Set 8

The common fraction form of the repeating decimal $0.323323323...$ is...

If $A$ is $22\frac{1}{4}\%$ of $25$ and $B$ is $\frac{1}{8}$ of $32$, then...

$x_0$ is the average of data $x_1, x_2, ..., x_{10}$. If the data changes following the pattern $\frac{x_1}{2} + 3, \frac{x_2}{2} + 5, \frac{x_3}{2} + 7$, and so on, then the average value becomes...

There are two boxes, both containing black and white balls. The number of balls in each box is $20$. One ball is taken from each box, and the probability that both balls are black is $\frac{3}{10}$. If the probability that both balls are white is $\frac{m}{n}$, then $m + n = \dots$

Set $A$ has $10$ members. The number of subsets of $A$ that have more than $3$ members is...

The operation $\odot$ on the set of integers is defined by $a \odot b = 3ab - 2(1 + b)$. The value of $(5 \odot 2) \odot 3 = \dots$

Three years ago, the ratio of Ali's age to Tika's age was $4:5$. If the ratio of their ages three years from now is $5:6$, then the difference in their current ages is...

Line $h$ passes through point $T(-1,3)$ and has a gradient $m$. For $h$ to intersect the graph $y = -x^2$ at two distinct points, it must be that...

For $(2m + 1)x^2 - 4(m + 1)x + m > -4$ to hold for every real $x$, the values of $m$ must satisfy...

Ali will depart from city A to city B at $09.15$ driving a car with an average speed of $60$ km/h. At the same time, Tika heads to city A from city B in her vehicle at a speed of $70$ km/h. The distance between city A and city B is $221$ km. If they take the same route, they will cross paths at...

The average mathematics exam score of a class is $7.5$. The ratio of male to female students in the class is $3 : 4$. If the average score of female students is $1.75$ higher than the average score of male students, then the average score of female students is...

A fabric company requires $20$ workers to complete an order in $12$ days. If the number of orders remains unchanged but only $15$ people can work on the order, then the additional time required to complete the order is ... days

A box contains $5$ red balls, $4$ white balls, and $3$ yellow balls. From the box, $3$ balls are drawn simultaneously at random. The probability of drawing $2$ red balls and $1$ white ball is...

Given that

The value of $x$ that satisfies the equation is...

Consider the following number sequence:

The correct number to complete the pattern is ...

The decimal value closest to the largest value among the fractions $\frac{34}{33}, \frac{6.1}{6}, \frac{56}{55}, \frac{12.5}{12.4}, \frac{26}{25}$ is...

A hemispherical water container with a radius of $15 \text{ cm}$ is full of water. All the water in the container is transferred into a cylindrical container with a radius equal to the radius of the hemisphere. The height of the water in the cylindrical container is...

In a class, there are $30$ students participating in extracurricular activities. There are $12$ students who join the scouts extracurricular and $15$ students who join the futsal extracurricular, and $7$ students who join both. The number of students who do not join either is...

The value $4$ inside triangle $Q$ is the result of arithmetic operations on all numbers outside triangle $Q$. Using the same operation pattern, the correct value inside triangle $R$ is...