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VTMO 2021 — Grade 4 — vtmo

Question 1

The $2021$ figure uses black and white cubes as shown. Which choice describes the black-cube fraction?

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  1. Greater than $\frac{1}{2}$
  2. Less than $\frac{1}{2}$
  3. $\frac{1}{2}$
  4. $\frac{1}{3}$
  5. $\frac{3}{7}$

Question 2

What is the least possible number of Mondays in a year?
  1. $48$
  2. $60$
  3. $52$
  4. $53$
  5. $54$

Question 3

How many squares in the grid contain $O$ but not $X$?

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

Question 4

Nhi adds her current age to her father’s, then he adds both birth years. What is the result? Age=current year−birth year, and the current year is $2021$.
  1. $2021$
  2. $2030$
  3. $4042$
  4. $4043$
  5. Not enough information

Question 5

Five congruent rectangular bricks, each with perimeter $24 \,\mathrm{cm}$, 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

An and Binh buy the same toy. An uses equal numbers of $1$-dollar and $5$-dollar notes; Binh uses equal numbers of $1 - , 2 - , 5$-dollar notes. An uses $10$ fewer notes. How many notes does An use?
  1. $110$
  2. $50$
  3. $60$
  4. $90$
  5. $80$

Question 7

Cards $1 \text{--} 9$ total $45$. Viet removes one card, leaving a multiple-of $5$ sum. Nam removes two more, again leaving a multiple-of $5$ sum. The product of the three removed values is odd. What is their sum?
  1. $15$
  2. $10$
  3. $5$
  4. $12$
  5. $20$

Question 8

Hung and Giang each sum five consecutive natural numbers, and Nghia multiplies their results. Which value cannot be that product?
  1. $10350$
  2. $5100$
  3. $9350$
  4. $12500$
  5. $16370$

Question 9

Tien, Son, Duc have equal money. Tien buys $3$ pencils $+ 4$ notebooks and has $7$ dollars left; Son buys $3$ pencils $+ 3$ notebooks and has $28$; Duc buys $1$ pencil $+ 4$ notebooks and has $21$. How many dollars more is a notebook than a pencil?
  1. $21$
  2. $14$
  3. $9$
  4. $7$
  5. $5$

Question 10

Labels $A , B , C , D , E$ are Apple, Grape, Orange, Cherry, Plum, all wrong. Swapping only $A \text{--} B , B \text{--} C$, or $C \text{--} D$ leaves exactly $4$ wrong labels in each case. Which actual $A \text{--} E$ fruit order is possible?

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  1. Grape–Orange–Plum–Apple–Cherry
  2. Plum–Apple–Grape–Orange–Cherry
  3. Grape–Orange–Apple–Plum–Cherry
  4. Plum–Apple–Cherry–Grape–Orange
  5. Orange–Apple–Grape–Plum–Cherry

Question 11

An $HH : MM$ clock $\left(00 : 00 \text{--} 23 : 59\right)$ gains $5$ minutes per real hour. At real midnight, what displayed time should be set so it shows $6 : 00$ and rings at real $6 : 00$ a.m.? Write four digits, e.g.$0515$.

Question 12

A machine halves even inputs and subtracts $1$ from odd inputs, repeating until $0$. What is the smallest number needing exactly $6$ steps? For example $3$→$2$→$1$→$0$ takes $3$.

Question 13

Squares are shaded according to the displayed sequence. How many black cells are in figure $6$?

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Question 14

The $3 \times 3$ square has equal row, column, and diagonal sums. Find A using the given entries.

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Question 15

Move exactly $2$ matchsticks in $2021$, without adding or removing any, to form the largest four-digit number using the illustrated digit shapes. Find it.

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Question 16

Among $10$ chickens, every three include at least one rooster. What is the least rooster count?

Question 17

Distinct letters are distinct digits in $\overline{VTMO}+\overline{LOVE}=\overline{MEET}$. Given $E = 9$, find VTMO.

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Question 18

All lights in $a = 3 \times 3$ grid are on. Touching one toggles itself and its edge-adjacent neighbors. What is the minimum number of touches to turn all off?

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Question 19

In the number pyramid, each cell sums the two below, as in the example. Fill $1 \text{--} 7$ once in the bottom row so the top is maximized at $350$. Find $A + B + C$ at the marked bottom positions.

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Question 20

Ten coins start face down. Four rounds flip $1 , 3 , 5 , 7$ coins respectively, ending with all face up. What is the maximum number flipped exactly $3$ times?