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VTMO 2026 - Grade 5 - Semifinal - SET 2 - Self-study

Question 1

If two days before yesterday was Thursday, how many more days from today will it be until Wednesday? (For example, Monday to Wednesday is 2 more days.)

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  1. 2
  2. 3
  3. 4
  4. 5
  5. 6

Question 2

The number $a$ leaves remainder 3 when divided by 9. What remainder does $5 a$ leave when divided by 9?

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  1. 0
  2. 3
  3. 5
  4. 6
  5. 8

Question 3

A boat travels downstream from A to B in 2 hours and upstream from B to A in 4 hours. How many hours does a patch of floating plants take to drift from A to B?

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  1. 8
  2. 6
  3. 4
  4. 3
  5. 2

Question 4

The figure shows 16 circles arranged in a square, with 12 black circles along the outside border. If 196 circles are arranged in the same way, how many black circles are on the outside border?

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  1. 42
  2. 44
  3. 48
  4. 50
  5. 52

Question 5

The figure is a net of a die. Which face is opposite the face marked with a diamond?

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  1. Triangle
  2. Circle
  3. Heart
  4. Four-way arrow
  5. Up arrow

Question 6

Two kinds of square tiles, of side lengths 2 m and 3 m, cover a floor of area 492 square metres. Exactly 98 tiles are used and none is cut. How many of the 2 m tiles are used?

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  1. 78
  2. 20
  3. 123
  4. 58
  5. 40

Question 7

Use each digit 2, 3, 4, 5, 6, 7 and 8 exactly once. The different letters $U,V,W,X,Y,M,N$ stand for these different digits. Find the minimum value of $\overline{UVW}-(\overline{XY}+\overline{MN})$.

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  1. 70
  2. 73
  3. 82
  4. 172
  5. 105

Question 8

Bình has a box of cards bearing numbers. Châu removes one card, and Bình says that the average of the remaining numbers is 2 less than before. Châu removes one more card, and the average of the remaining numbers returns to the original average. The difference between the numbers on the two removed cards is 64. How many cards were originally in the box?

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  1. 15
  2. 17
  3. 24
  4. 31
  5. 62

Question 9

Find the 2012th character (letter or digit) in the repeating sequence TOANIQ2012TOANIQ2012…

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  1. T
  2. O
  3. A
  4. 2
  5. N

Question 10

How many three-digit numbers are divisible by 8?

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  1. 26
  2. 111
  3. 112
  4. 124
  5. 125

Question 11

The balance in the figure is level. How many grams does each square weigh?

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  1. 16
  2. 12
  3. 8
  4. 9
  5. 7

Question 12

What is the smallest possible sum of two natural numbers whose product is 300?

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  1. 300
  2. 103
  3. 40
  4. 35
  5. 30

Question 13

The first Saturday of a month is the 5th. What day of the week is the 25th of that month?

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  1. Tuesday
  2. Wednesday
  3. Thursday
  4. Friday
  5. Saturday

Question 14

A teacher tells the class, “At least four of you have the same birth month.” What is the smallest class size that guarantees the teacher’s statement is true?

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  1. 4
  2. 12
  3. 36
  4. 37
  5. 48

Question 15

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

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  1. 30
  2. 35
  3. 40
  4. 45
  5. 39

Question 16

In the cryptarithm $I\times\overline{LOVE}=\overline{VTMO}$, different letters represent different digits and $O=0$. What is the largest possible value of $\overline{VTMO}$?

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Question 17

Replace different letters by different digits so that the sum $\overline{VIETNAM}+\overline{TITAN}+\overline{MATH}$ is as large as possible. Find $T+I+T+A+N$.

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Question 18

Two numbers form a “2022 pair” if both have four digits, one is divisible by 5 and the other by 6, and their difference is 2022. How many different such pairs are there? The pairs (a,b) and (b,a) count as the same pair.

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Question 19

Two squares overlap as shown. Their side lengths are natural numbers, but are not consecutive natural numbers. Region A has area 39 square centimetres more than region B. What is the area of the larger square, in square centimetres?

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Question 20

Dũng’s father packs apples into small and large boxes for sale. Either 10 small boxes and 8 large boxes, or 5 small boxes and 10 large boxes, hold exactly all the apples. If he uses only small boxes, how many boxes are needed to hold exactly all the apples?

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