CTJan27 Online Year 8 - Numerical Reasoning 09042026

A book's price was increased by 20%. A month later, the new price was decreased by 20%. What was the overall percentage change in the book's price from its original price?

In a box, the ratio of red marbles to blue marbles is $3:5$. After 18 red marbles are added to the box, the ratio of red marbles to blue marbles becomes $3:2$. How many blue marbles are in the box?

Working alone, Machine A can complete a task in 6 hours. Working alone, Machine B can complete the same task in 3 hours. If they start at the same time and work together, how many minutes will it take them to complete the task?

A positive integer $N$ leaves a remainder of 3 when divided by 5, and a remainder of 4 when divided by 6. Which of the following is a possible value for $N$?

Consider the sequence of figures made of dots. Figure 1 has 2 dots, Figure 2 has 5 dots, and Figure 3 has 10 dots. If the pattern continues, how many dots will be in Figure 6?

Figure 1: •• Figure 2: ••••• Figure 3: ••••••••••

Four friends, Ali, Ben, Chen, and Dan, are sitting in a row. Ben is sitting to the left of Chen. Ali is not sitting next to Ben. Dan is sitting at the far right end. Which of the following must be true?

In the diagram, a larger square contains a smaller square. The corners of the smaller square touch the midpoints of the sides of the larger square. What fraction of the larger square is shaded?

Triangle $ABC$ is similar to triangle $XYZ$. The length of side $AB$ is 6 cm and the length of the corresponding side $XY$ is 9 cm. If the area of triangle $ABC$ is 24 cm$^2$, what is the area of triangle $XYZ$?

A train travelling at a constant speed of 90 km/h enters a tunnel that is 1.5 km long. The length of the train is 500 metres. How long does it take from the moment the front of the train enters the tunnel to the moment the rear of the train leaves the tunnel?

The graph shows the 'skill level' achieved by a student using two different practice methods, A and B, over 8 weeks. In which week did Method A provide the greatest increase in skill level?

In a group of 50 students, 30 play soccer and 25 play basketball. If 12 students play both sports, how many students play neither soccer nor basketball?

Leo had a collection of stamps. He gave half of them to his friend Maya. Then, he gave one-third of the remaining stamps to his brother. After this, he had 60 stamps left. How many stamps did Leo have initially?

A number is called 'special' if it is a three-digit number where the product of its digits is 24. How many 'special' numbers are there?

In triangle $PQR$, angle $P$ is $70^\circ$. The point $S$ lies on the side $QR$ such that $PS$ bisects angle $P$, and $PS = SQ$. What is the size of angle $R$?

The graph shows the populations of Town A and Town B over a 10-year period. In which year was the difference in population between the two towns the smallest?

The average of five distinct positive integers is 10. The largest of these integers is 20. What is the greatest possible value for the median of these five integers?

A painter can paint a room in 4 hours. His apprentice can paint the same room in 6 hours. The painter works alone for 1 hour and is then joined by the apprentice. They work together to finish the room. How long do they work together?

A cyclist travels from Town P to Town Q. For the first half of the distance, the cyclist travels at 30 km/h. For the second half of the distance, the cyclist travels at 20 km/h. What is the average speed for the entire journey?

A shopkeeper bought an item for a certain price. He marked it up by 50%. He then sold it at a discount of 20% on the marked price. His profit was 60 dollars. What was the original price he paid for the item?

The sum of three different prime numbers is 40. What is the largest possible product of these three numbers?

A sequence of numbers follows a pattern. Find the next number in the sequence.

$3, 9, 7, 21, 19, 57, ...$

The chart below shows the planned budget distribution for a city council with a total budget of 8,123,500 dollars.

Which of the following is the best estimate for the combined budget for Parks and Admin?

The chart shows the number of units sold for four different products in Week 1 and Week 2.

Which product had the greatest percentage increase in sales from Week 1 to Week 2?

The numbers in the grid below follow a rule that applies to each row. What is the missing number in the third row?

A bag contains only red and blue marbles in the ratio $3:5$. After 8 red marbles are added to the bag, the ratio of red to blue marbles becomes $1:1$.

How many blue marbles are in the bag?

The line graph shows the number of members in the school's Coding Club and Debating Club over five years.

In which year was the number of members in the Coding Club the smallest proportion of the number of members in the Debating Club?

The price of an item in a store is 99 dollars. This price was calculated by first applying a 10% discount to the original price, and then adding a 10% sales tax to the discounted price.

What was the original price of the item?

What is the value of the expression $\frac{2024^2 - 2022^2}{2023}$?

A recipe for 12 cookies uses ingredients in the proportions shown. The recipe requires 200 grams of flour.

To make 30 cookies, how much butter is needed?

A sequence of numbers follows a pattern. The first six numbers are:

$7, 10, 9, 12, 11, 14, ...$

What is the next number in the sequence?

Which of the following values is the largest?

What is the value of $(102 \times 98) - (103 \times 97)$?

A number grid follows a consistent rule.

| Row 1 | 4 | 5 | 25 |
| Row 2 | 7 | 3 | 24 |
| Row 3 | 6 | 8 | ? |

What is the missing number in Row 3?

A bag contains only blue and red marbles. The ratio of blue marbles to red marbles is $3:5$. After 12 more blue marbles are added to the bag, the ratio of blue to red marbles becomes $3:4$. How many red marbles were in the bag originally?

The price of an item is increased by $20%$. The new price is then decreased by $20%$. What is the overall effect on the original price?

The sum of three consecutive positive odd integers is a value between 80 and 90. The sum is also a multiple of 9. What is the product of the smallest and largest of these integers?

The table shows the scores of four students in two tests.

Which student had the highest percentage increase in their score from Test 1 to Test 2?

A number processing machine follows a consistent two-step linear rule.

• When the input is 20, the output is 50.
• When the input is 32, the output is 80.
  What was the input if the output is 116?

Machine A produces 240 widgets in 6 hours. Machine B produces 300 widgets in 12 hours. If both machines work together, how many widgets can they produce in 4 hours?

A rectangular lawn is 19.8 metres long and 5.1 metres wide. A bag of fertilizer is advertised to cover approximately 25 square metres. Based on these values, what is the minimum number of whole bags of fertilizer that must be purchased to cover the entire lawn?