question 20

A hotel has 11 rooms and each staff member has keys to 7 different rooms. For each room, at least two staff members must hold its key. What is the minimum number of staff members the hotel must have?
  1. 3
  2. 4
  3. 5
  4. 6
  5. 7 Questions 21-25, 6 marks each