CTJan27 Online JMSS Numerical Reasoning

The first four terms are 3, 10, 21, 36. What is the next term in the sequence?

Consider the sequence: $2, -1, \frac{1}{2}, -\frac{1}{4}, ...$

What is the 7th term of this sequence?

A sequence follows a Fibonacci-like rule where each term is the sum of the two preceding terms. If the first term is 1 and the second term is 4, what is the 6th term of the sequence?

Find the next term in the following complex sequence: $2, 3, 4, 9, 8, 27, ...$

Calculate the product of $(4.5 \times 10^{-4})$ and $(3.0 \times 10^6)$. Express the result in standard scientific notation.

A manufacturing plant operates 15 identical machines for an 8-hour shift. Each machine is capable of producing 20 widgets per hour. If $\frac{2}{5}$ of the total widgets produced are designated for export, and of those exported widgets, $\frac{1}{4}$ are shipped to Europe, how many widgets are shipped to Europe in a single shift?

Five friends, three boys and two girls, are lining up for a photograph. If they arrange themselves in a random order, what is the probability that the two girls are standing at the ends of the line?

A sequence is generated by the rule: 'Double the previous term and subtract 3'. If the fourth term is 35, what is the first term?

In a school library, 40% of the books are fiction. Of the remaining books, 25% are reference books. The rest of the books are non-fiction. If there are 180 non-fiction books, what is the total number of books in the library?

The ratio of red marbles to blue marbles in a bag is $3:5$. The ratio of blue marbles to green marbles is $2:3$. If there are 45 green marbles, how many red marbles are there?

A rectangular tank measuring 50 cm by 20 cm by 30 cm is partially filled with water to a height of 12 cm. An additional 6 litres of water is poured into the tank. What is the new height of the water in the tank? ($1$ litre = $1000$ cm$^3$)

Two cyclists, Anna and Ben, start 150 km apart and cycle towards each other on a straight road. Anna's average speed is 30 km/h and Ben's average speed is 20 km/h. How long will it take for them to meet?

Five friends are sitting in a row on a bench. Chloe is at the far left end. Noah is sitting next to Chloe. Liam is not at either end. Maya is sitting immediately to the right of Oscar. Which statement must be true?

The shape below is made of a square with side length 14 cm and a semi-circle attached to one side. What is the total area of the shape? (Use $\pi \approx \frac{22}{7}$)

Let $N$ be a positive integer. $N$ has exactly three positive factors, including 1 and $N$ itself. Which of the following statements about $N$ must be true?

A jacket originally priced at 200 dollars is discounted by 20%. A month later, the discounted price is increased by 20%. What is the final price of the jacket?

A number machine follows a two-step rule. An input of 3 gives an output of 13. An input of 5 gives an output of 21. What is the output for an input of 8?

The mean weight of five packages is 18 kg. After a sixth package is added, the mean weight of the six packages becomes 20 kg. What is the weight of the sixth package?

A solid object is made from identical 1 cm cubes. Its front view has three columns with heights:

1, 1, 3 Its right-side view has two columns with heights:

2, 3. What is the minimum number of cubes required to build the object?

A bag contains 6 red balls, 4 blue balls, and 5 yellow balls. If two balls are drawn from the bag at random without replacement, what is the probability that both balls are red?

A solution contains acid and water in the ratio $2:3$. If 20% of the solution is removed and replaced with pure water, what is the new ratio of acid to water in the solution?

Four identical machines working together at a constant rate can produce 300 widgets in 6 hours. If two machines break down after 3 hours, how many more hours will it take for the remaining two machines to complete the job?

The sum of five consecutive even integers is 220. What is the value of the largest of these integers?

A concert ticket is priced at 200 dollars. It is first discounted by 15%. A 10% Goods and Services Tax (GST) is then calculated on the discounted price. What is the final price of the ticket?

To create a specific shade of green paint, a painter mixes blue, yellow, and white paint in the ratio $2:5:1$. If the painter needs to make exactly 4 litres of this green paint, how many millilitres (mL) of yellow paint are required? (1 litre = 1000 mL)

A rectangle's length is 5 cm more than twice its width. If the perimeter of the rectangle is 94 cm, what is its area?

In a survey of 300 students, 60% were girls. Of the girls, 25% play a musical instrument. Of the boys, 50% play a musical instrument. What percentage of the total number of students play a musical instrument?

