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SASMO 2019 Grade 6

Question 1

Grading on this platform: start at 0; Q1–15 award 2 points each and Q16–25 award 4 points each; wrong or blank answers score 0; maximum 70. Official SASMO reference rules: start at 15; Section A +2/−1/0 for correct/wrong/blank; Section B +4/0/0; maximum 85. The supplied volume prints the section rates and maximum 85, but does not explicitly print the initial 15; that baseline comes from the official format reference.

Find the sum of all digits of the following product: 693 × 333.
  1. 230769
  2. 229669
  3. 27
  4. 34
  5. None of the above

Question 2

In a school, 52 students were given vouchers for a bookstore or cafeteria. Twenty of them received bookstore vouchers and 39 students received cafeteria vouchers. How many students received both vouchers?
  1. 8
  2. 9
  3. 10
  4. 11
  5. None of the above

Question 3

A cube is a solid consisting of identical squares. A cube has 6 faces. A “dodecahedron” is a solid consisting of identical pentagons (5-sided shapes), as illustrated below. If a dodecahedron has 12 faces, how many edges does it have?

Question illustration

Question illustration
  1. 5
  2. 20
  3. 12
  4. 30
  5. None of the above

Question 4

William has 3 books: Charlotte’s Web, Little Prince and Hobbit. How many ways can he arrange these books in a row such that Hobbit and Charlotte’s Web are next to each other?
  1. 6
  2. 2
  3. 4
  4. 12
  5. None of the above

Question 5

Clayton gave 77 baseball cards to his friend and 112 baseball cards to his brother. In the end, Clayton is left with 441 baseball cards. What percentage of his original number of cards did Clayton give away?
  1. 70%
  2. 60%
  3. 40%
  4. 30%
  5. None of the above

Question 6

In the diagram, ABCD and CEFG are squares, and CED is an equilateral triangle. Find the measurement (in degrees) of angle \(\angle EAC\).

Question illustration

The rightmost vertex is F; its label is obscured in the original question scan. The source solution drawing makes the label visible.
  1. 45°
  2. 36°
  3. 32°
  4. 30°
  5. None of the above

Question 7

Annabelle, Betty, Cynthia and Dora are playing a new video game. After the first round:
- Cynthia’s gold coins equal the average of Annabelle’s and Betty’s.
- Annabelle’s coins are half of Betty’s.
- Betty and Dora have the same number.
- Dora has 10 more coins than Cynthia.

What is their total number of gold coins?
  1. 140
  2. 130
  3. 70
  4. Insufficient data
  5. None of the above

Question 8

Each of the 3-digit numbers ABC, BCA and CAB is even and divisible by 9. If A, B and C are different digits, find A + B + C.
  1. 18
  2. 9
  3. 20
  4. 12
  5. None of the above

Question 9

Consider all the whole numbers from 1 to 50. Which statement is NOT true?

Interpret “least occurring” as attaining the minimum, allowing ties.
  1. The number of even numbers is the same as the number of odd numbers.
  2. Writing all the digits, the digit 0 is the least occurring digit.
  3. There are more 2-digit numbers than 1-digit numbers.
  4. The number of multiples of 5 is the same as the number of multiples of 7.
  5. The average of the 50 numbers is not a whole number.

Question 10

A pipe can fill an empty tank in 4 hours. Due to leakage, the pipe fills the empty tank in 12 hours. If the tank is full and the pipe is removed, how long will the leakage take to empty it?

Assume constant filling and leakage rates throughout.
  1. 6 hours
  2. 8 hours
  3. 9 hours
  4. 16 hours
  5. None of the above

Question 11

Seventy days after the day before yesterday is Friday. Which day of the week is tomorrow?
  1. Friday
  2. Saturday
  3. Sunday
  4. Thursday
  5. None of the above

Question 12

At 12 p.m., the hour and minute hands point in the same direction. What is the exact time between 6 p.m. and 7 p.m. when they point in the same direction?
  1. 6:30 p.m.
  2. 6:\(32\frac8{11}\) p.m.
  3. 6:\(33\frac3{11}\) p.m.
  4. 6:\(32\frac7{11}\) p.m.
  5. None of the above

Question 13

Four athletes run in a marathon and make these statements:
- Tom: I’m the fastest.
- Jack: I’m the slowest.
- Lionel: I’m neither the slowest nor the fastest.
- Robert: I’m not the fastest.

If exactly 3 tell the truth, who is the slowest?

Assume all four athletes have distinct finishing positions, with no ties.
  1. Tom
  2. Jack
  3. Lionel
  4. Robert
  5. Insufficient data

Question 14

The product of all whole numbers from 2 to M is a multiple of 1365. What is the least possible value of M?
  1. 13
  2. 15
  3. 65
  4. 1365
  5. None of the above

Question 15

Find the missing figure in the diagram below.

Question illustration

Use one consistent position-by-position combination rule down every column.
  1. Figure A
  2. Figure B
  3. Figure C
  4. Figure D
  5. Figure E

Question 16

How many triangles are there in the diagram?

Question illustration

Count triangles of every size whose three full sides are drawn.

Input: enter the requested whole-number answer without units. You may omit leading zeroes from the paper answer grid.

Question 17

Find the numerator of the following sum in its simplest form: \(\frac12+\frac14+\frac18+\cdots+\frac1{128}\).

Input: enter the requested whole-number answer without units. You may omit leading zeroes from the paper answer grid.

Question 18

The bar chart shows Nicki’s phone usage time in four months. The percentage decrease stays the same each following month. Find the total usage time, in hours, during the four months, rounded to the nearest whole number.

Question illustration

Input: enter the requested whole-number answer without units. You may omit leading zeroes from the paper answer grid.

Question 19

What is the missing number in this sequence?

131, 228, 331, 430, 531, 630, 731, ?, 930

Intended pattern convention: interpret the terms using the months of a non-leap year.

Input: enter the requested whole-number answer without units. You may omit leading zeroes from the paper answer grid.

Question 20

Andrew, Barry, Cassie and Drake bought candies. Andrew’s number equals \(1/3\) of the total of Barry, Cassie and Drake. Barry’s number equals 25% of the total of Andrew, Cassie and Drake. The ratio of Cassie’s candies to the total of the other three is 2:5. Drake bought 3 fewer candies than Cassie. How many candies did they buy altogether?

Input: enter the requested whole-number answer without units. You may omit leading zeroes from the paper answer grid.