SASMO 2018 Primary 6 (Grade 6) Contest

Question 1

Which of the following is the smallest?

1. $\frac{3+4}{6+8}$
2. $\frac{34}{68}$
3. $\frac{4-3}{8-6}$
4. $\frac{3\times4}{6\times8}$
5. $\frac{3\div4}{6\div8}$

Question 2

Shreya places 10 gemstones in a line. The first is 2 cm from point X, the second is 4 cm from the first, the third is 6 cm from the second, and so on. How far is the tenth gemstone from X?

1. 18 cm
2. 20 cm
3. 22 cm
4. 24 cm
5. None of the above

Question 3

In a sequence, the sum of any three adjacent numbers is 37. The displayed terms are $A,11,B,A,11,B,A,11,13$. Find $A$.

1. 11
2. 13
3. 24
4. 37
5. None of the above

Question 4

A game awards 10, 25, 50, 100 and 190 gold coins in Rounds 1 through 5. Which transition has the least percentage increase?

1. Round 1 to 2
2. Round 2 to 3
3. Round 3 to 4
4. Round 4 to 5
5. None of the above

Question 5

Whole numbers are arranged with 1 in Row 1, 2-3 in Row 2, 4-6 in Row 3, and so on. Which row contains 209?

1. 19
2. 20
3. 21
4. 22
5. None of the above

Question 6

Cynthia creates a three-digit passcode and wants exactly two of its digits to be 6. How many passcodes can she create? A passcode may begin with 0. Examples include 663 and 066.

1. 24
2. 27
3. 30
4. 33
5. None of the above

Question 7

A roulette wheel has the numbers 1 to 10. Which bet gives the greatest chance of winning?

1. Numbers bigger than 7
2. Numbers 9 and 10
3. Numbers 1, 2, 3 and 4
4. Even numbers
5. Odd numbers bigger than 2

Question 8

In the diagram, $\angle ABC=70^\circ$ and $\angle DAF=\angle DFA=\angle ECG=\angle EGC$. Find the sum of the four shaded angles.

1. 220°
2. 250°
3. 280°
4. 320°
5. None of the above

Question 9

Thursdays of a certain month contain the greatest possible number of prime-numbered dates. What weekday is the 14th of that month?

1. Monday
2. Tuesday
3. Wednesday
4. Thursday
5. None of the above

Question 10

Given $\frac{40}{7}=T+\frac{1}{1+\frac{1}{V+\frac1V}}$, find $T+V$.

1. 6
2. 7
3. 8
4. 9
5. None of the above

Question 11

The three-digit number $8N5$ is divisible by 45. Also $5M7+278=8N5$. Find $M+N$.

1. 12
2. 15
3. 18
4. 21
5. None of the above

Question 12

The sum of the smallest and second-smallest factors of a whole number is 8, while the sum of its two largest factors is 392. Find the number.

1. 311
2. 343
3. 392
4. 419
5. None of the above

Question 13

How many times do the hour and minute hands form a $60^\circ$ angle from 12 pm to 11 pm?

1. 18
2. 22
3. 23
4. 24
5. None of the above

Question 14

Goofy runs at 12 m/s from 4:00 pm. Pluto starts at 4:03 pm at 18 m/s. When does Pluto catch Goofy?

1. 4:06 pm
2. 4:09 pm
3. 4:18 pm
4. 5:06 pm
5. None of the above

Question 15

A cube is split into Figures 1, 2 and 3 as shown. Which option is the missing Figure 3?

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

Question 16

The sum of a four-digit number and all of its digits is 2018. Find the four-digit number.

Question 17

Find the pattern and solve for $x$: $2205991\mapsto4$, $5492689\mapsto3$, $9377953\mapsto7$, $8626129\mapsto2$, $3788483\mapsto x$.

Question 18

How many triangles are there in the figure?

Question 19

Orange soda is sold in boxes of 9 cans for \$7. One free can is given for every 2 boxes bought, and 5 empty cans can be exchanged for one free can. What is the greatest number of cans obtainable with \$35?

Question 20

A bar chart shows caviar costing \$62.50 in 2015 and \$90 in 2017. The same percentage increase occurs each year. Find the cost in 2018.