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- Compute $\frac{2025-202.5-20.25}{2.025}$
A). 990
B) 199
C) 1000
D) 890
E) 89 - Lilly used a calculator to compute 50.625－0.4, but she got a wrong answer 20.25. Which incorrect input did she enter into the calculator instead of the correct one? (The others remained the same)
A) 30 instead of 50
B) 40 instead of 0.4
C) 20 instead of 50
D) $\div$ instead of $-$
E) $\times$ instead of $-$ - The square $ABCD$ is divided into two different types of small squares. What fraction of the entire figure is covered by the shaded region?
A) $\frac{5}{16}$
B) $\frac{1}{3}$
C) $\frac{11}{36}$
D) $\frac{7}{18}$
E) $\frac{13}{36}$ - Several cards are on the table. Each card contains a number, and it is a multiple of either 3 or 4. $\frac{2}{3}$ of the numbers are multiples of 3, and $\frac{3}{4}$ of the numbers are multiples of 4. If 30 cards contain multiples of 12, how many cards contain multiples of 3?
A) 40
B) 18
C) 48
D) 24
E) 54 - A regular pentagon and a regular hexagon lie on a straight line, as shown. Find $x$.
A) 87
B) 93
C) 97
D) 85
E) 95 - Divide the trapezoid into three triangles of equal area $A,B$, and $C$. What is the length of the upper base of the trapezoid $x$ in cm?
A) 16
B) 19
C) 17
D) 20
E) 18 - A ball with a radius of 1 cm is placed in a sealed cuboid box which is 4 cm long, 5 cm wide, and 6 cm high. The ball can roll inside the box at will, and the box can be flipped. Find the maximum sum of the areas of the six faces inside the box that the ball is able to touch in $\text{cm}^2$.
A) 54
B) 60
C) 52
D) 94
E) 148 - Three people Amy, Bill, and Celia take an exam. The average score of two people Amy and Bill is 2.5 points higher than the average score of three people. The average score of two people Bill and Celia is 1 point lower than the average score of three people. Given that Amy gets 93 points. How many points does Celia get?
A) 94
B) 86
C) 90
D) 88
E) 82 - Leon wants to paint a 3×3 grid to make the squares in each row, column, and diagonal have three different colors. How many colors does Leon need to use the least?
A) 3
B) 6
C) 5
D) 9
E) 4 - Three consecutive positive integers $n$, $n＋1$, and $n＋2$ have the same number of factors. Which number might $n$ be?
A) 25
B) 57
C) 98
D) 85
E) 104 - $A,B$, and $C$ are the three faces of a cuboid. The areas of $A,B,$ and $C$ are in the ratio of 8:6:3. If the perimeter of $C$ is 42 cm, find the perimeter of $A$ in cm.
A) 66
B) 72
C) 84
D) 77
E) 80 - 5 students each write a 6-digit number (its units digit is not a 0). Move the units digit of each 6-digit number to the left most position to form a new 6-digit number, and add the original 6-digit number to it. If the results are written in the options below, which answer is correct?
A) 766666
B) 172535
C) 826354
D) 1019456
E) 620708 - Compute $\frac{5}{6}\times\frac{1}{13}+\frac{5}{9}\times\frac{2}{13}+\frac{5}{18}\times\frac{6}{13}$.
A) $\frac{5}{18}$
B) $\frac{5}{13}$
C) $1$
D) $5$
E) $\frac{13}{18}$ - Daniel and Nancy set off at the two ends of a bridge and walked toward each other. Nancy had walked 2025m before Daniel set off. If the speeds of the two of them were in the ratio of 5:4; by the time they met, the distances that they had walked were in the ratio of 4:5, find the full length of the bridge in meters.
A) 8100
B) 10125
C) 9650
D) 10375
E) 12150 - A cuboid has three colored parts. Each part is formed with 6 closely connected
’s of the same color. Which option is Part 3?
- $(0.123456＋4)×2＋(3－0.123456)×0＋(2－0.123456)×2＋(1－0.123456)×5＝?$ (Round to twodecimal places)
- Today is July 26, 2025. The 7-digit number $\overline{ABCDEFG}$ happens to satisfy the following conditions: The first 5 digits $\overline{ABCDE}$ is a multiple of 2025. The last 5 digits $\overline{CDEFG}$ is a multiple of 726. Find the minimum value of the 4-digit number $\overline{ABFG}$.
- Given a mixed fraction. If its whole number part is reduced to $\frac{1}{2}$ of the original value, the fraction becomes $3\frac{5}{6}$. If its whole number part is reduced to $\frac{2}{7}$ of the original value, the fraction becomes $2\frac{1}{3}$. Find this mixed fraction.
- Tony uses identical small cubes to build a castle and notices that the images he sees from the four faces are identical. How many small cubes does he use the most?
- Cars in a parking lot are parked either perpendicular or parallel. Perpendicular cars can only move forward or backward. Parallel cars can only move left or right. Each time, only one car can move 1 square, and that takes 1 second. A car can only enter a square when it is empty. If the square is occupied by another car, the car cannot enter it. How many seconds does it take the least for the blue car to leave the parking lot and reach the EXIT square completely?
- An integer has 16 positive factors, and its units digit is 7. What is the possible minimum value of this integer?
- In the rectangle $PQRS$ are 3 identical squares. They form two overlapping parts $A$ and $B$, and the uncovered parts are $C,D$, and $E$. All of them are rectangles. If the ratio of the areas $A：B：C：D：E＝3：4：5：6：7$, find the ratio of the length to the width of $PQRS$.
- 12 black or white magnetic beads can form a bracelet. When 3, 4, 5, or 6 consecutive beads are removed, rotated, and placed back to the bracelet, it is called 1 “turn.” If Vivian wants to make the 6 black beads of the bracelet below link together, and make the 6 white beads link together, how many “turns” are needed the least?
- Fill in the nine □’s below with “＋” or “－” to make the equation established. How many ways arethere?
- 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 tofollow 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.
This topic was modified 5 hari ago by Admin dot
Posted : 22/05/2026 7:03 am
