SEAMO 2026 Paper C SET 2 – Self-practice

A new operation is defined as $m*n=\frac{m+n}{2}$. Evaluate $3*(6*8)$.

10 identical circles are arranged as shown. AB is a straight line that cuts through the centres of 2 circles. What is the ratio of the area above line AB to the area below line AB?

John writes the following numbers on the whiteboard: 8, 9, 10, 11, 12, 13, 14. Each time, he selects 2 numbers to erase. Then, he replaces them with another number that is 1 less than their sum. What will be the last number remaining on the whiteboard?

At 2:45 PM, the angle formed by the hour and minute hands is $x^\circ$, where $0<x<180$. What is the value of $x$?

There were 4 Thursdays and 5 Fridays in the month of October some years ago. On which day of the week was the 20th of October that year?

Source language discrepancy: the Vietnamese source instead states 4 Wednesdays and 5 Thursdays.

$p$ and $q$ are prime numbers. Given that $2p+5q=2019$, find $p-q$.

Jane is 3 years younger than her brother. The sum of their ages is half that of Mdm. Punitha's. 15 years from now, the sum of their ages will equal Mdm. Punitha's. How old is Jane?

One each of 1-, 2-, 4-, 8- and 16-gram weights are used on a balancing device. Given that the weight(s) can only be placed on one side of the device, how many different masses is the device capable of measuring?

A rectangle paper is folded along the diagonal as shown in the diagram below. Find the area of the shaded region.

Group A consists of 16 numbers whose sum is 98. Group B consists of some numbers whose average is 11. The average of all the numbers in both groups is 8. How many numbers are there in Group B?

In the diagram below, $\angle ADB=90^\circ$ and C is the midpoint of arc AB. Given that the area of the shaded region x is $12\text{ cm}^2$, find the area of the shaded region y in $\text{cm}^2$.

60% of the students at North Shore School were boys. 44% of the students took part in the sports meet, of which 52% were boys. What percentage of the North Shore girls did not participate?

Cindy and Diane each have some savings. If Cindy spends 20 dollars and Diane spends 10 dollars a day, Cindy will have 3500 dollars remaining when Diane finishes up her savings. If Cindy spends 10 dollars and Diane spends 20 dollars a day, Cindy will have 3950 dollars remaining when Diane finishes up her savings. How much money does Cindy have at first?

A bag contains 4 red and 4 black balls. When 3 balls are chosen at random, without replacement, the probability of getting 2 red balls and 1 black ball is $\frac nm$. Find $(m+n)$.

At least how many numbers from 1 to 30 must be chosen to ensure there always exists a number that is twice another?

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

An equilateral triangle of side length 1 is rotated pivoting at C. Then it is turned at point B. Find the distance travelled by the point A.

Find the value of $a$, when $(a-b)$ is minimum.

$\begin{array}{c|ccccccccc}&1&5&9&\cdots&a&\cdots&1325&1329&1333\\\hline&1000&997&994&\cdots&b&\cdots&7&4&1\end{array}$

Pipe A takes twice as long to fill a pool as compared with Pipe B. It takes them 12 hours to fill a pool when turned on together. If Pipe A alone is turned on for m hours and then turned off, Pipe B will take another 9 hours to fill the pool. Find m.

Given that $a=5^{39}$, $b=3^{52}$, $c=2^{91}$, which of the following statements is true?