Five boxes, labelled P, Q, R, S, and T, each contain a different whole number of marbles from 10 to 14.

• The number of marbles in P is a prime number.
• S has exactly two more marbles than T.
• R has fewer marbles than S but more than T.
• Q has the maximum possible number of marbles.
• How many marbles are in box P?

A train travels at a constant speed of 108 km/h. A car starts at the same point and travels in the same direction at a constant speed of 25 m/s. How far apart will they be after 10 minutes?

Liam invests 8000 dollars in an account that pays 5% per annum simple interest. Anika makes a one-time purchase of an item for 8000 dollars and sells it 18 months later for 9000 dollars. Who made a greater profit, and by how much?

A rectangular fish tank with a base of 60 cm by 40 cm contains water to a height of 25 cm. A solid metal cube with side length 20 cm is fully submerged in the tank. What is the new height of the water in the tank?

Compare the following two quantities: Quantity A: The number that is 250% greater than 20. Quantity B: 80% of one-fifth of 400.

A rectangular field has sides in the ratio $4:7$. If the area of the field is 700 square metres, what is its perimeter?

One pipe can fill a tank in 3 hours. A second, larger pipe can fill the same tank in 2 hours. A drain can empty the full tank in 6 hours. If the tank is empty and both pipes are opened while the drain is also open, how long will it take to fill the tank?

If $k$ is a positive integer, which one of the following expressions must result in an odd integer?

A library shelf holds a collection of books. One-third of the books are fiction. Of the remaining books, one-quarter are non-fiction. The rest are reference books. If there are 24 reference books, how many fiction books are on the shelf?

Four friends, Amy, Ben, Chloe, and Dan, are sitting in a row of four seats. Chloe and Dan must sit next to each other. Amy refuses to sit at either end of the row. In how many different arrangements can they be seated?

A pattern exists in the grid of numbers below. Determine the pattern and find the number that should replace the question mark.

$\begin{array}{|c|c|c|c|} \hline 9 & 3 & 6 & 8 \\ \hline 2 & 7 & 4 & 2 \\ \hline 8 & 2 & 9 & 7 \\ \hline 1 & 6 & 6 & ? \\ \hline \end{array}$

A software engineer is developing a system to assign a 'Simplicity Score' to programming languages. The score, $S$, is determined by a hidden quadratic rule based on the number of letters, $N$, in the language's name, of the form $S(N) = aN^2 + bN + c$. Analyze the scores below to determine the rule and find the score for 'Javascript'.

• Ruby (4 letters): Score of 6
• Scala (5 letters): Score of 10
• Python (6 letters): Score of 16

What is the Simplicity Score for Javascript (10 letters)?

A clothing store applies a 30% discount to a jacket originally priced at 200 dollars. A week later, the store offers an additional 20% discount on the already discounted price. What is the final selling price of the jacket?

Three robotics club members, Alex, Ben, and Chloe, share a box of 240 components in the ratio $2:3:7$. Chloe decides to give a quarter of her components to Alex. How many components does Alex have now?

A new mathematical operation $\oplus$ is defined as $a \oplus b = a^2 - ab + 5$. What is the value of $(4 \oplus 3) \oplus 2$?

The perimeter of a rectangle is 62 cm. Its length is 5 cm more than twice its width. What is the area of the rectangle in square centimetres?

Consider the sequence: $3, 7, 13, 21, 31, ...$. If the pattern continues, what is the 9th term in this sequence?

In a survey of 300 athletes, 160 participate in track events, 130 participate in field events, and 50 participate in neither. How many athletes participate in both track and field events?

Five friends, P, Q, R, S, and T, are standing in a line. Q is between P and T. S is not first and is somewhere to the right of R. P is at one of the ends. R is directly next to P. Which of the following is a possible order of the friends from left to right?

In the diagram, ABC is an isosceles triangle with $AB = AC$ and $\angle BAC = 36^\circ$. Point D lies on AC, and the line segment BD bisects $\angle ABC$. What is the measure of $\angle BDC$?

A freight train is 600 metres long and travels at a constant speed. It takes 90 seconds from the moment the front of the train enters a 2.1 km tunnel to the moment the rear of the train leaves the tunnel. What is the speed of the train in km/h?

A tech gadget is bought for 400 dollars. The retailer marks up the price by 50% to set the initial selling price. Due to low demand, the retailer then discounts the initial selling price by 30%. What is the final profit as a percentage of the original cost price?