SEAMO X 2020 — Paper C — Grade 5–6

Given $4*2=14$, $5*3=22$, $3*5=4$, find $6*9$ using the same rule.

If $A:B=5:3$, $B:C=6:7$, and $A:C=x:y$, find $x+y$.

Ms Nutcharut gives Class Courageous $1/5$ of her sweets plus twenty; then Class Dauntless $1/4$ of the remainder plus six; then Class Elegance $1/3$ of the remainder. Sixteen remain. How many sweets did she have initially?

Find the whole number $k$ such that $2^9\lt 5^k\lt 3^6$.

In triangle $ABC$, $AF=3AD$, $BD=3BE$, $BC=3FC$, as shown. If $[ABC]=81\text{ cm}^2$, find $[DEF]$.

The largest five-digit number of the form $\overline{a724b}$ divisible by twelve is chosen. Find $a+b$.

If $1+\frac13+\frac16+\frac1{10}+\frac1{15}+\frac1{21}+\cdots+\frac1{210}=m/n$, find $m+n$.

Three Super Maths classes A, B, C have equal enrolments in A and B. C has $7/20$ of all students and three more than A. Find the total.

Find the $2020$th term of $1;1,2;1,2,3;1,2,3,4;1,2,3,4,5;\ldots$.

A project is finished in ten days if eight workers are added to the original group, or twenty days if three are added. With two added, how many days are needed, assuming equal constant work rates?

A $3\times2$ cm rectangle contains two quadrants centred at $C,D$, as shown. If the difference between shaded areas A and B is $y$, find $100y$. Use $\pi=3.14$.

The road from A to B first climbs then descends. Uphill speed is $30$ km/h and downhill $42$ km/h. Going A to B takes three hours, B to A $2\frac25$ hours. If total distance is $d$, find $2d$.

Mr Smith has a seven-digit phone number. The first four digits interpreted as a number plus the last three equal $6861$. The first three plus the last four equal $4215$. Find the first three digits.

At $a\frac bc$ minutes after $4{:}00$ pm the clock hands form $90^\circ$. $a,b$ are one-digit numbers and $c$ a two-digit number. Find $a+b+c$.

Using odd digits $1,3,5,7,9$, form three-digit numbers $\overline{abc},\overline{def}$, each with distinct digits internally. How many pairs satisfy $\overline{abc}-\overline{def}=198$?