CTJan27 Online Year 8 Numerical Reasoning 19052026

The first five terms of a sequence are 3, 7, 10, 17, 27.

What is the next term in the sequence?

A box contains 48 red marbles and 52 blue marbles. Liam removes $\frac{1}{4}$ of the red marbles and $\frac{1}{2}$ of the blue marbles.

How many marbles are left in the box?

A school library has 1200 books. 30% of the books are fiction. Of the remaining books, $\frac{2}{3}$ are science books and the rest are history books.

How many history books are in the library?

The chart shows the travel times for the three sections of a bus journey.

If a bus departs from the start of its journey at 10:10 am, at what time does it arrive at its destination? Assume there is no waiting time between sections.

A cyclist travels at a constant speed of 18 kilometres per hour.

How many metres does the cyclist travel in 40 seconds?

Let K be a whole number greater than 10. K is divisible by 3. K is also divisible by 4. K is NOT divisible by 8.

Which of the following could be the value of K?

Three positive whole numbers, A, B, and C, have a sum of 15. Their product is 80. A is the smallest of the three numbers.

What is the value of A?

Consider the sequence defined by the rule that each term is the sum of the digits of the square of the previous term. The first term is 13.

What is the fourth term of this sequence?

In a school, the ratio of teachers to students is 3:40. The ratio of male students to female students is 5:7.

If there are 210 female students, how many teachers are there?

The chart shows the number of laptops sold by four different stores in 2022 and 2023.

For the store that had the highest percentage increase in sales from 2022 to 2023, what was that percentage increase?

January 1st, 2024 was a Monday.

What day of the week will January 1st, 2028 be? (Note: 2024 is a leap year.)

Amir, Beth and Chloe share a prize of 990 dollars. Amir receives twice as much as Beth. Chloe receives 90 dollars less than Amir.

How much does Beth receive?

P is the sum of the first 20 positive odd integers. Q is the sum of the first 20 positive even integers.

Which of the following statements is true?

The sequence 3, 5, 11, 29, 83, ... follows a logical rule.

What is the next number in this sequence?

The pie chart shows the composition of a 900-gram cereal box by weight.

If the manufacturer replaces half of the sugar content with an equal weight of extra oats, what will be the new weight of oats in the box?

After a 20% discount, the price of a coat is 144 dollars.

What was the original price of the coat?

Maya can paint a fence in 6 hours. Leo can paint the same fence in 4 hours.

If they work together at their constant individual rates, how long will it take them to paint the fence?

In a group of 100 students, a survey on participation in Tennis and Soccer was conducted. The chart shows the total number of students who play each sport. A total of 75 students play at least one of these two sports.

How many students play both Tennis and Soccer?

The graph shows the water depth in two tanks, A and B, over a period of 60 minutes.

At approximately what time are the water depths in Tank A and Tank B the same?

A positive two-digit integer N has exactly three positive divisors, including 1 and N itself. When N is divided by 5, the remainder is 4. When N is divided by 3, the remainder is 1.

What is N?

What is the next term in the sequence: 3, 4, 7, 11, 18, ...?

A jumper originally priced at 80 dollars is on sale with a 25% discount. What is the sale price of the jumper?

A project begins on a Wednesday and takes 24 full days to complete. On which day of the week does the project end?

A survey of 200 students asked for their favourite sport. The results are shown in the pie chart. How many more students chose Soccer than Tennis?

A tap fills a 60-litre tub in 5 minutes. What is the flow rate of the tap in litres per hour?

In a bag, the ratio of red marbles to blue marbles is 3:5. The ratio of blue marbles to green marbles is 2:3. If there are 30 green marbles, what is the total number of marbles in the bag?

Consider the sequence: 5, 8, 13, 12, 21, 16, ... What is the 8th term in this sequence?

A library has a collection of books. One-third are fiction. Of the remaining books, one-quarter are non-fiction. The rest are reference books. If there are 240 reference books, how many books are in the library in total?

The chart shows the number of cars sold by three dealers in 2022 and 2023. Which dealer had the greatest percentage increase in sales from 2022 to 2023?

