SEAMO 2018 — Paper C — Grade 5–6

Find the ones digit of $1^5+2^9+3^{13}+4^{17}+5^{21}+6^{21}+7^{29}+8^{25}$.

Thirteen squares of side $2$ cm form the diagram. Line $AB$ divides it into two equal areas. Find $AX$ in cm.

Evaluate $\frac1{1\times2\times3}+\frac1{2\times3\times4}+\cdots+\frac1{99\times100\times101}$.

How many shortest grid paths from $A$ to $B$ pass through both $P$ and $Q$?

The product of the positive integer numerator and denominator of a proper fraction is $420$. How many such fractions are possible?

Find the remainder when $\overline{abababab}\div\overline{ab}$ is divided by $9$, as represented by $\frac{\overline{abababab}}{\overline{ab}}\times\frac19$.

After water is added to a salt solution its salt content is $15\%$. Adding the same amount again makes it $12\%$. What percentage follows a third equal addition?

Figures $1,2,3$ have $3,6,10$ vertices respectively. Find the number of vertices in Figure $20$.

Miss Nutcharat drives from Bangkok to Chiang Mai. At $100$ km/h she is $30$ minutes late; at $120$ km/h she is $35$ minutes early. Find the distance.

The conversion formula is $F=\frac95C+32$. At what Celsius temperature is Fahrenheit $60$ greater than Celsius?

A large truck carries $8$ tonnes and uses $15$ litres of diesel per trip. A small truck carries $2$ tonnes and uses $4$ litres. What is the minimum diesel needed for $100$ tonnes?

In $2010$, Anand’s age is four times the sum of his two sons’ ages. In $2018$, it is twice their age sum. In which year was Anand born?

Sam, Rex and Ted each study two of English, Math, Science, Dance, Music and Art, with each subject assigned once. Science and Math students are neighbours. Rex is youngest. Sam exercises with the Dance, Music and Math students. Dance’s student is older than English’s. Rex plays chess with Music’s and English’s students. Which two subjects does Ted study?

In triangle $ABC$, $D$ lies on $BC$, $CD=3BD$, and $E$ is the midpoint of $AD$. Line $CE$ meets $AB$ at $F$. If $[ABC]=14\text{ cm}^2$, find the total shaded area $[AEF]+[DEC]$.

The digits $3,4,6,8$, used once each, form $24$ four-digit numbers. Find their average.

What is the maximum number of integers selected from $1,2,\ldots,50$ such that no two selected numbers have sum divisible by $7$?

Ten cards have primes $2,3,5,7,11,13,17,19,23,29$. Draw a card, record it, replace and shuffle, repeating for four draws. Which of $136,198,455,1925,2018$ cannot be the product?

Akani has two $20$-cent coins and three $1$-dollar coins. He draws two without replacement. What is the probability their total is $1.20$ dollars?

Two circles and a square of side $12$ cm are arranged as shown. Find the total shaded area.

Madam Evie drives from Bandung to Surabaya at $V$ km/h. Increasing speed by $20\%$ for the whole trip saves two hours. Travelling the first $100$ km at $V$, then increasing speed by $25\%$, also saves two hours. Find the distance.