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VTMO 2017 — Grade 5 — semifinal

Question 1

Find $N = \left(140 + 135 + 130 + 125 + 120 + 115\right) - \left(110 + 115 + 120 + 125 + 130 + 135\right)$.
  1. $10$
  2. $20$
  3. $30$
  4. $35$
  5. $40$

Question 2

Thanh writes every two-digit number containing $5$. How many are there?
  1. $10$
  2. $19$
  3. $20$
  4. $30$
  5. $18$

Question 3

How many three-digit numbers have digit sum $6$?
  1. $12$
  2. $16$
  3. $18$
  4. $20$
  5. $21$

Question 4

Four-digit numbers have hundreds digit $0$. Removing the thousands and hundreds digits makes each number $301$ times smaller. How many such numbers exist?
  1. $0$
  2. $1$
  3. $2$
  4. $3$
  5. $4$

Question 5

Today is Sunday $26$ November $2017$. Phuong’s birthday is $1$ January; Khang’s birthday is $6$ days before hers. What weekday is Khang’s birthday in $2017$?
  1. Sunday
  2. Monday
  3. Tuesday
  4. Wednesday
  5. Thursday

Question 6

A contains natural numbers with distinct digits and digit sum $18$. $D$ is its largest minus its smallest element. Find $D$’s digit sum.
  1. $14$
  2. $16$
  3. $18$
  4. $20$
  5. Other answer

Question 7

How many three-digit numbers have distinct digits, digit product $24$ and digit sum $11$?
  1. $2$
  2. $3$
  3. $4$
  4. $5$
  5. $6$

Question 8

Three pegs hold A on peg $1 , C$ above $B$ on peg $2$, and $D$ on peg $3$ as shown. Binh removes one disk at a time. How many removal orders are possible?

Question illustration
  1. $9$
  2. $10$
  3. $11$
  4. $12$
  5. Other answer

Question 9

How many squares in the grid do not contain the star?

Question illustration
  1. $30$
  2. $35$
  3. $40$
  4. $45$
  5. $39$

Question 10

$32$ people line up. Move the first to the back, seat the next, and repeat with those standing until one remains. What is the survivor’s original position?
  1. $1$
  2. $8$
  3. $4$
  4. $21$
  5. $16$

Question 11

Guess a four-digit number: $2896$ has exactly one correct digit, correctly placed; $5273$ has exactly two correct digits, wrongly placed; $1702$ has all four correct but all wrongly placed. Find the number.

Question 12

Append $3$ to a four-digit number. The new number exceeds the old by $9876$. Find the original.

Question 13

Reduce one square dimension $20 \%$ and increase the other $2 \,\mathrm{cm}$, creating an equal-area rectangle. Find the original square area.

Question 14

Ti can climb $1$ or $2$ steps at a time. How many ways climb $8$ steps?

Question 15

The pictured tower uses $84$ unit cubes of side $1 \,\mathrm{cm}$. Paint every exterior face except the bottom. Find painted area.

Question illustration