SEAMO 2026 Paper D SET 2 – Self-practice

Find the last 2 digits in the sum $1+2+3+4+\cdots+2017+2018$.

It is now 3:15 PM. After how many minutes will the minute-hand form an angle of 30° with the hour-hand?

When $n^5-n$ is divided by 5, where $n\in\mathbb Z^+$, the remainder is

Find g in the multiplication shown: $\overline{abcdef}\times f=\overline{gggggg}$.

It is known that p is a prime number. If $p^2+2$ is also a prime number, find p.

Find the number of digits in $4^{22}\times5^{40}$.

There are 7 black, 5 white and 4 orange balls in a bag. Four balls are drawn without replacement. Find the probability that at least 3 balls are white.

Given that the area of $\triangle ABC$ is 1 and $\frac{BD}{CD}=\frac{CE}{EF}=\frac{AF}{FD}=\frac12$, what is the area of $\triangle DEF$?

Find the positive integral solution of $\frac1x+\frac1y+\frac1z=\frac56$.

Today is Saturday. What day is it $3^{100}$ days later?

If $a-b=3$ and $a^2+b^2=5$, find $\frac1a-\frac1b$.

15 countries took part in The World Cup. Each team played exactly 2 matches. The winner scored 3 points and the loser scored 0 points. Each team got 1 point for a draw. How many more points at most did the champion score than the runner up?

It is known that m,n,p are positive integers with $m<n<p$. If $2^m+2^n+2^p=2336$, find m.

How many odd digits are there in the result of $1\,111\,111\,111\times9\,999\,999\,999$?

Let m be a positive integer such that $m\times874$ is a 5-digit number ending in 92. Possible value(s) of m is/are: i. 48; ii. 58; iii. 68; iv. 108.

In the figure below, ABCD is a rectangle, E and F are midpoints of AD and CE, respectively. If the area of $\triangle BDF$ is $7.5\text{ cm}^2$, find the area of ABCD in square centimetres.

The source figure is absent; the following is an authored reconstruction from the stated givens.

Two thirds of the journey from Lethbridge to Medicine Hat is highway; the remaining third is country road. St. Paul connects them. A van leaves Lethbridge for Medicine Hat at 100 km/h on highway and 60 km/h on country road. A car leaves Medicine Hat for Lethbridge at 70 km/h on country road and 110 km/h on highway. They pass 44 km from St. Paul. Find the distance between the two cities, in km.

Let n be a positive integer such that $n^2+15n+36$ is a perfect square. Find n.

The common chord AB of circles with centres m and n has length 2(3). It forms one side of an equilateral triangle in circle m and one side of a right hexagon in circle n. Find the ratio of their areas.

Starting from any letter M below, the word MADAM can be spelled by moving up, down, left or right to an adjacent letter. How many ways are there to spell MADAM?