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- Find the value of the following. $$\frac{2024^4-2023^4}{2024^2+2023^2}$$
A. 4046
B. 4047
C. 2024
D. 2023
E. None of the above - Which of the following fractions is the largest?
A. $\frac{12}{13}$
B. $\frac{123}{124}$
C. $\frac{1234}{1235}$
D. $\frac{12345}{12346}$
E. $\frac{123456}{123457}$ - If the length of each side of a cube is decreased by 20%, then the volume of the cube will decrease by what percentage?
A. 51%
B. 51.2%
C. 48%
D. 48.8%
E. None of the above - Find the value of the expression below. $$\frac{4^{16} \times \left(1 + \frac{1}{4} + \frac{1}{16 \times 64} + \frac{1}{256 \times 1024 \times 4096}\right) - 4}{4^{11} \times 21}$$
A. 1
B. 16
C. 21
D. 61
E. None of the above - Solve the equation below and find the integer value of $a+b$. $$\sqrt{a^3+125}+(2b^2-3b+7a)^4=0$$
A. 0
B. 5
C. 10
D. -5
E. None of the above - A positive integer A has exactly 6 positive factors with 7 and 11 being among them. What is the smallest possible value of A?
A. 77
B. 539
C. 847
D. 3773
E. None of the above - A group of 10 wizards and witches sat in a circle. Wizards always speak the truth while witches always lie. Each person pointed at the person on their left and declared whether this person was a witch. If everyone pointed and declared 'witch', how many wizards are there?
A. 5
B. 4
C. 10
D. 6
E. None of the above - What is the next number in the sequence below? $$1,4,26,85,205,416,...$$
A. 759
B. 754
C. 705
D. 927
E. None of the above - How many factors of 180000 are perfect squares?
A. 6
B. 9
C. 18
D. 36
E. None of the above - Let $k,l,m$ and $n$ be 4 positive integers such that $\frac{k}{l}\le \frac{m}{n}\le 1$. Which of the following inequalities is always true?
A. $\frac{k+m}{l+n}>1$
B. $\frac{k+m}{l+n}\ge \frac{k+l}{m+n}$
C. $\frac{k+m}{l+n}<\frac{k}{l}$
D. $\frac{k+m}{l+n}\le \frac{m}{n}$
E. None of the above - Given that $x,y$ and $z$ are distinct numbers such that $(x-y)^2=4(x-z)(z-y)$, find the value of $\frac{x+y}{z}$.
A. 0
B. 1
C. 2
D. 4
E. None of the above - In right-angled triangle $ABC$, points $D$ and $E$ are the midpoints of sides $AB$ and $BC$, respectively. If the area of triangle $CFE$ is 24 $\text{cm}^2$, find the area (in $\text{cm}^2$) of quadrilateral $BEFD$.
A. 24 $\text{cm}^2$
B. 36 $\text{cm}^2$
C. 48 $\text{cm}^2$
D. 60 $\text{cm}^2$
E. None of the above - Given that $3a^2+18ab+27b^2=2700,$ $a=5+2b$ and $a>0$, find the value of $ab$.
A. 5
B. 15
C. 75
D. 125
E. None of the above - The standard 6-sided dice is arranged with the numbers 1 through 6 such that the sum of the numbers on opposite faces is always 7. If six standard dice are stacked on the floor as shown, what is the largest possible sum of numbers on the 21 visible faces?
A. 88
B. 89
C. 90
D. 93
E. None of the above - How many 7-digit positive multiples of 9 can written using only digits 3 and 6?
A. 21
B. 42
C. 63
D. 84
E. None of the above - Tom constructed a large cube using 125 small cubes. He then painted the top, front, and right faces in red, while the remaining faces were painted in yellow. How many of the smaller cubes possess at least one red face and one yellow face?
- In Mathematics, it is given that $n!=n\times (n-1)\times ... \times 2\times 1$. For example, $5!=5\times 4\times 3\times 2\times 1=120$. How many consecutive zeros are there at the end of $2024!$?
- The sum of some consecutive possible integers is 2024. Find the largest of these integers.
- Emily's locker combination is a 4-digit number with the following properties:
-The number is greater than 5000.
-The hundreds digit is one less than the tens digit.
-The number is an even number that is divisible by 9.
How many unique locker combinations can Emily set for her locker? - A string of numbers is generated by writing integers from 1 to 60 in a continuous sequence: $$123456...5660$$ Samantha decides to remove every 10th digit from the string to create a revised number: $$12345689011121314516...$$ What is the sum of the digits in the new number?
- In square $ABCD$ below, points $E$ and $F$ are the midpoints of sides $AD$ and $AB$, respectively. Line $EB$ intersects lines $DF$ and $FC$ at points $G$ and $H$, respectively. If $HB=120$ cm, what is the length (in cm) of $GH$?
- Five friends, Alice, Bob, Carol, David and Eve, visited different attractions, Star Peak, Crystal Cove, Emerald Falls, Thunder Ridge and Mystic Valley, not necessarily in the same order. They each paid different amounts for their entry tickets, $\$20, \$40, \$60, \$80$ and $\$100$. Here are some clues:
-Alice paid $\$40$ for her entry ticket.
-The cost of admission to Emerald Falls was $\$40$ less than to Thunder Ridge.
-Carol paid $\$40$ more than David did for their entry tickets.
-The five different attractions visited are: Crystal Cove, the attraction where the entry ticket cost was $\$40$, the attraction where the entry ticket cost was $\$100$, the attraction with a $\$20$ entry ticket, and the attraction Carol visited.
-Eve visited Star Peak.
How much (in $\$$) was the entry ticket to Emerald Falls? - Lily and Jake started jogging on a circular track with a circumference of 308 metres from the same starting point at the same time. Lily jogs for the first 120 metres with a speed of $6\text{ m/s}$, then continues for the next 200 metres with a speed of $4\text{ m/s}$, repeating this pattern. Jake jogs with a constant speed of $5\text{ m/s}$ but in the opposite direction. How many metres has Lily jogged from the same starting point by the time they meet for the fourth time? Round your answer to the nearest integer.
- Given that $x + \frac{1}{x-3} - 5 = y + \frac{1}{y+2}$ and $x - y \neq 5$, find the value of $2xy + 4x - 6y$.
- In the following cryptarithm, all the different letters stand for different digits. If $S=8$, what is the value of the sum S+O+L+V+E?
Posted : 18/05/2026 6:11 am