A whole number $N$ is between 50 and 100. When $N$ is divided by 5, the remainder is 3. When $N$ is divided by 6, the remainder is 4. When $N$ is divided by 4, the remainder is 2. What is the value of $N$?

Let $x$ be the number of prime numbers between 10 and 30. Let $y$ be the number of multiples of 3 between 10 and 30, inclusive of 30. Which of the following statements is true?

A rectangular field has a perimeter of 90 metres. Its length and width are whole numbers, and its length is more than double its width. What is the largest possible area of the field in square metres?

The average score of four tests is 85. A student wants to raise their average score to exactly 87 after taking a fifth test. What score must they get on the fifth test?

A sequence is generated by the rule: 'double the previous term and subtract 3'. The fourth term of the sequence is 29. What is the first term?

The chart shows the average monthly rainfall for two cities over four months. What is the absolute difference between the total rainfall for the four months in City A and the total rainfall for the four months in City B?

Four friends, Ali, Ben, Chloe, and Dan, are standing in a line from left to right.

1. Ali is not last.
2. Chloe is directly between Ben and Dan.
3. Dan is somewhere to the right of Ali. Who must be first in line (furthest to the left)?

An item's price is increased by 20%. The new price is then decreased by 20%. If the final price is 192 dollars, what was the original price?

What is the next number in this sequence: 2, 5, 14, 41, 122, ...?

Machine A can sort 1000 letters in 30 minutes. Machine B can sort 1000 letters in 60 minutes. If both machines work together, how many minutes will it take them to sort 1000 letters?

A scatter plot's line of best fit is given by the equation $S = 5H + 60$, where $S$ is the test score and $H$ is the hours studied. Two students, Peta and Quentin, study for a combined total of 10 hours a week. Peta studies for more hours than Quentin. Their predicted scores differ by 20. How many hours a week does Quentin study?

The first five terms of a sequence are 3, 4, 7, 11, 18, ... and the sequence continues by following the same rule. What is the first term in the sequence to be greater than 100?

A bicycle's price is reduced by 20%. During a special sale, a further 10% discount is applied to the reduced price. The final sale price is 360 dollars. What was the original price of the bicycle?

The bar chart shows the number of sandwiches sold by a cafe from Monday to Friday. The number of sandwiches sold on Friday was what percentage greater than the average number of sandwiches sold per day over the entire five-day period?

Two trains depart from stations A and B, which are 450 km apart, at the same time and travel towards each other on parallel tracks. The train from A travels at a constant speed of 80 km/h. The train from B travels at a constant speed of 100 km/h. How far from station A will the trains pass each other?

A four-digit number, N, has the following properties:

• All its digits are different odd digits.
• The sum of its digits is 24.
• The thousands digit is the smallest digit in the number.
• The number is a multiple of 5.
• The tens digit is greater than the hundreds digit.

What is the number N?

In a bag, the ratio of red marbles to blue marbles is 3:5. After 12 red marbles are added to the bag, the ratio of red marbles to blue marbles becomes 3:4. How many blue marbles are in the bag?

The graph shows the populations of Northville and Southtown. Assuming the population trends shown between 2010 and 2020 for both towns continue at the same constant rates, in which year will Northville's population be 3000 greater than Southtown's population?

An orchard has a number of apple trees. On Monday, $\frac{1}{4}$ of the apples are picked. On Tuesday, $\frac{1}{3}$ of the remaining apples are picked. After Tuesday, there are 240 apples left on the trees. How many apples were on the trees initially?

The pie chart shows a council's 2.4 million dollars annual budget. Next year, the total budget will increase by 5%. The funding for Roads will increase by 10% from its current dollar amount, and Admin funding will decrease by 20% from its current dollar amount. The percentage allocation for Parks and Libraries will remain the same relative to the new total budget. What will be the new budget for Services?

The scatter plot shows the interior angle for several regular polygons. From the plot, we can see the interior angles for a square (4 sides) and a hexagon (6 sides). The hexagon's interior angle is exactly halfway between the square's interior angle and the interior angle of another regular polygon not shown in the graph. How many sides does this other polygon have?