CTJan27 Online JMSS - Numerical Reasoning 27052026

A sequence is defined by the rule: the next term is the sum of the digits of the square of the previous term. If the first term is 13, what is the 2025th term?

Two identical candles, A and B, are lit simultaneously. Candle A is designed to burn completely in 6 hours. Candle B is designed to burn completely in 9 hours. After how many hours will the height of Candle B be exactly double the height of Candle A?

A table shows the percentage change in the number of users for four different social media apps over three consecutive years.

If all four apps started with the same number of users at the beginning of Year 1, which app had the most users at the end of Year 3?

A rectangular garden has a perimeter of 52 metres. The area of the garden is 168 square metres. If the length of the garden is $L$ metres and the width is $W$ metres, with $L > W$, what is the value of $L - W$?

A shopkeeper increases the price of an item by 50%. Due to low sales, she then offers a discount on the new price. After the discount, the final price is 10% lower than the original price. What was the percentage discount offered?

A digital clock displays time in HH:MM format (from 00:00 to 23:59). How many minutes in a 24-hour period contain at least one digit '2' and at least one digit '5'?

Consider the sequence: 4, 7, 13, 25, 49, ... The terms are generated by a rule. What is the next term in the sequence?

A sum of money is invested at a simple interest rate of 5% per annum. After 4 years, the same sum of money is also invested in a second account at a simple interest rate of 3% per annum. The total interest earned from both investments after 8 years from the initial investment is 1040 dollars. What was the initial sum of money invested in each account?

A cube has its six faces labelled with six different positive integers. The sum of the numbers on any two opposite faces is always 20. The numbers on three faces that meet at one corner are given, but this information is not needed to find the sum of all integers on the cube. What is the sum of all six integers on the cube's faces?

A line graph shows the population of two cities, Metroville and Centropolis, over a 50-year period. In 1970, Metroville's population was 500,000 and Centropolis's was 800,000. Metroville's population grew linearly, reaching 1,250,000 in 2020. Centropolis's population also grew linearly, and its population in 2000 was equal to Metroville's population in 1980. In what year were the populations of the two cities equal?

The five-digit number $32A5B$ is divisible by 36. Given that $A$ and $B$ are distinct single digits and $A > B$, what is the value of $A - B$?

In a school, the ratio of boys to girls was 5:4. After 30 more boys and 30 more girls joined the school, the new ratio of boys to girls became 11:9. How many students were there in the school originally?

The table below shows the distribution of coloured marbles in a bag.

Some red marbles are removed from the bag. As a result, the percentage of green marbles in the bag increases to 50%. What percentage of the red marbles were removed?

If $x^2 - y^2 = 48$ and $x - y = 3$, what is the value of $x^2 + y^2$?

A sequence of figures is made of dots. Figure 1 has 1 dot. Figure 2 has 5 dots. Figure 3 has 13 dots. Figure 4 has 25 dots. The pattern continues. How many dots are in Figure 10?

Alex can paint a fence in 10 hours. Beatrice can paint the same fence in 12 hours. They start working together. After 2 hours, Beatrice leaves. How many more hours will it take Alex to finish painting the fence?

In a class of 100 students, 60 study Physics, 55 study Chemistry, and 30 study neither. How many students study both Physics and Chemistry?

A square of side length 8 cm has a circle inscribed within it, touching all four sides. A smaller square is then inscribed within the circle, with its vertices on the circumference. What is the area of the smaller square?

The average score of a class of 20 students on a test was 75. The average score of the 12 boys in the class was 72. What was the average score of the girls in the class?

A courier must deliver parcels to three locations A, B, and C. The travel times (in minutes) between the depot (D) and the locations are: D-A is 10, D-B is 12, D-C is 20. Travel times between locations are: A-B is 15, B-C is 18, A-C is 25. The courier must start at the depot, visit all three locations exactly once, and return to the depot. What is the shortest possible total travel time for the entire trip?

A sequence is defined by the recursive rule $T_{n+1} = 1 - \frac{1}{T_n}$. If the first term $T_1 = 3$, what is the value of the 2025th term, $T_{2025}$?

