3. 𝐵𝐷𝐸𝐹 is a square embedded in a rightangled triangle 𝐴𝐵𝐶.
QUESTIONS 1 TO 10 ARE WORTH
3 MARKS EACH
1. Find the missing number.
Given that 𝐴𝐸 = 10 𝑐𝑚 and 𝐸𝐶 = 15 𝑐𝑚 ,
find, in 𝑐𝑚2 , the area of the shaded
region.
A
F
cm
E
cm
B
(A)
(B)
(C)
(D)
(E)
(A)
(B)
(C)
(D)
(E)
20
18
24
52
48
(A)
(B)
2
5
(C)
4
7
(D)
2
3
(E)
5
8
SEAMO 2021 Paper C
C
65
70
75
80
120
4. Given that 𝑚 ⊝ 𝑛 = 𝑚2 − 𝑛 2.
Evaluate (2021 ⊝ 2020) ⊝ (2020 ⊝ 2019).
(A)
(B)
(C)
(D)
(E)
2. 3-digit numbers are formed by
selecting 3 numbers 0, 2, 3, 5 and 8,
each digit used exactly once each
time. What is the probability that the
number is even?
1
4
D
16016
16154
16158
16160
16162
5. The profit from the sale of an item is
$180 if it is sold at a discounted price
of 10%. The loss is $240 if it is sold at
a discount of 20%. What is the cost
price of that item?
(A)
(B)
(C)
(D)
(E)
1
$3400
$3600
$3800
$4000
$4200
6. In the figure shown, ∠𝐴 = 72°.
8. The diameter 𝐴𝐵 of the circle with
The bisector of ∠𝐴𝐵𝐶 and the bisector
centre 𝑂 is 14 . Find the area of the
of ∠𝐴𝐶𝐸 intersect at 𝐷.
shaded region.
Take π =
22
7
.
72°
Find ∠𝐷.
(A)
(B)
(C)
(D)
(E)
18°
24°
30°
32°
36°
7. A 2-digit number ̅̅̅
𝑎𝑏 , is descending if
𝑎 > 𝑏.
(A)
(B)
(C)
(D)
(E)
9. Study the number pattern.
How many such 2-digit numbers are
there?
(A)
(B)
(C)
(D)
(E)
57.25
57.50
57.75
58.00
58.25
1
1+3
1+3+5
1+3+5+7
42
45
48
54
60
= 1
= 4
= 9
= 16
…
…
=
=
=
=
1×1
2×2
3×3
4×4
Find the largest 𝑛 such that
1 + 3 + 5 + ⋯ + 𝑛 < 300
(A)
(B)
(C)
(D)
(E)
2
17
31
33
35
None of the above
SEAMO 2021 Paper C
10. It is known that 𝑚 is a whole number 13. How many triangles are there in the
figure below?
smaller than 100. And the average of
𝑚, 99, 100, 101, … , 104 is a whole
number. Find the sum of all possible
values of 𝑚.
(A)
(B)
(C)
(D)
(E)
735
748
750
754
759
(A)
(B)
(C)
(D)
(E)
QUESTIONS 11 TO 20 ARE WORTH
4 MARKS EACH
20
21
22
23
24
11. 7 identical bean bags are to be put
into 4 baskets. There must be at
least one bean bag in each basket.
Given that each basket is labelled 14. Evaluate
from A to D, how many ways are
1
1
1
1
(1 + ) × (1 − ) × (1 + ) × (1 − ) × …
there to do so?
2
3
4
5
(A)
(B)
(C)
(D)
(E)
19
20
21
22
23
× (1 +
1
1
) × (1 −
)
2020
2021
(A)
(B)
(C)
(D)
(E)
2
3
4
5
None of the above
(A)
(B)
(C)
(D)
(E)
13
14
15
16
17
12. Abel tells lies on Monday, Tuesday
and Wednesday and tells the truth
for the rest of the week. Bernice tells
lies
on
Thursday,
Friday
and 15. Find the smallest positive integer 𝑘
Saturday and tells the truth for the
such that (269 + 𝑘) is divisible by 31.
rest of the week.
