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QUESTIONS 1 TO 10 ARE WORTH 3 MARKS EACH
4. Find the value of g in
1. Find the last 2 digits in the sum. 1 + 2 + 3 + 4 + ⋯ + 2017 + 2018 (A) (B) (C) (D) (E)
75 71 56 63 None of the above
(A) 9 (B) 5 (C) 7 (D) 4 (E) None of the above
2. It is now 3:15 PM. After how many minutes will the minute-hand form an angle of 30° with the hour-hand?
5. It is known that . is a prime number. If ./ + 2 is also a prime number, find ..
9 11 3 (B) 5 11 9 (C) 6 11 9 (D) 6 12 (A) 5
(A) 2 (B) 3 (C) 5 (D) 7 (E) None of the above
(E) None of the above 6. Find the number of digits in 4// × 512 . (A) 22 3. When (45 − 4) is divided by 5, where
(B) 23
4 ∈ ℤ: , the remainder is
(C) 40 (D) 42
(A) 0
(E) None of the above
(B) 1 (C) 2 (D) 3 (E) 4
SEAMO 2018 Paper D © TCIMO
1
7. There
are
7
black,
5
white
and 9. Find the positive integral solution of
4 orange balls in a bag. Four balls are
1 1 1 5 + + = ; < = 6
drawn without replacement. Find the probability that at least 3 balls are
(A) (2 , 4 , 12)
white.
(B) (2 , 6 , 6) (C) (3 , 3 , 6)
23 362 (B) 1 18 (C) 23 363 (D) 1 19 (A)
(D) (3 , 4 , 4) (E) All of the above
10. Today is Saturday. What day is it 3100 days later?
(E) None of the above (A) Sunday (B) Monday
8. Given that the area of ∆BCD is 1 and
EF GF
=
GH HI
=
JI IF
=
K /
(C) Tuesday
, what is the area
(D) Wednesday
of ∆LMN?
(E) None of the above QUESTIONS 11 TO 20 ARE WORTH 4 MARKS EACH 11. If O − P = 3 and O/ + P / = 5 , then the value of
(A) (B) (C) (D) (E)
K Q
K
− R is
(A) 1 2
7 75 8 75 8 27 1 3 9 21
(B) 1 (C) 3 2 (D) 2 (E) None of the above
2
SEAMO 2018 Paper D © TCIMO
12. 15 countries took part in The World 15. It is known that S is a positive integer such that S × 874 is a 5-digit number Cup. Each team played exactly 2 ending with 92. Possible value(s) of S matches. The winner scored 3 points is/are and the loser scored 0 points. Each i. 48
team got 1 point for a draw. How many more points at most did the
ii. 58
iii. 68
iv. 108
(A) i only
champion score than the runner up?
(B) ii only (C) i and iii
(A) 48
(D) ii and iv
(B) 51
(E) i, ii and iii
(C) 53 (D) 56 (E) 59
16. In
the
figure
below, BCDL is
a
rectangle. E and F are mid-points of 13. It
is
known
that S, 4 and . are
AD and CE, respectively. If the area of
positive integers, where S < 4 < . .
∆CLN is 7.5 cm2, find (in cm2) the
If 2U + 2V + 2W = 2336, find the value
area of rectangle BCDL.
of S. (A) 4 (B) 5 (C) 6 (D) 7 (E) Unable to determine
14. How many odd digits are there in the (A) 45
result of 1 111 111 111 × 9 999 999 999?
(B) 56 (A) 10
(C) 58
(B) 11
(D) 60
(C) 8
(E) None of the above
(D) 9 (E) None of the above
SEAMO 2018 Paper D © TCIMO
3
17.
/ of the journey from Lethbridge to 19. The chord AB, common to the circles X
with centres m and n, has length 2√3.
Medicine Hat is highway, while the remaining Connecting
K X
is
the
country highway
It forms 1 side of an equilateral
road. to
triangle in circle m and 1 side of a
the
right hexagon in circle n. Find the
country road is the town of St. Paul.
ratio of the areas of both circles.
A van left Lethbridge for Medicine Hat,
travelling
at
100
km/h
on
highway and 60 km/h on country road. A car left Medicine Hat for Lethbridge, travelling at 70 km/h on country
road
and
110
km/h
on
highway. The car and the van passed each
other
44
km
away
from
St. Paul. Find, in km, the distance from Lethbridge to Medicine Hat.
(A) 1 ∶ √3 (B) 3 ∶ 2√3
(A) 248
(C) 1 ∶ 3
(B) 339
(D) √3 ∶ 4
(C) 441
(E) None of the above
(D) 453 (E) None of the above
18. Let 4 be a positive integer such that 4/ + 154 + 36 is a perfect square. Find the value of 4. (A) 13 (B) 14 (C) 15 (D) 16 (E) None of the above
4
SEAMO 2018 Paper D © TCIMO
20. Starting from any letter ‘M’ below, 22. It
is
known
that 4 is
a
10-digit
[[[[[[[[[[[[[[[[[ , form 2017;2018