Alloy A contains copper and zinc in a ratio of $3:4$ by mass. Alloy B contains copper and zinc in a ratio of $5:2$ by mass. A new alloy, C, is created by mixing Alloy A and Alloy B in a mass ratio of $2:3$. What is the ratio of copper to zinc in Alloy C?

An investment portfolio's value increases by 20% in the first year. In the second year, its value decreases by 25%. In the third year, its value increases by 10%. What is the equivalent single percentage change in the portfolio's value over the entire three-year period?

A city's quarterly water billing is based on usage tariffs and a fixed charge, as shown below.

Metroville Tariffs:

• Fixed Charge: 80 dollars
• Band 1 (0-50 kL): 2.50 dollars per kL
• Band 2 (>50 kL): 4.00 dollars per kL

Coastburg Tariffs:

• Fixed Charge: 95 dollars
• Band 1 (0-40 kL): 2.80 dollars per kL
• Band 2 (>40 kL): 3.50 dollars per kL

Family A lives in Metroville and used 65 kL of water. Family B lives in Coastburg and used 70 kL. What is the positive difference in their quarterly water bills?

Two new mathematical operations are defined as: $a \oplus b = \frac{a+b}{a-b}$ $x \otimes y = x(y+1)$ What is the value of $(6 \oplus 2) \otimes (8 \oplus 4)$?

Two runners, A and B, start at the same point on a 400-metre circular track and run in opposite directions. Runner A's speed is 5 m/s and Runner B's speed is 3 m/s. How many times will they pass each other in the time it takes Runner A to complete exactly 10 laps?

A three-digit number has the following properties:

1. The sum of its digits is 15.
2. It is a multiple of 5.
3. The hundreds digit is one less than the tens digit.
4. All three digits are distinct.

What is the product of the digits of this number?

The digits 1, 2, 3, 4, and 5 are placed into the five cells of the cross shape below, with one digit per cell.

[Diagram described: A 5-cell cross shape with one central cell, and one cell each to the top, bottom, left, and right of the centre.]

The following rules apply:

• The sum of the three numbers in the vertical column is 10.
• The sum of the three numbers in the horizontal row is 8.
• The number in the top cell is greater than the number in the bottom cell.

What number is in the central cell?

A positive two-digit integer, $N$, has two properties. When $N$ is divided by the sum of its digits, the quotient is 7 with a remainder of 3. When the digits of $N$ are reversed, the new number is 18 less than $N$. What is the value of $N$?

Which of the following is the best approximation for the value of the expression below?

$\frac{\sqrt{1598} \times 2.05^3}{0.49 \times \sqrt{80}}$

A rectangular water tank has a volume of 5.4 cubic metres. The tank is initially $\frac{1}{3}$ full of water. Water flows into the tank at a constant rate of 150 millilitres per second. How long will it take to fill the remaining part of the tank? ($1 \text{ m}^3 = 1,000,000 \text{ mL}$)

A retailer buys an appliance for 400 dollars. She marks up the price by 50% to set the 'marked price'. She then offers a 20% discount on the marked price during a sale. A 10% Goods and Services Tax (GST) is calculated on the discounted price and added to the final amount the customer pays. What is the retailer's actual profit in dollars from the sale?

Given that $y$ and $z$ are positive integers, and the values $x$, $y$, and $z$ are related by the equations: $x = 1 - \frac{1}{y}$ and $y = 1 + \frac{1}{z}$. Which of the following statements must be true?

The average age of a group of 5 friends is 28 years. When a sixth friend, Chloe, joins the group, the average age increases to 29.5 years. Later, another person, David, whose age is 6 years less than Chloe's, joins the group and the oldest of the original friends, Peter, leaves. The average age of this new group of 6 people becomes 28 years. What is Peter's age?

If $p$ and $q$ are positive integers such that $p^2 - q^2 = 81$, what is the maximum possible value of $p+q$?

