SEAMO 2018 Paper D © TCIMO 1 1 Find the last 2 digits in the sum 1 + 2 + 3 + 4 +⋯+ 2017 + 2018 (A) 75 (B) 71 (C) 56 (D) 63 (E) None of the above 4 Find the value of g in (A) 9 (B) 5 (C) 7 (D) 4 (E) No[.]
QUESTIONS TO 10 ARE WORTH MARKS EACH Find the value of g in Find the last digits in the sum + + + + ⋯ + 2017 + 2018 (A) (B) (C) (D) (E) 75 71 56 63 None of the above (A) (B) (C) (D) (E) None of the above It is now 3:15 PM After how many minutes will the minute-hand form an angle of 30° with the hour-hand? It is known that is a prime number If / + is also a prime number, find 11 (B) 11 (C) 11 (D) 12 (A) (A) (B) (C) (D) (E) None of the above (E) None of the above Find the number of digits in 4// × 512 (A) 22 When (45 − 4) is divided by 5, where (B) 23 ∈ ℤ: , the remainder is (C) 40 (D) 42 (A) (E) None of the above (B) (C) (D) (E) SEAMO 2018 Paper D © TCIMO There are black, white and Find the positive integral solution of orange balls in a bag Four balls are 1 + + = ; < = drawn without replacement Find the probability that at least balls are (A) (2 , 4 , 12) white (B) (2 , 6 , 6) (C) (3 , 3 , 6) 23 362 (B) 18 (C) 23 363 (D) 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 Given that the area of ∆BCD is 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 MARKS EACH 11 If O − P = and O/ + P / = , then the value of (A) (B) (C) (D) (E) K Q K − R is (A) 75 75 27 21 (B) (C) (D) (E) None of the above 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 ending with 92 Possible value(s) of S matches The winner scored points is/are and the loser scored points Each i 48 team got 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, and are AD and CE, respectively If the area of positive integers, where S < < ∆CLN is 7.5 cm2, find (in cm2) the If 2U + 2V + 2W = 2336, find the value area of rectangle BCDL of S (A) (B) (C) (D) (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) (E) None of the above (D) (E) None of the above SEAMO 2018 Paper D © TCIMO 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 side of an equilateral road to triangle in circle m and 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) ∶ √3 (B) ∶ 2√3 (A) 248 (C) ∶ (B) 339 (D) √3 ∶ (C) 441 (E) None of the above (D) 453 (E) None of the above 18 Let be a positive integer such that 4/ + 154 + 36 is a perfect square Find the value of (A) 13 (B) 14 (C) 15 (D) 16 (E) None of the above SEAMO 2018 Paper D © TCIMO 20 Starting from any letter ‘M’ below, 22 It is known that is a 10-digit [[[[[[[[[[[[[[[[[ , form 2017;2018< the word MADAM can be spelled by number moving up, down, left or right to an where ; and < can be any integer to adjacent letter How many ways are How many such numbers are there to spell MADAM? there that are divisible by 33? of the 23 It is known that O , P and \ are constants and when ; = 1, ; X + O; / + P; + \ = (A) 90 when ; = 2, (B) 120 ; X + O; / + P; + \ = (C) 144 (D) 169 when ; = 8, (E) None of the above ; X + O; / + P; + \ = ] when ; = −5, QUESTIONS 21 TO 25 ARE WORTH MARKS EACH ; X + O; / + P; + \ = ^ 21 It is known that ^V:K = Find (] − ^) 1+^ V for = 1, 2, 3, 4, … , 2017, 2018 Evaluate 24 Given that (; − 3) is a positive integer ^K ^/ + ^/ ^X + ^X ^1 + ⋯ + ^/2K` ^/2Ka and a factor of 3; / − 2; + 9, find the where ^K = sum of all possible values of ; SEAMO 2018 Paper D © TCIMO 25 It is known that circles with centres bK and b/ are tangent at point M AB and CD are external tangents to both the circles Given that b/ M ⊥ bK B , ∠BbK D = 120° and b/ C = 1 \S, find the area of the shaded region Leave your answer in terms of e End of Paper SEAMO 2018 Paper D © TCIMO SEAMO 2018 Paper D – Answers Multiple-Choice Questions Questions to 10 carry marks each Q1 B Q2 C Q3 A Q4 A Q5 B Q6 D Q7 E Q8 C Q9 E Q10 E Questions 11 to 20 carry marks each Q11 C Q12 D Q13 B Q14 A Q15 D Q16 D Q17 C Q18 A Q19 C Q20 C Free-Response Questions Questions 21 to 25 carry marks each 21 22 23 24 25 2017 2018 559 96 4√3 − © SEAMO 2018 Paper D 11 +