SEAMO X 2021 — Paper C — Grade 5–6

Given $5*2=5+55=60$ and $7*4=7+77+777+7777=8638$, find $8*5$.

For a four-digit number $\overline{abba}$, both $\overline{ab}$ and $\overline{ba}$ are prime, with $a\ne b$. How many numbers are possible?

Positive whole numbers $A,B$ satisfy $1/15=1/A+1/B$. Find the smallest three-digit value of $A+B$.

Positive integers $m,n$ have least common multiple $50$. How many pairs are there?

Sandar and Thaunder leave Mandalay for Bagan together. Sandar arrives thirty minutes earlier and travels another forty-five km before Thaunder arrives. Sandar is $18$ km/h faster. Find the city distance.

Three students and their teacher have ages totaling one hundred. The youngest is seven, the students have different ages, and everyone’s age is prime. Find the greatest possible teacher age.

Printing cost rises $10\%$ in $2021$, selling price stays unchanged, and profit falls $40\%$. What is the new printing cost as a percentage of the selling price?

Use $1^2+2^2+\cdots+n^2=n(n+1)(2n+1)/6$. Find the difference between $1+2+\cdots+500$ and the sum of all square numbers less than five hundred.

Distinct positive integers satisfy $a\lt b\lt c\lt d$, $a+(b+c+d)/3=17$, $d+(a+b+c)/3=29$, and $b-a\lt 2$. Find $d$.

Three edge cuts unfold the triangular pyramid, and seven unfold the quadrilateral right prism, as shown. How many edge cuts unfold the dodecahedron into the displayed connected net?

What is the maximum number of distinct selections from $1,2,\ldots,50$ such that no sum of two selected numbers is divisible by seven?

Triangle $ABC$ has area $12\text{ cm}^2$, $BD=DC$, $AD=3DF$, as shown. Find the area of quadrilateral $CDFE$.

The Fibonacci sequence starts $1,1,2,3,5,8,13,21,\ldots$, each subsequent term the sum of the preceding two. Find the remainder of its $2021$st term divided by eleven.

A goat is tied outside an equilateral triangular fence of side five metres at the vertex shown, with a six-metre rope. Find the total roaming area in terms of $\pi$.

Evaluate $\sum_{k=1}^{59}\left(\frac{k}{k+1}+\frac{k}{k+2}+\cdots+\frac{k}{60}\right)$.