Problems And Solutions SEAMO PAPER D 2016

16. A circle of circumference 2 m rolls around the equilateral triangle of a perimeter of 6 m. How many turns does the circle make as it rolls around the triangle once, without slipping?

(A) 3
(B) 4
(C) 5
(D) 6
(E) None of the above

17. How long will it be before the minute hand next lies directly over the hour hand?

(A) 1 hour 15 minutes
(B) 2 hours 40 minutes
(C) 4 hours
(D) 12 hours
(E) None of the above

18. There are 9 white, 5 red and 6 black balloons. 10 balloons are picked at
random such that there are at least 2 but not more than 8 white, there are at least 2 red and there are not more than 3 black balloons. How many ways are there to do this?

(A) 4
(B) 9
(C) 16
(D) 18
(E) 21

19. Candle A took 3 hours to finish burning. Candle B took 5 hours to finish burning. Candle B is shorter and thicker than Candle A. They were lit at the same time and had the same height two hours later. What was the ratio their heights at first?

(A) 8 : 5
(B) 9 : 5
(C) 8 : 3
(D) 5 : 3
(E) None of the above

20. Find the largest number \(n\) such that there
is only one whole number \(k\) that satisfies

\(\frac{9}{17}<\frac{n}{n+k}<\frac{8}{15}\)

(A) 100
(B) 104
(C) 108
(D) 112
(E) 116

21. Fill in each circle with numbers from 1 to 10, without repetition, such that the average of any group of 5 adjacent numbers is the minimum.

22. Evaluate

\(\frac{1}{1+2}+\frac{1}{1+2+3} + \frac{1}{1+2+3+4}+…+\frac{1}{1+2+3+4+…+100}\)

23. The figure shows a \(4 ×4\) grid. The sum of \(4\) numbers in each row, column and diagonal is 2016. Find \((a + b + c + d)\).

24. The figure below shows a right-angled triangle with semicircles A, B and C
constructed using its sides as diameters. The circumference of semicircle A is 13π. The area of semicircle B is 12.5π. What is the radius of semicircle C?

25. \(AE ⊥ BE , AF ⊥ CD\) in the parallelogram shown below. Given that \(∠EAF = 60°\) , \(BE = 2\; cm\) and \(DF = 3\; cm\) , find \(∠ABC\) and the length of \(CD\).