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- If $$\frac{2024}{2025}\times 2026=\frac{2024}{2025}+A=2025-B,$$ find $A\times B$.
A) 1
B) $2025\times 2026$
C) $\frac{2024}{2025}$
D) 2
E) $\frac{2026}{2025}$ - If $p$ is a prime number, $q$ is a composite number, which option below must be a composite number?
A) $p+q$
B) $p+q+2$
C) $\frac{p\times q}{2}$
D) $(p-2)\times q$
E) $(p+2)\times q$ - $Cecil$ tosses a regular 6-sided die with numbers 1, 2, 3, 4, 5, and 6. What is the probability that the number on the vertical lateral face of the die is 5?
A) $\frac{1}{6}$
B) $\frac{1}{3}$
C) $\frac{1}{4}$
D) $\frac{2}{3}$
E) $\frac{1}{2}$ - The ratio of the average number of the two numbers $A$ and $B$ to $C$ is $\frac{11}{5}$. Find the ratio of the average number of the three numbers $A,B,$ and $C$ to $C$.
A) $\frac{27}{5}$
B) $\frac{33}{5}$
C) $\frac{6}{5}$
D) $\frac{9}{5}$
E) $\frac{12}{5}$ - If $\frac{a}{b}$ can be simplified to $\frac{1}{25},\frac{a+20}{b+20}$ can be simplified to $\frac{1}{20}$, find $a+b$.
A) 2028
B) 1976
C) 2132
D) 1274
E) 1404 - Compute $0^3＋1^3＋2^3＋3^3＋4^3＋5^3＋6^3＋7^3＋8^3＋9^3＋10^3$. (Hint: $2^3＝2×2×2$)
A) 2035
B) 2025
C) 2125
D) 3025
E) 4025 - Daniel and Nancy worked on a report together. If the two of them had worked on the report in a 1:3 ratio as planned, they would have finished it simultaneously. When they started doing the report, Nancy’s efficiency decreased by 50％ compared to the plan because she didn’t feel well, and Daniel’s efficiency was as scheduled. After Daniel finished his part, he helped Nancy immediately, and they completed the report 120 minutes later. If Daniel had worked on the report alone from the beginning, how many minutes would he have needed to finish the report?
A) 480
B) 800
C) 640
D) 400
E) 720 - A cuboid with dimensions $6×6×3$ is cut from another cuboid with dimensions $12×9×6$, as shown on the left. Combine two such cuboids together, as shown on the right. What is its surface area?
A) 640
B) 540
C) 792
D) 720
E) 848 - Company W imports goods from Asia to sell in the US. The original profit is $x$％. Due to tariff increase, import costs have risen by 25％. If the selling price remains unchanged, the profit will dropto ($x-60$)％. Find $x$.
A) 85
B) 150
C) 105
D) 200
E) 185 - Three circular boards each with a radius of 9cm $A,B,$ and $C$ are placed in a straight line. Both $A$ and $C$ rotate around $B$ without sliding. It takes $A$ 36 seconds to rotate counterclockwise once. $C$ rotates clockwise at 2 times the speed of $A$. If they rotate simultaneously, how many seconds later will $A$ collide with $C$?
A) 6
B) 3
C) 4
D) 2
E) 8 - The area of a regular hexagon $ABCDEF$ is $18\text{ cm}^2$. Each black point is the midpoint of each side. Find the area of the shaded region in $\text{cm}^2$.
A) 5
B) 4
C) $4\frac{1}{2}$
D) 6
E) $5\frac{1}{2}$ - Mary accidentally erases the symbol of a repeating decimal, and it becomes 0.987654321. If the 2025th digit after the decimal point of the original repeating decimal is 5, and the repeating period consists of at least 2 digits, which digit is the initial digit of the repeating period of the original repeating decimal?
