Question 48. Tom travels from home to cinema at 60 km/h. He returns along the same route. His average speed for the round trip is 72 km/h. What is his speed (in km/h) from cinema to home?
**Editorial input convention:** Use travelling time only, with a constant speed on each leg and no stop included. Enter the return speed in km/h, as a number only.
Exercise 14. For any two numbers $x$ and $y$, their LCM and GCD are related by the following formula:
$$\operatorname{GCD}(x,y)\times\operatorname{LCM}(x,y)=xy.$$
Given that the product of two numbers is 3240 and their GCD is $2\times3^2$, find the LCM in index notation.
**Editorial input convention:** Take x and y to be positive integers. Enter prime powers in increasing prime order, using ^ for powers and * for multiplication, no spaces; omit exponent 1. Format example, not the answer: 2^3*7.
Question 12. When Clara totaled her scores, she inadvertently reversed the units digit and the tens digit of one score. By which of the following might her incorrect sum have differed from the correct one?
Exercise 17. Rectangle $ABCD$ has sides $CD=3$ and $DA=5$. A circle of radius 1 is centered at $A$, a circle of radius 2 is centered at $B$, and a circle of radius 3 is centered at $C$. Find the area of the region inside the rectangle but outside all three circles.
**Editorial input convention:** Enter the exact area in the form `a-b*pi/c`, where b/c is a reduced positive fraction; use the letters pi, with no spaces or units. Format example, not the answer: `8-5*pi/3`.
Exercise 6. Alice has 24 apples. In how many ways can she share them with Becky and Chris so that each of the people has at least 2 apples?
**Editorial input convention:** Distribute all 24 indistinguishable apples among Alice, Becky and Chris, including Alice as a recipient. Count allocations by the three named amounts, with at least two apples per person.
Question 30. Father’s age is six times his son’s age. In four years, the age of the father will be four times of his son’s age. The current ages of the son and the father is:
Exercise 4. A seven-digit number, $2\,006\,\square\square\square$, is divisible by 3, by 4 and by 25. Find the possible values of the missing digits.
**Editorial input convention:** List every complete three-digit ending in increasing order, separated by semicolons, with no spaces. Format example, not the answer: 012;345.
Question 25. Two semicircles are inscribed in a square with the area of $400\text{ cm}^2$, as shown. Find the area of the shaded region. (Use the approximation 3.14 for $\pi$.)
**Editorial input convention:** Enter the shaded area in square centimetres, using 3.14 for pi as instructed, as a number only.
Example 1. A small community consists of 10 women, each of whom has 3 children. If one woman and one of her children are to be chosen as mother and child of the year, how many different choices are possible?
Example 15. Fill in the table. Write here the sum of the numbers in these empty blanks.
**Editorial input convention:** Fill the four table blanks in your working; enter only their requested sum. Base and Leg are perpendicular legs of a right triangle, and Hypotenus means hypotenuse.
Question 44. The speed of light is approximately 186,000 miles/second. If $186,000=2^A\times3^B\times5^C\times31^D$, compute the simplified value of $(A-B)\times(C+D)$.
**Editorial input convention:** Use the nonnegative integer exponents in the prime factorisation of the stated integer.
Question 10. The Incredible Hulk can double the distance it jumps with each succeeding jump. If its first jump is 1 meter, the second jump is 2 meters, the third jump is 4 meters, and so on, then on which jump will it first be able to jump more than 1 kilometer?
