Exam grading: platform starts at 0; Q1–15 award 2 points each, Q16–25 award 4 each; no penalties; maximum 70. Official reference: starts at 15; Section A +2/−1/0 for correct/incorrect/blank, Section B +4/0/0; maximum 85. Duration: 90 minutes (official-reference default).
At a flower shop, four roses cost 7 dollars and three lilies cost 8 dollars. Billy buys some roses and lilies for 86 dollars. Which could be the number of roses bought? Assume constant unit prices and whole flowers.
What is the least number of positive integer-gram weights needed to weigh any object of integer mass from 1 to 35 grams? All weights used must be on one pan and the object on the other.
Every face of a soccer ball is a pentagon or a hexagon. Each pentagon is adjacent to five hexagons; each hexagon is adjacent to three pentagons and three hexagons. There are 12 pentagonal faces. How many hexagonal faces are there?
Alice, Jane, Philip and Victor were born in the distinct years 1982, 1983, 1984, 1985 and in the distinct cities Athens, Moscow, Paris, Singapore, not respectively. The person born in Paris is one year older than the person born in Singapore. Victor was born one year later than the person born in Paris. Philip was born in Moscow. Alice was born two years later than Victor. In which year was Jane born?
Henry has 13 yellow, 7 brown, 25 red and 10 green balls in a bag. They have the same size and shape. What is the least number he must draw without looking to guarantee balls of three different colours?
The chart shows the responses of all Secondary 1 students at Integrity Secondary School to a multiple-choice question. Horizontal grid lines are equally spaced. A correct response scores 2 points, no response 0, and a wrong response −1. The total is −120 points. If B is correct, how many students answered correctly? These scoring rules are part of this word problem, independent of platform exam scoring.
Chart label: “No response” means no answer.
Answer format: enter one whole number without units. The printed paper uses four answer-sheet digits with leading zeros when needed; ordinary numeric entry is used here.
Andrea and Claire leave Woodlands and HarbourFront respectively at the same time and travel towards each other. When Andrea reaches HarbourFront, Claire still has 5 km to travel to Woodlands. Andrea travels 20% faster than Claire. Find the distance in km between the two places. Assume constant speeds along the same route.
Answer format: enter one whole number without units. The printed paper uses four answer-sheet digits with leading zeros when needed; ordinary numeric entry is used here.
Find the smallest positive integer n for which $3993n$ is a multiple of 2475.
Answer format: enter one whole number without units. The printed paper uses four answer-sheet digits with leading zeros when needed; ordinary numeric entry is used here.
Four identical circles touch the large circle and pass through its centre, arranged as shown. The large circle has diameter 28 cm. Find the shaded area in square centimetres, using $\pi=22/7$.
Answer format: enter one whole number without units. The printed paper uses four answer-sheet digits with leading zeros when needed; ordinary numeric entry is used here.
Define $\{n\}=1+3+5+\cdots+(2n-1)$ for positive integers n. For example, $\{5\}=1+3+5+7+(2\times5-1)$. If $\frac{\{m\}}m+m=2020$, find m.
Answer format: enter one whole number without units. The printed paper uses four answer-sheet digits with leading zeros when needed; ordinary numeric entry is used here.
