Dr. Hazma, Dr. Tan and Dr. Gupta created vaccines in their labs. Their vaccines showed 98%, 92% and 93% effectiveness respectively. What is the probability that all three are simultaneously effective? Assume independent trials. Round the percentage to two decimal places.
Four shaded right-angled triangles with leg lengths 1 cm × 4 cm, 2 cm × 4 cm, 3 cm × 4 cm and 4 cm × 4 cm fit together to form a quadrilateral. It fits inside a 5 cm × 8 cm rectangle as shown. Find the area of the quadrilateral, in square centimetres. The legs are the two sides beside the right angle.
Which of the following numbers has an odd number of even prime factors? Count prime factors with repetition: for example, 12 = 2 × 2 × 3 has two even prime factors. This edition allows more than one correct option.
There are 5 green, 9 orange, 6 red and 4 blue candies in a bag. At least how many candies must Sam take out without looking to ensure that he gets his first red candy? Candies are not put back.
Tom’s PIN is a five-digit number with all digits different. The thousands digit is twice the ten-thousands digit; the hundreds digit is 50% more than the thousands digit; the tens digit is 1 more than the ten-thousands digit; and the ones digit is 2 more than the tens digit. What is Tom’s PIN divided by 65?
In the cryptarithm MINED + DENIM, different letters represent different digits. Find the last three digits of the largest possible sum. Both addends are five-digit numbers. For example, if the sum were 1234, write 234.
Enter exactly the last three digits, without spaces.
Two regular six-sided dice were rolled on the ground. All numbers on their visible faces add to 31. What is the difference between the two numbers facing the ground? Each die has faces 1 to 6, and “visible” means all five faces other than the bottom face.
Among Jack, Jade and James, one is a painter, one is a lawyer and one is a firefighter. Jack is older than the firefighter, while the lawyer is younger than James. Jade and the lawyer are not the same age. Who is the firefighter? Use Jack = 1, Jade = 2, James = 3.
The large rectangle below is made of 6 squares and 3 rectangles. How many times as large is the area of the largest square as the area of the smallest rectangle? For this edition, interpret the two narrow rectangles at the top left as having equal widths, as intended by the drawing.
In the multiplication $\overline{AB}\times\overline{BA}=\overline{A45B}$, A and B are different digits, AB and BA are two-digit numbers, and A45B is a four-digit number. If AB is less than BA, what is AB?
The scale shows a rectangle, a triangle and an oval with total weight 20 kg. The rectangle weighs 2 kg more than the triangle. The oval weighs 3 kg less than the triangle. What is the weight of the rectangle, in kilograms?
