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VTMO 2021 — Grade 5 — vtmo

Question 1

Circle+square $= 60$ and circle=three squares, as pictured. Find the circle’s value.

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  1. $15$
  2. $20$
  3. $30$
  4. $45$
  5. $60$

Question 2

How many grid squares contain the circular check mark but not the square check mark?

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  1. $1$
  2. $11$
  3. $12$
  4. $24$
  5. None of them

Question 3

In $2021$, the difference between mother’s birth year and age is $1961$. Find her age.
  1. $25$
  2. $30$
  3. $32$
  4. $35$
  5. $60$

Question 4

Jerry writes three digits. Spike forms the largest three-digit number and Tom the smallest. What is the greatest possible difference?
  1. $899$
  2. $801$
  3. $864$
  4. $885$
  5. $792$

Question 5

Five identical rectangular bricks, each area $32 \,\mathrm{cm}^{2}$, are arranged as shown. Find the combined perimeter.

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  1. $64 \,\mathrm{cm}$
  2. $68 \,\mathrm{cm}$
  3. $60 \,\mathrm{cm}$
  4. $120 \,\mathrm{cm}$
  5. $160 \,\mathrm{cm}$

Question 6

Tien, Son, Dung start with equal money. Tien buys $3$ pencils and $4$ notebooks, retaining $7 USD$; Son $3$ pencils and $3$ notebooks, retaining $28 USD$; Dung $1$ pencil and $4$ notebooks, retaining $21 USD$. Find each initial amount.
  1. $84 USD$
  2. $91 USD$
  3. $105 USD$
  4. $112 USD$
  5. $133 USD$

Question 7

January $13 , 2017$ is Friday. In which listed year is January $13$ not Friday?

$A$. $2023$

$B$. $2034$

$C$. $2042$

$D$. $2011$

$E$. $2047$

Question 8

In equal times, A makes $18$ items while $B = 14$; $B$ makes $10$ while $C = 8$. When A makes $45$, how many does $C$ make?
  1. $20$
  2. $28$
  3. $36$
  4. $40$
  5. $54$

Question 9

Use two different numbers from $1 \text{--} 6$ as numerator and denominator, then reduce. How many distinct fraction values can be formed?
  1. $22$
  2. $18$
  3. $17$
  4. $30$
  5. None of them

Question 10

$A = 3 \times 3$ square has equal row, column and diagonal sums. Given $64$ top-left, $6$ top-middle, $14$ bottom-right, and central A as pictured, find $A$.

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  1. $22$
  2. $56$
  3. $31$
  4. $39$
  5. $47$

Question 11

Nhi and five friends roll a die, getting six different results. The friends’ five results have product congruent to $4$ modulo $7$. What did Nhi roll?

Question 12

Ten coins start on one face. Four rounds flip $3 , 5 , 7 , 9$ coins, ending all on the opposite face. What maximum number are flipped exactly three times?

Question 13

A solid made of $1 \,\mathrm{cm}$ unit cubes has the pictured front and right projections. What is its maximum total surface area?

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Question 14

The black-square pattern is shown in figures $1 \text{--} 4$. How many black cells are in figure $9$?

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Question 15

A machine divides an even number by $2$ and subtracts $1$ from an odd number, stopping at $0$. Find the smallest number requiring exactly seven steps. Example $6$→$3$→$2$→$1$→$0$ takes four steps.

Question 16

Different letters represent different digits, and $I \times LOVE =$ VTMO with $O = 0$, as pictured. Find the maximum VTMO.

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Question 17

One-third of a rope is $1 m$ too short to measure a well; one-half is $6 m$ too long. Find well depth.

Question 18

Matchsticks form $2021$ as shown. Move exactly three sticks, without adding or removing, to make the largest four-digit number using the pictured digit patterns. Find it.

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Question 19

Rectangle $ABCD$ is split into $AEFD$ and $BCFE$ as pictured. $BCFE$ has twice the perimeter and four times the area of $AEFD$. $AD = 10 \,\mathrm{cm}$. Find $AB$.

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Question 20

Twenty students’ mean age is half the teacher’s age. Including the teacher, the class mean is $20$ years below the teacher’s age. Find the teacher’s age.