Problem and Solution SEAMO 2019 paper C. Soal ini bersumber dari seamo-official.org
1.A new operation is defined as
\(m*n=\frac{m+n}{2}\)
Evaluate \(3 * (6 * 8)\)
(A) 2
(B) 3
(C) 4
(D) 5
(E) None of the above
2. 10 identical circles are arranged as shown.
AB is a straight line that cuts through the centres of 2 circles.
What is the ratio of the area above line AB to the area below line AB ?
(A) 2 : 7
(B) 2 : 3
(C) 7 : 13
(D) 9 : 11
(E) None of the above
3. John writes the following numbers on the whiteboard:
8, 9, 10, 11, 12, 13, 14
Each time, he selects 2 numbers to erase. Then, he replaces them with
another number that is 1 less than their sum. What will be the last number remaining on the whiteboard?
(A) 23
(B) 29
(C) 69
(D) 71
(E) None of the above
4. At 2:45 PM, the angle formed by the hour and minute hands is \(x°\) , where \(0° < 3 < 180°\). What is the value of \(x°\) ?
(A) 163°
(B) 169°
(C) 172.5°
(D) 175°
(E) None of the above
5. There were 4 Thursdays and 5 Fridays in the month of October some years ago. On which day of the week was the \(20^{th}\) of October that year?
(A) Monday
(B) Tuesday
(C) Wednesday
(D) Thursday
(E) Sunday
6. \(p\) and \(q\) are prime numbers. Given that \(2p+5q=2019\), find \(p-q\)
(A) 992
(B) 984
(C) 889
(D) 968
(E) None of the above
8. 1-, 2-, 4-, 8- and 16-gram weights are used on a balancing device. Given that the weight(s) can only be placed on one side of the device, how many different masses is the device capable of measuring?
(A) 28
(B) 29
(C) 30
(D) 31
(E) None of the above
9. A rectangle paper is folded along the diagonal as shown in the diagram
below. Find the area of the shaded region.
(A) 11
(B) 12
(C) 13
(D) 14
(E) None of the above
10. Group A consists of 16 numbers whose sum is 98.
Group B consists of some numbers whose average is 11.
The average of all the numbers in both groups is 8.
How many numbers are there in Group B?
(A) 9
(B) 10
(C) 11
(D) 12
(E) None of the above
11. In the diagram below, \(∠ADB= 90°\) and \(C\) is the midpoint of arc \(AB\).Given that the area of the shaded region \(x\) is \(12 cm^2\) , find the area of the shaded region \(y\) in \(cm^2\).
(A) 12
(B) 14
(C) 12π
(D) 14π
(E) None of the above
12. 60% of the students at North Shore School were boys. 44% of the students took part in the sports meet, of which 52% were boys. What percentage of the North Shore girls did not participate?
(A) 60%
(B) 64%
(C) 68%
(D) 72%
(E) None of the above
13. Cindy and Diane each have some savings. If Cindy spends $20 and Diane spends $10 a day, Cindy will have $3500 remaining when Diane finishes up her savings. If Cindy spends $10 and Diane spends $20 a day, Cindy will have $3950 remaining when Diane finishes up her savings. How much money does Cindy have at first?
(A) $3900
(B) $4100
(C) $4300
(D) $4500
(E) None of the above
14. A bag contains 4 red and 4 black balls. When 3 balls are chosen at random, without replacement, the probability of getting 2 red balls and 1 black ball
is \(\frac{n}{m}\).
Find \(m+n\).
(A) 5
(B) 6
(C) 7
(D) 8
(E) None of the above
15. At least how many numbers from 1 to 30 must be chosen to ensure there always exists a number that is twice another?
(A) 17
(B) 18
(C) 19
(D) 20
(E) None of the above
16. Find the integer part of
\(\frac{1}{\frac{1}{71}+\frac{1}{72}+\frac{1}{73}+\frac{1}{74}+\frac{1}{75}}\)
(A) 14
(B) 13
(C) 12
(D) 15
(E) None of the above
17. An equilateral triangle of side length 1 is rotated pivoting at B. Then it is turned at point C. Find the distance travelled by the point A.
(A) \(\frac{7}{5}π\)
(B) \(\frac{6}{5}π\)
(C) \(\frac{5}{3}π\)
(D) \(\frac{4}{3}π\)
(E) None of the above
18. Find the value of \(a\), when \((a-b)\) is minimum.
(A) 573
(B) 575
(C) 577
(D) 579
(E) None of the above
19. Pipe A takes twice as long to fill a pool as compared with Pipe B.
It takes them 12 hours to fill a pool when turned on together.
If Pipe A alone is turned on for m hours and then turned off, Pipe B will take another 9 hours to fill the pool.
Find m.
(A) 14
(B) 16
(C) 18
(D) 20
(E) None of the above
20. Given that
\(a=5^{39}, b=3^{52}, c=2^{91}\)
which of the following statements is true?
(A) \(a>b>c\)
(B) \(b>c>a\)
(C) \(b>a>c\)
(D) \(c>a>b\)
(E) None of the above
21. Find the remainder if the following expression is divided by 11.
\(\underbrace{2\times 2\times 2\times 2\times …\times 2\times 2\times 2}_{\mbox{2019}}\)
22. \(\overline{abc}\) is a 3-digit number with no repeated digits. Given that
\(\overline{ab}+\overline{ba}+\overline{ac}+\overline{ca}+\overline{bc}+\overline{cb}=\overline{abc}\)
the sum of digits of \(\overline{abc}\) are multiples of ….
23. At 9:00 AM, Cars A and B left Towns X and Y, respectively, and travelled towards each other with their speeds in the ratio 5 : 4. After the two cars passed each other, Car A’s speed reduced by 20% while Car B’s speed increased by 20%.
Given that Car B was still 10 km away from Town X when Car A reached Town Y, find the distance between the towns.
24. The sum of a whole number \(n\) and
125 is a square number. The sum of \(n\) and 176 is also a square number. Find the value of \(n\).
25. Evaluate
\(\frac{1}{7}+\frac{3}{8}+\frac{7}{36}+\frac{29}{56}+\frac{37}{63}+\frac{41}{72}+\frac{53}{77}+\frac{29}{84}+\frac{3}{88}\)baca juga Contoh Soal Lomba KST Kelas 7 Tingkat SMP/MTs