WMI Preliminary Round 2021 [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 2021

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1. If \(\frac{3}{4}𝑥 =\frac{7}{12}\), find \(𝑥\)

(A) \(\frac{7}{9}\)
(B) \(\frac{9}{7}\)
(C) \(\frac{7}{8}\)
(D) \(\frac{3}{7}\)

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Solution

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2. Compute \((6\frac{6}{7}− 3\frac{9}{13}) ÷ 2\frac{7}{13}\)

(A) \(1\frac{19}{91}\)
(B) \(1\frac{17}{77}\)
(C) \(1\frac{17}{91}\)
(D) \(1\frac{19}{77}\)

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Solution

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3. Suppose the 6-digit number 21578◻ is divisible by 12, what is the number in the square?

(A) 8
(B) 6
(C) 4
(D) 2

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Solution

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4. Divide the product of 36158 and 273 by 7, what is the remainder?

(A) 0
(B) 1
(C) 2
(D) 3

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Solution

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5. Two cars A and B drive on the same road. If their time ratio is 3：4, what is their speed ratio?

(A) 3 : 4
(B) 4 : 3
(C) 3 : 7
(D) 7 : 3

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Solution

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6. In the class, the number of girls is half the number of boys. If the average weight for boys is 35kg, the average weight for girls is 32kg, find the average weight for the class in kg.
(A) 32.5
(B) 33
(C) 33.5
(D) 34

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Solution

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7. Make the hand  spin. What is the probability that it stops at an even number?

(A) \(\frac{1}{2}\)
(B) \(\frac{1}{3}\)
(C) \(\frac{1}{4}\)
(D) \(\frac{2}{3}\)

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Solution

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8) Given that \(a, b, c,\) and d aren’t \(0\). Set \(P＝a÷b×c÷d\), which expression below equals \(P\)?

(A) \(a×b÷d÷c\)
(B) \(a×d÷c÷b\)
(C) \(a÷(b÷c)÷d\)
(D) \(a÷b÷c÷d\)

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Solution

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9.  [A] represents the number of natural number A’s factors. For example, 4 has three factors 1, 2, and 4, so it can be written as [4]＝3. Find [18]÷[7].

(A) 1
(B) 2
(C) 3
(D) 4

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Solution

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10. \(\frac{1}{5}\) of number \(A\) equals \(\frac{1}{4}\) of number \(B\). \(25\%\) of number \(A\) equals \(20\%\) of number \(C\). Compare the three numbers \(A, B,\) and \(C\). Which option below is correct?

(A) A＞B＞C
(B) C＞B＞A
(C) A＞C＞B
(D) C＞A＞B

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Solution

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11. Use 3 sticks to form a triangle. Place the sticks as below. How many sticks are needed to form 100 triangles?

(A) 3×100
(B) 3×50＋50＋1
(C) 2×100＋1
(D) 3×100－100

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Solution

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12. There are three different squares whose side lengths are \(a, b,\) and \(c\), respectively. If \(a, b\), and \(c\) are integers, and the total area of the three squares is \(202\), find \(𝑎𝑏𝑐\).

(A) 48
(B) 84
(C) 96
(D) 120

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Solution

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13. Use a 32 long iron wire to make a rectangle. If its length and width are primes, how many different values does its area have?

(A) 6
(B) 4
(C) 3
(D) 2

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Solution

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14) Given a 3-digit number. Divide it by 3, and the remainder is 1. Divide it by 4, and the remainder is 1. Find the largest possible value of this number.

(A) 998
(B) 997
(C) 996
(D) 995

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Solution

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15. Use four identical rectangles and a small square (as shown on the right) to form a large square whose area is 49 m². If the area of the small square is 4 m², find the length of the shorter side of the rectangle in m.

(A) 2
(B) 2.3
(C) 2.4
(D) 2.5

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Solution

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