On which day of the week do they
both say, “I lied yesterday”?
(A)
(B)
(C)
(D)
(E)
Monday
Tuesday
Wednesday
Thursday
Friday
SEAMO 2021 Paper C
3
16. Find the unit digit of
19. It is observed that the numbers with
factors 3 or 7 are removed from the
following array of odd numbers:
13243 + 17381 + 42021.
(A)
(B)
(C)
(D)
(E)
4
5
6
7
8
1, 5, 11, 13, 17, 19, 23, 25, 29, 31, 37, 41, …
Find the 2021st number in the series.
17. The perimeter of the parallelogram
𝐴𝐵𝐶𝐷 is 75 cm, with 𝐴𝐸 ⊥ 𝐵𝐶, and 𝐴𝐸
equals to 14 cm. 𝐴𝐹 ⊥ 𝐶𝐷 and
𝐴𝐹 = 16 𝑐𝑚. Find the area of 𝐴𝐵𝐶𝐷.
D
A
cm
cm
B
(A)
(B)
(C)
(D)
(E)
E
F
(A)
(B)
(C)
(D)
(E)
20. Town A and Town B are 3600 m
apart. At 8:00:00 AM, two dogs run
towards each other, from Town A and
Town B, respectively. The dogs are
running at a speed of 350 m/min and
450 m/min, respectively.
C
After running for 1 minute, they turn
around again and run for 2 minutes,
and so on, each time running for 1
minute longer than previously, before
turning around.
280
285
290
300
None of the above
At what time do the 2 dogs meet?
(A)
(B)
(C)
(D)
(E)
18. A triangle is such that the length of
all its sides are whole numbers and
its perimeter is 27 cm. How many
such triangles are possible?
(A)
(B)
(C)
(D)
(E)
7013
7029
7041
7052
7073
8:41:10
8:42:15
8:43:00
8:44:30
8:45:00
AM
AM
AM
AM
AM
17
18
19
20
21
4
SEAMO 2021 Paper C
24. In trapezium 𝐴𝐵𝐶𝐷 , 𝐴𝐵 = 6 𝑐𝑚 and
𝐶𝐷 = 4 𝑐𝑚 . 𝐴𝐵 ∥ 𝐶𝐷 and 𝐴𝐶 intersects
𝐵𝐷 at 𝑂.
QUESTIONS 21 TO 25 ARE WORTH
6 MARKS EACH
21. The remainder is the same when
551, 745, 1133 and 1327 is divided
by 𝑚. Find the largest possible value
of 𝑚.
Given that the area of 𝐴𝐵𝐶𝐷 is
25 cm2, find the area of ∆𝑂𝐵𝐶.
D
22. Find the value of (𝑚 − 𝑛), given that
A
4
(1 + 2 + 3) × (1 + 2 + 3 + 4)
𝑚
𝑛
End of Paper
23. Early one morning, Uncle Sam woke
up between 5:00 AM and 6:00 AM.
He saw that the number 6 on the
clockface was right in the middle of
the hour- and minute-hand.
If Uncle Sam woke up at exactly
𝐶
AM, find the value of 𝐴𝐵 − 𝐶.
SEAMO 2021 Paper C
B
Given that 100𝑥 + 𝑦 = 2𝑥𝑦 , find the
smallest possible sum of 𝑥 and 𝑦.
100
(1 + 2 + 3 + ⋯ + 99)(1 + 2 + 3 + ⋯ + 100)
𝐵
cm
25. It is known that 𝑥 and 𝑦 are both
integral numbers.
+⋯+
5: 3𝐴
C
O
2
+
1 × (1 + 2)
3
+
(1 + 2) × (1 + 2 + 3)
=
cm
5
!
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