# WMI Preliminary Round 2020 [Grade 6A]

World Mathematics Invitational (WMI) is the first international competition founded by Taiwan. It gathers institutes and organizations worldwide that make efforts in promoting and popularizing mathematics. Through interacting with other math-loving students that represent their countries, students can expand their worldview, experience different cultures, and thus their horizon as well as their future will be broaden. (sc : http://www.wminv.org/)

Berikut ini soal dan solusi WMI grade 6A tahun 2020

1. Computed

$$8\frac{2}{5}÷\frac{3}{10}+ 20 ×\frac{3}{10}$$

A. $$32$$
B. $$32\frac{3}{5}$$
C. $$34$$
D. $$36$$

$$8\frac{2}{5}÷\frac{3}{10}+ 20 ×\frac{3}{10}$$
$$=\frac{42}{5}×\frac{10}{3}+ 6$$
$$= 14 × 2 + 6 = 34$$

2. If $$□－9×2＝28$$, find $$□$$.

(A) 5
(B) 10
(C) 23
(D) 46

$$□－9×2＝28$$
$$□－18＝28$$
$$□＝28+18=46$$

3. May joins a 6 day tour, and the average expense is 3500 dollars per day. Given that the average expense for the first 5 days is 3100 dollars per day, find the percentage of the expense on the 6th day.

(A) 17%
(B) 20%
(C) 26%
(D) 28%

Misalkan banyak uang hari ke-6 adalah $$x$$, dengan menggunakan rumus rata-rata

$$\frac{5(3100) + 𝑥}{6}= 3500$$
$$⇒ 15500 + 𝑥 = 21000$$
$$⇒ 𝑥 = 21000 − 15500 = 5500$$

jadi percentasenya adalah $$\frac{5500}{21000} × 100\% = 26\%$$

4. Given that the trapezoid and the parallelogram have the same area and height. Suppose the upper base of the trapezoid is longer than its lower base by 12cm, find the length of its lower base in cm. (A) 12
(B) 18
(C) 20
(D) 24 Diketahui $$𝐴 − 𝐵 = 12$$ dan misalkan tinggi jajarangenjang dan trapezium adalah $$𝑡$$

Luas trapezium = Luas jajaran genjang
$$\frac{1}{2}(𝐴 + 𝐵)𝑡 = 30𝑡$$
$$𝐴 + 𝐵 = 60$$

Jumlahkan $$A-B=12$$ dan $$A+B=60$$, diperoleh $$2𝐴 = 72⇒A=36$$

Jadi nilai $$B$$ nya adalah $$B = 60 – 36 = 24$$

5. Walker goes mountain climbing. He climbs up for 6hr in the speed of 2.5km/hr, and climbs down for 4hr while taking a 2km detour on the way. Find Walker’s average climbing speed in km/hr.
(A) 3
(B) 3.2
(C) 3.5
(D) 5

6. John saves 10000 dollars in the savings account where the annual interest rate is 2.4% compounded once a year. How much will the savings be after 2 years?
(A) 10240
(B) 10245.76
(C) 10480
(D) 10485.76

7. Given that $$□$$ is an integer. Suppose the remainder of $$138÷□$$ is 3, the reminder of $$87÷□$$ is 6, find the largest remainder of $$101÷□$$.

(A) 2
(B) 11
(C) 13
(D) 20

8. Regarding axioms of equality, which option below is wrong?
(A) A×C＝B×C⇒A＝B
(B) A＋C＝B＋C⇒A＝B
(C) A＝B⇒A－C＝B－C
(D) A＝B⇒A×C＝B×C

9. On the map is a rectangular land which is 3cm long and 2 cm wide. If the scale of the map is 1:500, find its actual area in m².
(A) 3000
(B) 300000
(C) 150
(D) 1500000

10. Given a solid whose base is a parallelogram. Find its surface area in cm². (A) 1920
(B) 1440
(C) 1280
(D) 3600

11. The table shows the average life expectancy of three countries in 2019. Which country has the highest average life expectancy? (A) A
(B) B
(C) C
(D) Not sure

12) The small gear has 80 teeth, and the large gear has 128 teeth. If the point that the two gears meet is painted red, how many more rotations will the small gear make than the large gear when they meet at the red point again?
(A) 3
(B) 5
(C) 8
(D) 10

Misalkan banyak putaran untuk roda bergigi $$80$$ adalah $$n$$ dan banyak putaran untuk roda bergigi $$128$$ adalah $$m$$, maka

$$80𝑛 = 128𝑚$$
$$\frac{𝑛}{𝑚}=\frac{128}{80}=\frac{8}{5}$$

Jadi gigi yang berwarna merah bertemu kembali ketika roda kecil berputar 8 kali dan roda besar berputar 5 kali, selisih putarannya adalah 3.

13. Given that 9 workers mend a $$1\frac{7}{5}$$
km road in 4 days. How many days are needed for 14 workers to mend a 20km road?
(A) 21
(B) 27
(C) 30
(D) 36

14) Compute $$0.99×0.1＋9.9×0.47＋0.52×9.9$$.
(A) 99
(B) 99.8
(C) 9.9
(D) 99.9

15. The pie chart shows the football clubs that are favored in Lilly’s class. Lilly then draws the pie chart into the bar chart. Which club is wrong? (A) Chelsea
(B) Arsenal
(C) Manchester United
(D) Liverpool

WMI Preliminary Round 2021 [Grade 6A]