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SEAMO 2027 - Paper A - SET 03 - Self-study

Question 1

SEAMO self-study edition 2027; not an official 2027 paper. Original source years are retained. 25 questions, 90 minutes; Q1–10: 3 points, Q11–20: 4 points, Q21–25: 6 points, total 100. Original response types and all subparts are preserved. Verified is an editorial convention; source defects, necessary assumptions and unresolved mathematical uncertainty are disclosed.

What number between 37 and 47 is exactly divisible by both 2 and 3?

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Question 2

Find the missing number: \(1,4,9,16,25,36,(\quad),\ldots\).

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Question 3

How many triangles are there in the figure below?

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Question 4

Find the value of \(1+2+3+\cdots+9+10+9+\cdots+3+2+1\).
  1. 98
  2. 100
  3. 102
  4. 104
  5. 106

Question 5

Dots form a series of patterns as shown. Find the number of dots in Figure 8.

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Question 6

Three students had 88, 87 and 92 stickers, respectively. A fourth student joined the group and gave some stickers to each of them. In the end, everyone had 95 stickers. How many stickers did the fourth student have at first?

Question 7

The sum of the dates of all Wednesdays in a certain month is 66. On which day of the week was the first day of the month?

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  1. Monday
  2. Tuesday
  3. Wednesday
  4. Thursday
  5. Friday

Question 8

Peter turns ON his ceiling fan by flipping the switch once. Is the ceiling fan ON or OFF if he flips the switch another 27 times?

Question 9

Town A and Town B are 650 km apart. At 9:00 AM, a truck leaves Town A for Town B and a car leaves Town B for Town A. The truck travels 60 km in one hour and the car travels 70 km in one hour. At what time do the vehicles pass each other?

Treat both vehicles as travelling towards each other along the same route at the stated constant speeds.

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Question 10

Find the value of the star in the picture.

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

Question 11

Evaluate \(1+2+3+\cdots+9+10+9+8+\cdots+2+1\).
  1. 89
  2. 90
  3. 99
  4. 100
  5. None of the above

Question 12

Which of the numbers listed below are not divisible by 7?
21, 35, 63, 45, 70, 17

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  1. 35 and 70
  2. 35 and 63
  3. 63 and 45
  4. 45 and 17
  5. None of the above

Question 13

What is the time in Figure 4?

Follow the time pattern shown; the hour hands in the original drawing are approximate.

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  1. 10:20 AM
  2. 10:25 AM
  3. 10:30 AM
  4. 10:35 AM
  5. None of the above

Question 14

Find the value of \(1+11+21+31+41+9+19+29+39+49\).

Question 15

A box contains four balls of different colours (red, green, yellow and blue) in a row. The green ball is not second. The red ball is neither first nor last. The yellow ball is next to neither the red nor the blue ball. What is their order from first to last? Use B = blue, R = red, G = green and Y = yellow.

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Question 16

Baby Sophie is 2 years old. In 3 years, Mummy will be 5 times as old as Sophie. How old is Mummy now?

Question 17

Find the value of \(11+12+13+14+15+16+17+18+19\).
  1. 131
  2. 135
  3. 137
  4. 140
  5. 141

Question 18

Find the number of shortest paths from A to B using the gridlines shown below.

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  1. 42
  2. 37
  3. 36
  4. 24
  5. None of the above

Question 19

There are 26 chickens and rabbits on a farm. The farmer counts 80 legs altogether. How many rabbits are there?

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  1. 14
  2. 15
  3. 16
  4. 17
  5. None of the above

Question 20

There are 10 ostriches and goats on a farm. An ostrich has 2 legs and a goat has 4. The farmer counts 32 legs altogether. How many goats are there?

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  1. 6
  2. 7
  3. 8
  4. 11
  5. 12