SEAMO 2018 Paper C © TCIMO 1 1 Find the ones digit in 1" + 2% + 3''''( + 4''''* + 5,'''' +6,'''' + 7,% + 8," (A) 5 (B) 6 (C) 7 (D) 8 (E) 9 3 Evaluate 1 1 × 2 × 3 + 1 2 × 3 × 4 + 1 3 × 4 × 5 +⋯ + 1 99 × 100 × 101[.]
QUESTIONS TO 10 ARE WORTH MARKS EACH Evaluate 1 + + +⋯ 1×2×3 2×3×4 3×4×5 + 99 × 100 × 101 Find the ones digit in 1" + 2% + 3'( + 4'* + 5,' +6,' + 7,% + 8," (A) (B) (C) (D) (E) (A) 5049 20200 (B) 10099 20200 (C) (D) 10099 10100 (E) None of the above The figure is made of 13 squares, each of side length cm It is known that line AB divides the figure into regions of equal areas Find the length How many shortest paths are there from point A to point B passing through of AX, in cm P and Q? (A) (B) 4 (C) (D) 4 (A) (B) (C) (D) (E) (E) None of the above SEAMO 2018 Paper C © TCIMO 48 54 60 66 72 The product of the numerator and After a certain amount of water is denominator of a proper fraction is added to a bottle of sodium chloride, 420 How many such possible proper its salt content becomes 15% fractions are there? The same amount of water is added (A) the 2nd time and the salt content (B) becomes 12% (C) (D) 10 (E) None of the above Find the remainder in 7777777777777 56565656 × 777 56 (A) What is the salt content, in %, after (B) the same amount of water is added a (C) 3rd time? (D) (A) (E) (B) (C) (D) (E) None of above SEAMO 2018 Paper C © TCIMO There are 3, and 10 vertices in 10 The formula to convert temperature Figures 1, and 3, respectively in Celsius to Fahrenheit is 89:;99 9?@ , >8 = 3G8 and 8I = FI times the sum of the ages of his Given two sons In 2018, Anand’s age is 14 cm2, find the total area, in @J, , of twice the sum of the ages of his two the shaded regions that the area of ∆FG> is sons In which year is Anand born? (A) 1962 (B) 1963 (C) 1964 (D) 1966 (E) None of the above (A) 13 Three scholars Sam, Rex and Ted, (B) study English, Math, Science, Dance, (C) Music and Art • (D) The Science and Math students (E) None of the above are neighbors • The youngest among them is Rex • Sam exercises with the Dance, 15 Twenty-four 4-digit numbers can be Music and Math students formed using the digits 3, 4, and 8, The Dance student is older than without repeat Find the average of • the English student • • these 4-digit numbers Rex plays chess with the Music and English students (A) 5250 Each student studies two subjects (B) 5625.5 (C) 5832.75 Which two subjects does Ted study? (D) 5830 (E) None of the above (A) Science and Art (B) Math and English (C) Math and Science (D) Dance and Music (E) None of the above SEAMO 2018 Paper C © TCIMO 16 How many numbers at maximum can 18 Akani be selected from: that the two 20¢ and three $1 coins in his pocket He picks out 1, 2, 3, … , 49, 50 such has sum of the any two coins at random, one after another, without replacement What numbers cannot be divided by 7? is the probability that the total value of the two coins is $1.20? (A) 19 (B) 20 (A) (B) (C) (D) (C) 21 (D) 22 (E) 23 17 There are ten cards numbered: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29 Each time a card is drawn, the (E) None of the above number is recorded, then put back into the deck and shuffled After repeating the process times, the 19 The figure shows two circles and a square of side 12 cm Find the total product of all the recorded numbers area of the shaded regions is M Which of the following numbers cannot be M? 136, 198, 455, 1925, 2018 (A) 455 and 2018 (B) 136 and 455 (C) 136 and 198 (D) 1925 and 2018 (A) 14N @J, (E) None of the above (B) 16N @J, (C) 18N @J, (D) 20N @J, (E) None of the above SEAMO 2018 Paper C © TCIMO 20 Madam Evie drives from Bandung to 23 Find the difference between the area Surabaya at a constant speed of the three squares and the area of V km/h If she increases her speed the four triangles in the figure below by 20%, she will arrive hours ahead of schedule If she travels the first 100 km at V km/h, the increases her speed by 25%, she will still arrive hours ahead of schedule Find the distance, in km, between Bandung and Surabaya (A) (B) (C) (D) (E) 480 520 560 600 None of the above 24 A queue is building up at a constant rate at the museum before its opening at 10:30 AM If entrances are opened, the queue clears at 10:39 AM If entrances are opened, QUESTIONS 21 TO 25 ARE WORTH MARKS EACH the queue clears at 10:35 AM What time did the 1st visitor start queuing? 21 A new operation is defined as: J ⨁ = = J × (J + 1) × (J + 2) × … × (J + = − 1) 25 A number from to is filled into each circle below, such that the sum of numbers on any face is the Given that (J ⨁ 3) ⨁ 2 = 3660 , find same and cannot divide 45 Which the value of m number cannot be used? 22 Evaluate (2, + 4, + ⋯ + 100, ) − (1, + 3, + ⋯ + 99, ) + + + ⋯ + + 10 + + ⋯ + + + End of Paper SEAMO 2018 Paper C © TCIMO SEAMO 2018 Paper C – Answers Multiple-Choice Questions Questions to 10 carry marks each Q1 B Q2 C Q3 A Q4 E Q5 B Q6 A Q7 E Q8 C Q9 C Q10 B Questions 11 to 20 carry marks each Q11 D Q12 A Q13 D Q14 B Q15 C Q16 E Q17 A Q18 D Q19 C Q20 D Free-Response Questions Questions 21 to 25 carry marks each © SEAMO 2018 21 22 23 24 25 50.5 122 $%& 9:45 AM Paper C