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Singapore Mathematical Society
Singapore Mathematical Olympiad (SMO) 2023
Junior Section (Round 1)
Tuesday, 30 May 2023 0930-1200 hrs
Instructions to contestants
1. Answer ALL 25 questions.
2. Enter your answers on the answer sheet provi订ed.
3. For the multiple choice questions, enter your answer on the answer sheet by shading the bubble
containing the letter (A, B, C, D or E) corresponding to the correct answer.
4. For the other short questions, write your answer on the answer sheet and shade the appropriate
bubble below your answer.
5. No steps are needed tojustify your answers.
6. Each question carries I mark.
7. No calculators are allowed.
PLEASE DO NOT TURN OVER UNTIL YOU ARE TOLD TO DO SO.
Multiple Choice Questions
1. In a certain company, one-third of the employees have a university degree. Half of the
employees who have a university degree are men and 40% ofthe employees who do not have
a university degree are women. If102 ofthe employees are men, how many of the employees
are women?
(A) 58 (B) 78 (C) 98 (D) 108 (E) 118
2. How many non-congruent triangles with integer side lengths have perimeter 7?
(A) I (B) 2 (C) 3 (D) 4 (E) 5
3. The median and mean of five distinct numbers, 4, 7, 10, 11, N, are equal. Find the sum of
all possible values of N.
(A) 18 (B) 21 (C) 26 (D) 29 (E) 35
4. The following diagram shows two semicircles whose diameters lie on the same line. AB is
a chord of the larger semicircle that is tangent to the smaller semicircle at the point Candis
parallel to the diameter DE of the larger semicircle. If IAB I= 16 cm, what is the
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