SASMO 2016 Secondary 3 (Grade 9) Contest

Question 1

Calculate the value of
99x2+999X3+9999x4+99999 x5

1. 111 010
2. 110 110
3. 111 001
4. 110 011
5. None of the above

Question 2

In the SASMO contest, there are 15 multiple choice questions. 2 points are
awarded for a correct answer and 1 point is deducted for a wrong answer. No
points are deducted or awarded for an unanswered question. Albert answered 12
questions and left the remaining unanswered. If his total score is less than 17,
find the maximum number of questions he answered correctly.

1. 7
2. 8 Gg, 9
3. See the source image for option C.
4. 10 EB. df
5. See the source image for option E.

Question 3

How many digits are there in the number 52°16 x 41006?
i A. 2012
i B, 2013
i Cc. 2014
D. 2015
i E. 2016
let
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See ee ee eS SSS el

1. 2012
2. 2013
3. 2014
4. 2015
5. 2016

Question 4

Given that 1 — sin(x) + ,/3y — x = 0, where 0 ‹ x ‹ a. Find the value of x — y.

1. 60 «
2. See the source image for option B.
3. 22
4. on
5. See the source image for option E.

Question 5

If the five-digit number A9828 is divisible by 45, find the sum A + B.
AS

1. 5
2. 8
3. 13
4. 17
5. None of the above

Question 6

Which of the following has the largest value?
2016**
A 20164?
2016**-1

1. 201642
2. 201642-1
3. 2016
4. 4064 256
5. Options A & D

Question 7

E | How many positive even 2-digit numbers are divisible neither by 3 nor by 7?

1. 21
2. 29
3. 43
4. 56
5. None of the above

Question 8

Given that

: 1 vx 1 3 Jy _8
7‹a 55 and Pee gaat)
where x and y are whole numbers.
= Find the smallest possible value of x — y.

1. —32
2. 9
3. —55
4. —56
5. —57

Question 9

ES] How many factors of 324 000 are perfect cubes?
ES]

1. 3
2. See the source image for option B.
3. See the source image for option C.
4. See the source image for option D.
5. 9 i - fat ee ee SS SSS SSE

Question 10

The year 2016 is an interesting number because it is divisible by 1, 2, 3, 4, 6, 7,
8 and 9. When was the previous year that has the same properties as above?

1. 504
2. 1522
3. 1512
4. 2520
5. None of the above

Question 11

There are 60 people in a tourist bus. 15 of them are going to Orchard and 30 of
them are going to Sentosa. (Some people are going to both). What is the
greatest number of people who are neither going to Orchard nor to Sentosa.

1. 15
2. 20
3. 30
4. 45
5. None of the above

Question 12

How many triangles are there in the diagram below?

1. 24
2. 40
3. 48
4. 50
5. None of the above

Question 13

What is the greatest amount of numbers which must be selected (not randomly)
from 108 numbers: 1, 2, 3,..., 108, to ensure that there are no two numbers
(among selected) with the product of 108?

1. 96
2. 102
3. 103
4. See the source image for option D.
5. None of the above6

Question 14

Amy, Emily and Raisa each has one cat. The names of the cats are Bella, Kitty
and Max. The three cats have different colours: calico, ginger and grey. It is
known that:
i) Kitty does not belong to Emily, and the calico cat does not belong to Raisa.
ii) Bella is the calico cat.
iii) Max's colour is not ginger.
iv) Raisa’s cat is not Kitty.
Which of the following statement is correct?

1. The calico cat is Max, who belongs to Emily.
2. The ginger cat belongs to Raisa, and Amy has a grey cat.
3. Raisa has a grey cat named Max.
4. Emily’s cat is Bella and Amy's cat is Max.
5. None of the above.

Question 15

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1. See the source image for option A.
2. See the source image for option B.
3. See the source image for option C.
4. See the source image for option D.
5. See the source image for option E.

Question 16

How many integers n satisfy the inequality
2010 ‹ /n(n—1) ‹ 2016?
Easy

Question 17

i | Find the smallest possible value of the expression
FS} (9—a)(5—a)(a+9)(a+5),
; where a is a real number.

Question 18

Find P in the sequence below
61,52, 63,94, 46, P

bE

f
SS EE

Question 19

The numbers 1, 2,3, 4,...,99, 100 are written on a whiteboard. Tom choose any
two numbers a and b, erases them and then writes down their sum a+b. He
continues the same process until one number is left on the whiteboard. What is
this number?

Question 20

122 309 is the product of two prime numbers. Find the largest of the two prime
numbers.