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VTMO 2016 — Grade 4 — semifinal

Question 1

Find $N$: $7\times6\times5\times9=30\times N$.
  1. $42$
  2. $30$
  3. $45$
  4. $63$
  5. $54$

Question 2

Two brothers have $40$ marbles total; the elder has $4$ more. How many does the elder have?
  1. $22$
  2. $18$
  3. $20$
  4. $19$
  5. $21$

Question 3

The teacher writes $\frac23$ and $\frac32$. Nam multiplies them, Hung adds them, and Trung subtracts Nam’s result from Hung’s. What is Trung’s result?
  1. $\frac15$
  2. $\frac76$
  3. $0$
  4. $\frac85$
  5. $\frac56$

Question 4

Find the digit sum of $101\times101\times101$.
  1. $3$
  2. $4$
  3. $5$
  4. $6$
  5. $8$

Question 5

Eleven consecutive natural numbers sum to $352$. What is the smallest?
  1. $27$
  2. $28$
  3. $29$
  4. $30$
  5. $26$

Question 6

How many squares are in the figure below?

Question illustration
  1. $4$
  2. $5$
  3. $6$
  4. $11$
  5. $12$

Question 7

How many three-digit numbers have digit sum $5$ (for example $113$ and $302$)?
  1. $12$
  2. $13$
  3. $14$
  4. $15$
  5. $16$

Question 8

A mother gives $20$ candies to three siblings, each receiving a distinct number. The youngest gets the most. What is the smallest possible amount for the youngest?
  1. $5$
  2. $6$
  3. $7$
  4. $8$
  5. $10$

Question 9

Two squares with positive integer side lengths in cm are joined as shown, with total area $52$ square centimeters. What is the combined perimeter?

Question illustration
  1. $30 \,\mathrm{cm}$
  2. $28 \,\mathrm{cm}$
  3. $36 \,\mathrm{cm}$
  4. $32 \,\mathrm{cm}$
  5. $40 \,\mathrm{cm}$

Question 10

Use each digit $2 , 3 , 4 , 5 , 6 , 7 , 8$ once in $\overline{UVW}-(\overline{XY}+\overline{MN})$. What is the minimum?
  1. $70$
  2. $73$
  3. $82$
  4. $172$
  5. $165$

Question 11

A box contains marbles labeled $1 , 4 , 7 , 10$, with at least two of each. Two are drawn. How many different sums are possible?

Question 12

Pi thinks of a three-digit number whose tens digit is three times its hundreds digit and whose units digit is twice its tens digit. What is it?

Question 13

A group’s average age is $10$. Binh, age $15$, joins, raising the mean to $11$. How many people were initially in the group?

Question 14

A square is divided into six identical rectangles arranged in $2$ columns and $3$ rows. Each rectangle has perimeter $20 \,\mathrm{cm}$. Find the square’s area.

Question illustration

Question 15

Among $65$ pupils wearing white or blue, there are $25$ boys in white, $23$ pupils in blue, and $28$ girls. How many girls wear blue?