A, B, C and D are four numbers. The average of A and B is 40, the average of B and C is 34 and the average of C and D is 22. Find the average of A and D.
The square below is divided into 4 congruent rectangles. The perimeter of each of the 4 congruent rectangles is 50 units. How many units are there in the perimeter of the square?
A sociologist chose 300 students at random from each of two schools and asked each student how many siblings he or she has. The results are shown in the table below.
Students’ Sibling Survey
| Number of siblings | Lincoln School | Washington School |
|---|---:|---:|
|0|120|140|
|1|80|110|
|2|60|30|
|3|30|10|
|4|10|10|
There are a total of 2,400 students at Lincoln School and 3,300 students at Washington School. What is the median number of siblings for all the students surveyed?
The figure below shows a square ABCD with two shaded triangles inside. Given that the total area of the shaded triangles is 242cm², find the length, in cm, of AB.
In the following cryptarithm, different letters represent different digits and an asterisk * may represent any digit. The product $\overline{MATH}$ is a four-digit number less than 5000. What number does $\overline{MATH}$ represent?
$\overline{EH}\times\overline{EH}=\overline{MATH}$. The first partial product is **6; the second is **8, shifted one place left.
6 arrows land on the target shown below. Each arrow is in one of the regions of the target. Which of the following total scores is possible: 16, 19, 26, 31, 41, 44?
A spider has 8 legs and a dragonfly has 6 legs. There are 14 spiders and dragonflies altogether. There are 100 legs in all. Find the number of spiders and the number of dragonflies.
Answer entry: enter spiders;dragonflies, separated by semicolons.
**Editorial input note:** Use no spaces before or after semicolons.
In a building, there are 25 steps in the staircase leading from one storey to another. How many steps are there from the second to the tenth storey in that building? (Assume the number of steps in the staircase is the same)
Two pipes A and B can fill a cistern in $37\frac12$ minutes and 45 minutes respectively. Both pipes are opened. For how many minutes is pipe B turned on so that the cistern will be filled in just half an hour?
Operating convention used in the source solution: A stays on throughout all 30 minutes; the cistern starts empty and both rates are constant.
At a party, 60% of the guests were Chinese. 40% of the remaining guests were Malays and the rest were Indians. There were 48 more Indians than Malays. How many guests were at the party?
Jane had $\frac13$ as many stickers as Mary. Mary had 120% as many stickers as Paul. After Mary gave 16 stickers to Paul, Mary had the same number of stickers as Paul. How many stickers did the 3 children have altogether?