A) 9
B) 8
C) 7
D) 6
E) 5 - On the table are three cylindrical cups $A,B$, and $C$ with base areas of $100\text{ cm}^2$, $120\text{ cm}^2$, and $140\text{ cm}^2$ respectively. Each cup is 25 cm deep and contains 10 cm of water. Dave pours some of the water from cups $A$ and $B$ into cup $C$ so that the water levels in the three cups achieve a ratio of 4:3:6. Disregarding the thickness of the cups, find the water height in cup $A$ in cm.
A) 9
B) 9.1
C) 7.5
D) 8
E) 8.6 - The result of the expression $\frac{7}{6}+\frac{13}{12}+\frac{21}{20}+\cdots +\frac{2025\times 2026+1}{2025\times 2026}$ is between an integer $n$ and $n+1$. Find $n$.
A) 2026
B) 2025
C) 2024
D) 4050
E) 4048 - Four people Mary (SAP Entertainment), Lilly (RR Entertainment), Cindy (RR Entertainment), and Daisy (JYK Entertainment) form a girl group, and they belong to different agencies. A program today requires two of them to participate in filming. SAP says, “If Mary goes, Lilly must go.” RR says, “If Cindy can’t go, Lilly can’t go, either.” JYK says, “If Cindy goes, Daisy will not go.” In the end, which two people participate in filming?
A) Mary, Lilly
B) Mary, Daisy
C) Cindy, Daisy
D) Lilly, Cindy
E) Mary, Cindy - If $\frac{a}{3}=\frac{b}{4}=\frac{c}{5}=202320242025$, find $\frac{3a+2b-2c}{2c-b+3a}$.
- Divide a cube into 3 cuboids $A,B,$ and $C$. The surface areas of $A,B,$ and $C$ are in a ratio of 7:6:5. Find the ratio of the volumes of $A,B,$ and $C$.
- How many values of $n$’s less than 2025 can make the units digit of the result of this expression $$\underbrace{2023 \times 2023 \times \dots \times 2023}_{n\text{'s}} + \underbrace{2025 \times 2025 \times \dots \times 2025}_{n\text{'s}} + \underbrace{2027 \times 2027 \times \dots \times 2027}_{n\text{'s}} + \underbrace{2029 \times 2029 \times \dots \times 2029}_{n\text{'s}}$$ equal to 4?
- Use ten digits 0～9 to form a 1-digit number, a 2-digit number, a 3-digit number, and a 4-digit number which are all non-zero perfect squares. For example, 7056, 324, 81, and 9. Find the maximum value of the sum of these four perfect squares.
- Two circles with radii of 1cm and 2cm are in a rectangle $ABCD$. If the two circles remain attached to the sides of the rectangle and move around its interior once, find the area in the rectangle that only a circle can pass through in $\text{cm}^2$. ($\pi＝3.14$)
- In a quadrilateral $ABCD,\overline{AF}=\frac{1}{4}\overline{AD},\overline{EB}=\frac{1}{4}\overline{AB}$, the area of the quadrilateral $AEOF$ is 64. Find the area of the parallelogram $OBCD$.
- Compute $2025\times (1+\frac{1}{2}+\frac{1}{3}+\cdots +\frac{1}{2024})-[1+(1+\frac{1}{2})+(1+\frac{1}{2}+\frac{1}{3})+\cdots +(1+\frac{1}{2}+\frac{1}{3}+\cdots +\frac{1}{2024})]$.
- The sum of 8 different positive integers is 2025. Find the maximum value of the greatest common factor of these 8 positive integers.
- A puzzle is shown. Enter from Start and move toward Goal. How many ways are there?
1. When entering into a square with an arrow, you have to follow its direction.
2. From a colored square (including Start), you can move to any adjacent square above, below, left, or right.
3. You can’t enter the square that you visited before.
- In order to celebrate the 13th WMI, the teacher designs a number puzzle. Fill in the □’s below with 1～23 to make the sum of the numbers in each row and column 60. A few numbers have been filled in. What number is ★?
This topic was modified 2 hari ago by Admin dot
Posted : 25/05/2026 9:19 am
