SASMO 2017 Primary 6 (Grade 6) Contest

Question 1

Find $112\times112-111\times113$.

1. 0
2. 1
3. 2
4. 10
5. 100

Question 2

There are 50 students in classroom A. Two fifths learn piano. One fifth of those who learn piano wear spectacles. How many learn piano but do not wear spectacles?

1. 4
2. 6
3. 16
4. 24
5. None of the above

Question 3

Isabella learns 1 new word every Monday, 2 every Tuesday, 3 every Wednesday, and so on up to 7 every Sunday. Starting on Monday, on which weekday will she learn the 90th word?

1. Saturday
2. Sunday
3. Monday
4. Tuesday
5. Wednesday

Question 4

Find the next number in $2,12,30,56,90,\ldots$.

1. 100
2. 116
3. 124
4. 132
5. None of the above

Question 5

The sum of five consecutive numbers is 625. What is the largest number?

1. 125
2. 127
3. 129
4. 130
5. None of the above

Question 6

The figure is made from a square and three rectangles. The square area is 64 cm². Find the area of the shaded triangle.

1. 9 cm²
2. 16 cm²
3. 24 cm²
4. 32 cm²
5. Not enough information

Question 7

How many two-digit numbers are divisible by both 6 and 4?

1. 4
2. 5
3. 6
4. 8
5. 9

Question 8

Ten workers take 2 days to dig a 5-metre well. How long will 4 workers take to dig a 10-metre well, assuming equal rates?

1. 2 days
2. 4 days
3. 8 days
4. 10 days
5. None of the above

Question 9

Find $X$ such that $2017-7\times2\div X\times5=267$.

1. 25
2. 5
3. 0.25
4. 0.04
5. 0.0016

Question 10

A rectangle's breadth is increased by 50%. By what percentage should its length decrease so that the area is unchanged? Round to the nearest whole percent.

1. 67%
2. 66%
3. 50%
4. 34%
5. 33%

Question 11

A coin of perimeter 44 cm rolls 2017 cm to a wall. Which direction will its arrow point when it reaches the wall?

1. Figure A
2. Figure B
3. Figure C
4. Figure D
5. Figure E

Question 12

A pie chart shows how Primary 6 students travel to school. The train sector is $88^\circ$ and the bus sector $140^\circ$. If 110 students travel by train, how many travel by bus?

1. 170
2. 175
3. 180
4. 185
5. None of the above

Question 13

In the diagram, $CDEF$ is a square, $E$ is the midpoint of $DG$, $AD=2DC$, and $\angle ABC$ and $\angle ADG$ are right angles. If $\angle BAG=105^\circ$, find $\angle BCA$.

1. 15°
2. 20°
3. 25°
4. 30°
5. 45°

Question 14

Ken, Ronald and Wendy each make two statements about whether the food is fries, burger, pie or hotdog. One person makes two true statements, one makes one true and one false, and one makes two false statements. What is the food?

1. Fries
2. Burger
3. Pie
4. Hotdog
5. Not enough information

Question 15

A square paper is folded as shown and three differently shaped holes are punched. Which option shows the holes after the paper is unfolded?

1. Figure A
2. Figure B
3. Figure C
4. Figure D
5. Figure E

Question 16

A three-digit number has digit sum 25 and digit product 567. Find the greatest such number.

Question 17

Tom thinks of a number, adds 12, then multiplies by 7. The result is 10 times the original number. What number did he think of?

Question 18

Each numbered cell indicates how many surrounding cells must be shaded. How many cells are shaded after completing the grid according to the rules?

Question 19

A clock shows 6:00. After how many minutes will the hour and minute hands first form an angle of $15^\circ$?

Question 20

In a 200-m race, when Usain finished, Yohan was 20 m behind and Nickel was 36 m behind Yohan. At constant respective speeds, how far was Nickel from the finish when Yohan finished?