HKIMO 2017 Grade 7 National Final (Heat) Set 04

Nonzero digits $A,D$ form two-digit numbers. $\overline{DA}$ is prime, while $\overline{AD}$ is a product of two primes greater than 5. Find $\overline{DA}$.

Andy walks 20 km north, then 15 km east. How far is he from his starting point?

How many times do the hour and minute hands of a clock form a right angle in one day? Use the usual continuously moving 12-hour clock over 24 hours.

Amy reads 1 page on day 1,2 pages on day 2,3 pages on day 3, and so on, stopping when her cumulative total first becomes a multiple of 56. How many pages has she read then?

There are 4 pairs of white chopsticks,6 pairs of yellow chopsticks and 3 pairs of brown chopsticks mixed together. What is the least number of individual chopsticks drawn at random that guarantees a pair of each colour?

Find $y$ if $(2 y+24)+(9 y-79)=0$.

Positive integers $x,y$ satisfy $2 x+4 y=48$. Find the largest value of $x+y$.

How many integers $x$ satisfy $777>9 x+25>-29$?

Positive real numbers $a,b$ satisfy $a^2-b^2=102$ and $a=b+6$. Find $a+b$.

Factorise $x^2+11 x+30$.

Find the sum of all positive divisors of 7777.

Among integers 1 through 2018 inclusive, how many are divisible by both 3 and 4 but not by 8?

An integer $B$ has the property that $B^{17}$ is a 21-digit number with units digit 6. Find $B$.

If $x>0$ and $x+1/x=3$, find $x^2+1/x^2$.

Two square numbers differ by 348. Find the smallest possible larger square.

A cube of side 12 is cut into unit cubes. Find the increase in total surface area.

A wire forms a circle of radius 14. It is reshaped into a rectangle. Find its greatest possible area. Take $\pi=22/7$.

Unit cubes are stacked in the pattern shown. Find the volume when there are 31 layers.

A right triangle has hypotenuse 10. Find its maximum area.

An interior angle of a regular $n$-gon is five times an exterior angle. Find $n$.