A pie chart shows the distribution of a city council's 36 million dollar annual budget. The allocations are: Parks 15%, Roads 30%, Health Services 25%, Administration 10%, and Community Projects the remainder. The following year, the total budget remains the same, but the budget for Roads is decreased by 10%, and this exact amount of money is reallocated to Community Projects. What is the new angle on the pie chart for Community Projects, to the nearest degree? (A circle has 360 degrees).

A sequence is generated using the following rule: the next term is the sum of the digits of the square of the previous term. If the first term is 13, what is the 100th term of the sequence?

At a school fete, the ratio of adults to children was initially 5:8. After 30 adults and 30 children left, the new ratio of adults to children became 4:7. How many people (adults and children combined) were at the fete initially?

A library contains only fiction and non-fiction books. 60% of the books are fiction. 75% of the fiction books are paperbacks. The number of non-fiction paperbacks is exactly one-third the number of fiction hardcovers. What percentage of the entire library collection consists of paperbacks?

A digital clock displays time in a 24-hour HH:MM format (from 00:00 to 23:59). For how many minutes during a full day does the clock's display show at least one digit '7'?

A sequence is defined by the rule $T_1 = 2$, $T_2 = 3$ and $T_n = (T_{n-1} \times T_{n-2}) - 1$ for $n > 2$. What is the value of the sixth term, $T_6$?

Two containers, P and Q, hold a chemical solution. Initially, the ratio of the volume of the solution in P to that in Q is $5:3$. First, 16 litres of the solution are poured from P to Q. Then, 10 litres of solution are poured from Q back to P. After these transfers, the ratio of the volume in P to Q is $7:5$. What was the initial total volume of the solution in both containers combined?

A full water tank loses $\frac{1}{5}$ of its contents due to evaporation on Day 1. On Day 2, it loses 25% of the remaining water. On Day 3, it is refilled with an amount of water equivalent to 50% of its current volume. The tank now contains 630 litres. What is the full capacity of the tank?

In the number pyramid shown below, the number on any brick is the product of the numbers on the two bricks directly beneath it. All bricks contain positive integers. What is the value of C?

[Diagram Description: A pyramid with one brick on top, two in the middle, and three at the bottom. The top brick has the value 384. The bottom row has bricks with values 3, C, and 2 from left to right.]

Two new operations are defined for positive numbers $a$ and $b$ as follows: $a \oplus b = a(a-b)$ $a \otimes b = \sqrt{a+b}$

Given that $x$ is a positive integer, find the value of $x$ that satisfies the equation: $5 \oplus (x \otimes 7) = 10$.

A courier travels from Town A to Town B at a constant speed of 60 km/h and immediately returns along the same route to Town A at a constant speed of 90 km/h. A second courier also travels from Town A to Town B and back, starting and finishing at the exact same times as the first courier. The second courier maintains the same constant speed for the entire journey. What was the second courier's constant speed?

Five boxes are numbered 1 to 5. Each box contains a different number of coins, chosen from the set {15, 20, 25, 30, 35}. The following conditions are met:

1. For exactly three of the boxes, the box number and the number of coins it contains have the same parity (both are even or both are odd).
2. The total number of coins in the odd-numbered boxes (1, 3, and 5) is exactly 60.
3. The number of coins in Box 4 is double the number of coins in Box 1.

How many coins are in Box 2?

A retailer buys an item for 200 dollars. They set a marked price to achieve a 60% profit on their cost price. A customer purchases the item during a sale where a 10% discount is applied to the marked price. Finally, a 10% Goods and Services Tax (GST) is calculated on and added to the discounted sale price. What is the final amount the customer pays?

The mean score of a class of 29 students on a test was 78.0. Later, it was found that one student's score, which was incorrectly recorded as 53, should have been 82. After this correction was made, the highest-scoring student, who now has a score of 95, leaves the class. What is the mean score of the remaining students in the class, correct to one decimal place?

A rectangular swimming pool is 12.5 metres long, 6 metres wide, and has a uniform depth of 1.6 metres. The pool is to be filled using a hose with a flow rate of 80 litres per minute. How long will it take to fill the pool to 90% of its total capacity? Express your answer in hours and minutes.