SASMO 2015 Secondary 1 (Grade 7) Contest

Question 1

Given that -3 ‹ x ‹ 4, find the least possible value of x?.

1. 16
2. 9 G fd
3. See the source image for option C.
4. 0
5. None of the above

Question 2

Find the largest odd number between 1 and 100 that is divisible by 6 and by 7.
A 42

1. 42
2. 54
3. 56
4. 84
5. None of the above

Question 3

Find the next term of the following sequence: 3, 1, 4, 5, 21, ...

1. 45
2. 46
3. 47
4. 106
5. 2015

Question 4

If both n and 2 are positive integers, how many possible values of n are there?
A 4

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

Question 5

A palindromic number is a whole number that reads the same forward and
backward. For example, 1221 is a palindromic number. How many 5-digit
palindromic numbers are there?

1. 190
2. 900
3. 1000
4. 90000
5. None of the above

Question 6

An operator ¢ acts on two numbers to give the following outcomes:
3¢2= 15
5¢3= 28
1¢6= -57
4¢9=-513
What is 5 @ 7 equal to?

1. 122
2. 212
3. -122
4. -212
5. None of the above

Question 7

The diagram shows how an equilateral triangle can be cut into four pieces and
rearranged to form a square. This solution of the Haberdasher’s Puzzle is
discovered by Henry Dudeney (1857 — 1930).
If the length of the square is 19 cm and the height of the triangle is 25 cm, find
the length of the triangle, correct to the nearest whole number.

1. 27cm
2. 28cm
3. 29cm
4. 30cm
5. 31cm

Question 8

Some people are standing equally spaced around a circle, and they were
numbered starting from the number 1 in a clockwise direction. If the person
numbered 14 is directly opposite the person numbered 40, how many people
are there?

1. 48
2. 50
3. . 52
4. 54
5. 56 an

Question 9

If the five-digit number 4567N is divisible by 8, find N.

1. 8
2. 6 ca 4 Byars
3. See the source image for option C.
4. See the source image for option D.
5. 0

Question 10

A big cube is made up of 27 small cubes. All the faces of the big cube are then
painted. How many of the small cubes have exactly two painted faces?

1. 4
2. 8 Gy 12
3. See the source image for option C.
4. 16
5. None of the above

Question 11

The figure shows a circle with 4 points on its circumference. Each point is
joined to every other point by a line (called a chord). The chords divide the
circle into 8 regions.
Find the maximum number of regions formed by the chords for a circle with 5
points.

1. 14 Beis
2. See the source image for option B.
3. See the source image for option C.
4. 17
5. None of the above

Question 12

The product of two numbers is 10 000. Neither of the two numbers has 10 as a
factor. Find the difference of these two numbers.

1. 45
2. 210
3. 609
4. 1242
5. Not enough given information to find

Question 13

Find the smallest whole number n for which 108n is a multiple of 360.

1. 3
2. 5
3. 10
4. 30
5. None of the above

Question 14

A circle and a quadrilateral are drawn on a flat surface. What is the biggest
number of regions that can be formed on the surface?

1. 6
2. 8 G10
3. See the source image for option C.
4. 12
5. 14

Question 15

70 cakes are packed in two different box sizes. The small box holds 6 cakes and
the big box holds 8 cakes. If more than 10 boxes are used and all the boxes are
fully packed, how many small boxes are used?
AD:
B. 5
C7
Dd, 9
Bead

1. 2
2. 5 G7
3. See the source image for option C.
4. 9 Er di
5. See the source image for option E.

Question 16

Jane is at a road junction with four possible roads to her friend's house, but she
Bee! did not know which road to take. So she asks some passersby for direction.
First Passerby: Your friend’s house is not on Road 1.
Second Passerby: I did not want to live near your friend, so I moved from
Road 2 to Road 4.
Third Passerby: I have taken Road 2 to the beach before, but I have not passed
by any house.
Fourth Passerby: Your friend stays on Road 3.
If only one of the passerby is telling the truth, on which road does Jane's friend
live?
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Question 17

Elsie has 20 pens. She divides them into 4 piles so that each pile has a different
number of pens. Find the smallest possible number of pens in the biggest pile.
ie
lig 23

iS
Se ee ee

Question 18

Anna thinks of 7 different positive integers. None of the integers is a multiple of
each other. What is the least possible sum of these 7 integers?

Question 19

The diagram shows a square, an equilateral triangle and parts of a regular
polygon. How many sides does the latter polygon have?

Question 20

In the figure below, the ratio of the area of AABC to the area of AADE to the
area of AAFG is 7: 8: 15. Given that \$ of the area of AADE is shaded, what
fraction of the figure is shaded?

A BD F

€
E
G
Se ne eens ae Se ee Se
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