VTMO 2026 - Grade 4 - Semifinal - SET 7 - Self-study

An’s class takes a 45-minute mathematics test. They begin at 8:30. At what time do they hand in their papers?

Mother gives two brothers a bag containing 30 marbles. Father gives them another bag containing twice as many marbles as Mother’s bag. The younger brother receives four times as many marbles as the older brother. How many marbles does the younger brother receive?

Original choices (kept for reference): A. 15; B. 18; C. 36; D. 45; E. 90.

Practice clarification: none of these choices matches the stated data. Enter the number of marbles instead of a choice letter.

Minh takes five tests. His score on each test is an odd number. Which of the following could be the sum of his five scores?

What is the least number of different colors needed to color the cardboard below so that regions sharing an edge have different colors?

The teacher writes $\frac 23$ and $\frac 32$ on the board. Nam multiplies the two fractions, Hung adds them, and Trung subtracts Nam’s result from Hung’s result. What is Trung’s correct result?

A number consists of 2014 digits, all of them 7. What is the smallest number of digits 7 that must be deleted to obtain a number divisible by 63?

A salesperson labels five boxes as follows: A: Apple; B: Grape; C: Orange; D: Cherry; E: Plum. All five labels are wrong.
If only the labels of A and B are swapped, four boxes still have wrong labels.
If only the labels of B and C are swapped, four boxes still have wrong labels.
If only the labels of C and D are swapped, four boxes still have wrong labels.
Which choice could give the actual fruit in boxes A, B, C, D, E, in that order?

Black and white circles follow a pattern. Two letters T cover part of the pattern. Which option shows the hidden part? The original options A-E are shown below the pattern.

Write digits from left to right. The first two digits are 1 and 2. Each later digit is the units digit of the sum of the previous two digits. The sequence begins 1235831459437. Which of the following strings cannot appear as consecutive digits in this sequence?

An has three older brothers: Binh, Dung and Hung. An and Binh are twins. Their four ages add up to 13 years. What is the greatest possible age of Dung?

Practice clarification: ages are positive whole numbers of completed years. Older siblings may have the same completed-year age; no minimum age gap is specified.

Consider the sequence of figures below. How many white triangular regions are there in figure 6?

A “symmetrical hour pair” consists of two times whose hour hands and minute hands are mirror images about the vertical dashed line. For example,1:15 and 10:45 form such a pair, as shown.
The third clock shows the current time. After at least how many more minutes will it show the time paired with the current time?

Practice clarification: the printed clock hands are simplified drawings. Read the intended times from the hour and minute marks, and reflect the times on a 12-hour clock.

Place the digits 1,2,3,…,9 in the nine circles below, using each once, so that the three numbers on each straight line have the same sum. When this common sum is as large as possible, what is T?

If the four-digit number $\overline{11 N 2}$ is divisible by 4, how many possible values of the digit N are there?

Two days before yesterday was Thursday. How many more days from today until Wednesday? (For example, Monday to Wednesday is 2 more days.)

The five boxes contain the letters A,B,O,R,V as shown. Some letters are removed from each box so that exactly one letter remains in each box, and the remaining letters in different boxes are different. Which letter remains in box 5?

Boxes A and B contain the numbered balls shown. In each turn, move one ball from A to B and one ball from B to A. What is the smallest number of turns needed so that the sum of the numbers in A and the sum in B have ratio 2:5?

Machine 1 makes 30 products per minute. Machine 2 makes 40 products per minute. Both work for 5 minutes. How many more products does machine 2 make than machine 1?

At the start of semester I, the ratio of boys to girls in the Titan mathematics club is 3:4. During the semester, two boys leave and two girls join. At the end of semester I, the ratio of boys to girls is 2:5. How many students are then in the club?

The teacher writes the digits 8,7,6,5,4,3,2,1 in this order. Students may insert only addition signs between the digits, without changing their order.
Example: $8+7+65+4+3+21=108$.
How many ways of inserting addition signs give a total of 90?