VTMO 2026 - Grade 4 - Final - SET 5 - Self-study

Tom writes a sequence of consecutive two-digit odd numbers, containing more than one term. Their sum is 161. What is the middle term?

Nine balls are labelled 1 through 9. An, Bình, Châu and Dũng each take two balls in that order. An’s two labels sum to 10; Bình’s labels differ by 1; Châu’s labels have product 24; and the quotient of Dũng’s larger label by his smaller label is 3. What is the label of the remaining ball? Explain your reasoning.

An and Bình both travel from S to F along the perpendicular paths shown. An follows $S\to A_1\to A_2\to A_3\to A_4\to A_5\to A_6\to A_7\to A_8\to A_9\to F$. Bình follows $S\to B_1\to B_2\to F$. Their total distances are equal. Given $SA_1=30$ m and $SB_1=50$ m, find $A_2A_3+A_4A_5+A_6A_7$ in metres.

Last week, Biển Đông Hotel was closed for repairs on Monday and Tuesday. Rooms could be booked on the other five days. Saturday had 18 rooms booked, strictly more than on any other day; Wednesday had 15 rooms booked, strictly fewer than on any other day. Each room was booked exactly four times during those five days. How many rooms does the hotel have? Explain your reasoning.

Today is Sunday. Minh starts reading a 127-page book. He reads 4 pages every day except Sunday, when he reads 25 pages. If he does not miss any day, on what day of the week will he finish the book? Explain your reasoning.

Mother is 36 years old now. Four years ago, when Bình was born, Bon was 4 years old. In how many years will the sum of Bon’s and Bình’s ages equal their mother’s age at that time?

Mr Nam’s farm has some cows. Both the number of cows and the total number of their legs are three-digit numbers. Together these two numbers use the digits 1, 2, 3, 4, 5, 7 exactly once each. How many cows are there?

An, Bình and Châu always lie. Each owns one stone, either blue or red. An says, “My stone is the same colour as Bình’s.” Bình says, “My stone is the same colour as Châu’s.” Châu says, “Exactly two of us have red stones.” How many of the following statements are true? (1) An has a blue stone. (2) Bình has a blue stone. (3) Châu has a red stone. (4) An and Châu have different-coloured stones.

The large square is divided into three horizontal rectangles of equal area, as shown. The total area of the small shaded rectangles is 13 cm². Find the unshaded area of the large square.

A supermarket sells three kinds of rice bags: a 5 kg bag costs 80 thousand đồng, a 10 kg bag costs 153 thousand đồng, and a 15 kg bag costs 210 thousand đồng. Hạnh buys at least one bag of each kind. The average cost per kilogram of all the rice is 15 thousand đồng. What is the smallest possible total number of bags she buys? Explain your reasoning.

In the morning, Anh runs once around a lake in stages of exactly 100 m, resting for 30 seconds between consecutive stages. After the last stage, Anh is back at the starting point. In the afternoon, Anh again runs one lap, this time in stages of exactly 150 m, with a 30-second rest between consecutive stages, and finishes at the starting point. The total rest time over both laps is 14 minutes. How long is the path around the lake?

In rectangle EFGH, D lies on diagonal FH. The lines through D form rectangle DXGY and square DCEA as shown. Given $DX=4$ cm and $DY=9$ cm, find the area of EFGH in cm².

Pi is thinking of a four-digit natural number. One of its digits is 1. The hundreds digit is three times the thousands digit; the units digit is four times the tens digit; and the thousands digit is 2. What is the sum of its digits?