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BBB 2021 - Grade 5 - Preliminary Round

Question 1

Find the average of 10 numbers: 45, 55, 65, 70, 60, 80, 85, 35, 30, 35.
  1. 56
  2. 57
  3. 58
  4. 59

Question 2

If $2\oplus2=2+4$, $3\oplus5=3+6+9+12+15$. Find the value of $6\oplus4$.

Editorial interpretation: for this question, use $a\oplus b=a+2a+\ldots+ba$. This is the intended pattern suggested by the examples, rather than a uniquely specified operation.
  1. 10
  2. 24
  3. 60
  4. 48

Question 3

Use 2, 3, 6 and 9 without repetition. How many different 3-digit numbers can be formed?
  1. 48
  2. 36
  3. 12
  4. 24

Question 4

Taxis' Flagfall fares (first 2-km) is \$16. For the next 0.1km, the fares will be \$1.4 per 0.1 km. If Nick travels 5.5km, how much does he need to pay in dollars?
  1. 65
  2. 77
  3. 49
  4. 75

Question 5

Find the value of $\left(\frac{15}{16}+\frac{15}{32}+\frac{15}{64}+\frac{15}{80}\right)\div\left(\frac9{32}+\frac9{64}+\frac9{128}+\frac9{160}\right)$.
  1. $\frac{14}3$
  2. $\frac{10}3$
  3. $\frac{15}{32}$
  4. $\frac{11}3$

Question 6

It is known that the sum of 8 consecutive even numbers is 1032. Find the value of the smallest number.
  1. 126
  2. 124
  3. 120
  4. 122

Question 7

A train travelled as 252km/h. How many meters does this train travel within 1 second?
  1. 126
  2. 140
  3. 70
  4. 252

Question 8

Find the value of $3+5+7+9+\ldots+41+43+45$.
  1. 582
  2. 852
  3. 258
  4. 528

Question 9

Find the value of $\frac3{6\times7}+\frac3{7\times8}+\frac3{8\times9}+\ldots+\frac3{81\times82}+\frac3{82\times83}+\frac3{83\times84}$.
  1. $\frac{13}{84}$
  2. $\frac{13}{28}$
  3. $\frac{39}{28}$
  4. $\frac{13}{41}$

Question 10

Nick has 33 \$2 coins and \$5 coins altogether in a total of \$117. How many \$5 coins does Nick have?
  1. 15
  2. 16
  3. 17
  4. 18

Question 11

Today is 10th October 2021 (Sunday). Which year will satisfy that 15th October will be Sunday for the earliest case?
  1. 2023
  2. 2022
  3. 2027
  4. 2028

Question 12

Find the value of $128-121+114-107+100-93+\ldots+16-9+2$.
  1. 63
  2. 171
  3. 173
  4. 65

Question 13

Find the number of all positive factors of 2160.

Editorial language note: the English original specifies positive factors; that domain is used for both languages.
  1. 10
  2. 20
  3. 30
  4. 40

Question 14

How many 3-digit numbers that can be divisible by 4 or 7 are there?
  1. 32
  2. 321
  3. 353
  4. 28

Question 15

If a 9-digit number $\overline{42697A713}$ is divisible by 13, find the value of $A$.
  1. 1
  2. 0
  3. 2
  4. 3

Question 16

Find the value of $\frac{(667\times2435-2001)}{(1311+3709\times437)}$.
  1. 3
  2. 2
  3. 1
  4. 4

Question 17

It is known that $x=\cfrac{2}{3+\cfrac4{5+\cfrac6{7+\cfrac8{9}}}}$. Find the value of $x$.
  1. $\frac{888}{1511}$
  2. $\frac{818}{1511}$
  3. $\frac{188}{1511}$
  4. $\frac{818}{1151}$

Question 18

B and E are the mid-points of AD and DF respectively. If the area of triangle ADF is 48, find the area of quadrilateral BCDE.

Question illustration
  1. 20
  2. 12
  3. 36
  4. 24

Question 19

Between 7pm and 8pm, when do the hour hand and the minute hand on the clock overlap?
  1. $19\!:\!38\frac2{11}$
  2. $19\!:\!39\frac2{11}$
  3. $19\!:\!40\frac2{11}$
  4. $19\!:\!41\frac2{11}$

Question 20

A 4-digit natural number is divided by 13, 8 and 6 to get the same remainder of 3. What is the minimum value of this number?
  1. 1251
  2. 1245
  3. 1003
  4. 1215