SEAMO 2019 — Paper C — Grade 5–6

Define $m*n=(m+n)/2$. Evaluate $3*(6*8)$.

Ten identical circles are arranged as shown. Straight line $AB$ passes through the centres of two circles. Find the ratio of the circles’ area above $AB$ to that below it.

John writes $8,9,10,11,12,13,14$. Repeatedly erase any two and replace them by one less than their sum. What is the final number?

At $2{:}45$ pm the smaller angle between the clock hands is $x^\circ$, with $0\lt x\lt 180$. Find $x$.

An October has four Thursdays and five Fridays. What weekday is October $20$?

Primes $p,q$ satisfy $2p+5q=2019$. Find $p-q$.

Jane is three years younger than her brother. Their age sum is half Madam Punitha’s age. In fifteen years their age sum will equal hers. How old is Jane?

Weights of $1,2,4,8,16$ grams may be placed on only one side of a balance. How many different positive masses can be measured?

A $4$ cm by $8$ cm rectangle is folded along its diagonal as shown. Find the shaded triangular area.

Group A has sixteen numbers totaling $98$. Group B has mean $11$. The combined mean is $8$. How many numbers are in B?

In the quarter circle, $\angle ADB=90^\circ$ and $C$ is the midpoint of arc $AB$. A semicircle has diameter $DB$. If shaded region $x$ has area $12\text{ cm}^2$, find shaded region $y$.

At North Shore School $60\%$ of students are boys. $44\%$ of all students participate in sports, of whom $52\%$ are boys. What percentage of the girls do not participate?

Cindy and Diane have savings. If they spend respectively $20$ and $10$ dollars per day, Cindy has $3500$ left when Diane runs out. If they spend $10$ and $20$ per day, Cindy has $3950$ left then. Find Cindy’s initial savings.

A bag has four red and four black balls. Draw three without replacement. The probability of two red and one black is $n/m$. Find $m+n$.

How many distinct numbers from $1$ to $30$ must be chosen to guarantee that one selected number is twice another?

Find the integer part of $\frac1{1/71+1/72+1/73+1/74+1/75}$.

An equilateral triangle of side $1$ rotates clockwise about $C$, then about its moved vertex $B$, as shown. Find the total distance travelled by vertex $A$.

Top row: $1,5,9,\ldots,a,\ldots,1325,1329,1333$. Bottom row: $1000,997,994,\ldots,b,\ldots,7,4,1$. The printed question asks for $a$ when $a-b$ is minimum.

Pipe A takes twice as long as pipe B to fill a pool. Together they take $12$ hours. A alone runs for $m$ hours, then B alone finishes in nine hours. Find $m$.

Given $a=5^{39},b=3^{52},c=2^{91}$, which order is correct?