SEAMO self-study edition 2027; not an official 2027 paper. Original source years are retained. 25 questions, 90 minutes; Q1–10: 3 points, Q11–20: 4 points, Q21–25: 6 points, total 100. Original response types and all subparts are preserved. Verified is an editorial convention; source defects, necessary assumptions and unresolved mathematical uncertainty are disclosed.
Find the value of $\sqrt[3]{\sqrt{30}-\sqrt3}\times\sqrt[3]{\sqrt{30}+\sqrt3}$.
Suppose $n_1,n_2$ are positive integers with $1\le n_1\lt n_2\le99$. When all possible values of $n_1/n_2$ are arranged in ascending order, find the fraction immediately after $17/76$.
Answer format: enter a reduced fraction as numerator/denominator, with no spaces.
A fair die has faces numbered 1 to 6. Let $a,b,c$ be the results of the first, second and third throws, respectively. What is the probability that $a\gt b\gt c$?
Mr. Woodley paid 650,000 dollars for two commercial properties. A year later, the market value of the first property rose by 20%, while that of the second dropped by 25%. The two properties then had the same market value. What was the market value of the first property at first?
Positive integers $a_1,a_2,\ldots,a_{30}$ satisfy $a_1+a_2+\cdots+a_{30}=2024$. Let $d$ be the maximum possible greatest common divisor of these 30 integers. Find $d$.
If the radius of a sphere increases by 5%, what is the corresponding percentage increase in its volume, rounded to 1 decimal place? Use $V=\frac43\pi r^3$.
A teacher wrote 4875, 4563 and $N$ on the whiteboard, where $N$ is a positive integer, and asked the class to compute their lowest common multiple. One student misread 4875 as 4275 but still obtained the correct answer. What is the least possible value of $N$?
