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VTMO 2015 — Grade 4 — semifinal

Question 1

Which expression has value $17$?
  1. $4\times5+6-3$
  2. $4\times5+6:3$
  3. $6:3+5-4$
  4. $3\times4:6+5$
  5. $3+4\times5-6$

Question 2

A rectangle has perimeter $42 \,\mathrm{cm}$ and width $4 \,\mathrm{cm}$. What is its length in cm?
  1. $17$
  2. $19$
  3. $21$
  4. $34$
  5. $38$

Question 3

An’s birthday is Wednesday. Binh’s is $17$ days later. What weekday is Binh’s birthday?
  1. Wednesday
  2. Thursday
  3. Friday
  4. Saturday
  5. Sunday

Question 4

Which number cannot be a remainder when dividing a natural number by $94$?
  1. $0$
  2. $9$
  3. $19$
  4. $93$
  5. $99$

Question 5

Using digits $2 , 3 , 5 , 6 , 7$, how many two-digit numbers with distinct digits are divisible by $3$? For example, $27$.
  1. $3$
  2. $4$
  3. $5$
  4. $6$
  5. $8$

Question 6

Define $a\otimes b=a\times b+a+b$; for example $8\otimes5=53$. Find $9\otimes3$.
  1. $36$
  2. $39$
  3. $42$
  4. $45$
  5. $48$

Question 7

The digits of a four-digit number sum to $3$. What is their product?
  1. $0$
  2. $1$
  3. $3$
  4. $4$
  5. $1\times2\times3\times4$

Question 8

Minh takes five tests, each with an odd score. Which number could be the total?
  1. $30$
  2. $35$
  3. $40$
  4. $42$
  5. $50$

Question 9

Three-digit numbers $UVW$ and $XYZ$ use six distinct digits. What is the maximum of $\overline{UVW}-\overline{XYZ}$?
  1. $678$
  2. $864$
  3. $885$
  4. $888$
  5. $975$

Question 10

Color each cube face with one color so adjacent faces have different colors. What is the minimum number of colors?
  1. $2$
  2. $3$
  3. $4$
  4. $5$
  5. $6$

Question 11

The mean of $11$ consecutive even numbers is $20$. What is the sum of the smallest and largest?
  1. $18$
  2. $20$
  3. $30$
  4. $40$
  5. $50$

Question 12

Five consecutive natural numbers sum to $2015$. What is the largest?
  1. $401$
  2. $403$
  3. $405$
  4. $406$
  5. $407$

Question 13

Six squares of side $2 \,\mathrm{cm}$ form the figure below. Find its perimeter in cm.

Question illustration
  1. $18$
  2. $20$
  3. $22$
  4. $24$
  5. $26$

Question 14

Each time Pi cuts one sheet into $4$ smaller sheets. After $7$ cuts there are $30$ sheets. How many were there initially?
  1. $3$
  2. $5$
  3. $7$
  4. $9$
  5. $11$

Question 15

At $3 : 47$ the displayed digit sum is $14$. After at least how many minutes will the hour-and-minute digit sum be $20$?
  1. $42$
  2. $132$
  3. $192$
  4. $251$
  5. $301$

Question 16

Minh has $5000$ dong left after buying $3$ notebooks but is $19000$ dong short of buying $5$. What is one notebook’s price? (Choices are in dong.)
  1. $5000$
  2. $10000$
  3. $12000$
  4. $19000$
  5. $24000$

Question 17

Rectangle $PQRS$ has $PS = 2 \,\mathrm{cm}$; $JKLM$ is a square of side $8 \,\mathrm{cm}$. Find the total shaded area.

Question illustration
  1. $16\text{ cm}^2$
  2. $32\text{ cm}^2$
  3. $48\text{ cm}^2$
  4. $56\text{ cm}^2$
  5. $62\text{ cm}^2$

Question 18

Pupils are evenly distributed among buses. One breaks down and its pupils are evenly reassigned to the other buses, adding $3$ to each and making $27$ on each. How many pupils are there?
  1. $216$
  2. $218$
  3. $224$
  4. $240$
  5. $254$

Question 19

All three balances are level as shown. How many times the square’s value is the circle’s value?

Question illustration
  1. $3$
  2. $4$
  3. $5$
  4. $6$
  5. $7$

Question 20

One of An, Binh, Chau and Dung breaks a window. An says “Binh did it”; Binh says “Dung did it”; Chau and Dung both say “Chau did not do it.” Who did it, given that exactly one person tells the truth?

Original choices: $A$. An; $B$. Binh; $C$. Chau; $D$. Dung; $E$. Insufficient information