Day 2 Year 6 Math Trial Test

At least 15 percent of the students in Anastacia’s class dropped out before the end of the term.

The term’s drop-out rate for Cullen’s class was 20 percent greater than that of Anastacia’s class. 

If 120 students remained in the class of Cullen by the end of the term, which of the following could be the number of students in Cullen’s class at the start of the term?

   I. 147 students

  II. 162 students

 III. 185 students

The ratio of filling rates of pipes A and B is 3:2, respectively.

If the two pipes together can fill 5/6 of a tank in 20 minutes, how many minutes will pipe B alone take to fill the same tank?

The number of candidates rejected in a certain admission process was four times greater than the number of candidates accepted.

Which of the following could be the total number of candidates that applied for this admission process?

One morning, each member of Homer’s family drank an 8-litre mixture of coffee with milk.

The amounts of coffee and milk varied from cup to cup but were never zero. 

If Homer drank a quarter of the total amount of milk and a sixth of the total amount of coffee, how many people are in the family?

On Monday, Elmo puts a bag of bird seeds, 25 percent of which are millet, into a bird feeder.

On each successive day, he adds another bag of the same mix of seeds without removing any seeds that are left, and each day the birds eat only 25 percent of the millet in the feeder, but they eat all of the other seeds. 

On which day, just after Elmo has placed the initial bag of seeds, will the birds find that more than half the seeds in the feeder are millet?

The ratio of men to women employed at ACME Corporation is m to w, and the ratio of employees with a bachelor’s degree to employees with a master’s degree is b to m.

There are 75 men and 85 employees with master’s degrees among the 150 employees at ACME Corporation. 

If all employees at ACME Corporation have a degree, which of the following could be the number of women with bachelor’s degrees?

The Book Club, with x members, has between 32 and 101 members.

The members of the club can be separated into groups of which all but one group, which will have 3 members, will have 4 members. 

The members can also be separated into groups so that all groups but one group, which will have 1 member, will have 5 members. 

Which of the following could be the value of 3x?

When viewed through a microscope, objects appear 120 times larger.

If an amoeba appears to have a length of 49.2 centimetres, what is the actual length of the amoeba?

By looking at a rectangular box, a carpenter estimates that the length of the box is between 2 to 2.1 metres, inclusive, the width is between 1 to 1.1 metres, inclusive, and the height is between 2 to 2.1 centimetres, inclusive.

The actual length, width, and height of the box do indeed fall within the respective ranges estimated by the carpenter.

Which of the following is the closest to the maximum possible magnitude of the percentage error that the carpenter can make in calculating the volume of the rectangular box?

The daily average production of widgets in a factory is given by 5n + 20, where n is the number of workers.

In the first d days, 500 widgets are produced, and then 5 workers are added to the team. 

After another d days, the cumulative total production is 1 250 widgets. 

How many workers were part of the latter production run?

A ticket to a school play costs d dollars, where d is a whole number.

A group of boys buys tickets costing a total of $48, and a group of girls buys tickets costing a total of $64. 

How many values for d are possible?

Harry the Hare and Jack the Jackal are running a race.

Three leaps of Harry are equal to four leaps of Jack, and for every six leaps that Harry makes, Jack makes 5 leaps. 

What is the ratio of Harry’s speed to Jack’s speed?

If N represents a single digit in the four-digit number 1 7N6, how many different values of N are there such that 1 7N6 is divisible by 8?

Since Travis started earning $3 500 annually, he donates 2.5 percent of that amount quarterly to the local charity.

If Travis had donated $525 so far, for how many years now has Travis been earning $3 500 annually?

A group of 630 children is arranged in rows for a group photograph session.

Each row contains three fewer children than the row in front of it. 

What number of rows is not possible?

Dexter scored 40 percent on a test, and after review, even though his score increased by 50 percent, he failed the test by 35 points.

Had his post-review score increased by 20 percent, he would have 7 points more than the passing score. 

What score is needed to pass the test?

Of 128 boxes of oranges, each box contains at least 120 and at most 144 oranges.

What is the least possible number of boxes containing the same number of oranges?

A rectangular sheet of construction paper 2 metres wide was cut lengthwise into two smaller rectangular pieces.

The shorter piece was one-third the length of the longer of the two new pieces and had an area of 12 square metres. 

What was the length of the original sheet of construction paper before cutting?

A wholesaler bought walnuts and peanuts, at which the price of walnuts per kilogram was thrice that of the price of peanuts per kilogram.

He then sold 8 kilograms of peanuts at a profit of 10 percent and 16 kilograms of walnuts at a profit of 20 percent to a shopkeeper. 

However, the shopkeeper lost 5 kilograms of walnuts and 3 kilograms of peanuts in transit and decided to mix the remaining nuts and sold the mixture at $166 per kilogram, making an overall profit of 25 percent. 

At what price did the wholesaler buy the walnuts?

In a certain science experiment, a 30-centimetre line is marked at each centimetre, and an insect is placed at every centimetre.

Nine frogs are trained to jump a constant distance, with the first one jumping 2 centimetres in every leap, the second one jumping 3 centimetres, and so on until the ninth one jumping 10 centimetres in every leap.

The frogs then eat any insect that is available at the spot they land. 

If all of them start from the start line and finish the entire 30 centimetres, how many insects were still left on the line after the experiment?

One machine produces only nuts at the rate of 100 nuts per minute and needs to be cleaned for 5 minutes after production of every 1 000 nuts.

Another machine produces only bolts at the rate of 75 bolts per minute and needs to be cleaned for 10 minutes after production of every 1 500 bolts. 

If both machines start production at the same time, what is the least duration required for producing 9 000 pairs of nuts and bolts?

What is the highest positive integer less than 1 800 that is divisible by each of the numbers 2, 3, 4, 5, 6, and 7?

A box only contains 5-gram balls, 10-gram balls, and 25-gram balls.

The number of 25-gram balls is twice the number of 10-gram balls, and the number of 10-gram balls is twice the number of 5-gram balls.

What is the ratio of the combined mass of the 25-gram balls to the combined mass of the 5-gram balls in the box?

In the figure below, ABDE is a rectangle, and CDEF is a square.

Note: Figure not drawn to scale.

If the area of CDEF is half the area of ABDE, what is the ratio of ED to AF?

A vendor purchased five tables and seven chairs for $5 850.

The vendor then sold the tables at a profit of 10 percent and the chairs at a profit of 16 percent. 

If the vendor’s overall gain was $711, what total price did the vendor pay for one table and one chair?

Old MacDonald has two plots of land of different sizes, and each plot of land is planted with corn and wheat.

In one plot, the ratio of corn to wheat by land area is 7 to 3, and in the other plot, the ratio of corn to wheat by land area is 11 to 4. 

If the ratio of corn to wheat by land area of the two plots combined is 24 to 9, what is the ratio of the total area of the smaller plot to the total area of the larger plot?

After distributing the candies equally among 25 children, 8 candies were left.

Had the number of children been 28, there would have been 22 candies left after equally distributing. 

Which of the following could be the total number of candies?

A cube of side length 24 metres is cut into 512 smaller cubes of equal dimensions.

What is the ratio of the combined surface area of the smaller cubes to the total surface area of the original cube?

Amazoom’s website attracts 448 000 users per day.

The users only visit the website between 8:00 AM and 10:00 PM and do so evenly between these time points. 

Before noon, two percent of users buy something from the website, and after noon, only one percent of users buy something from the website. 

How many users buy something from the website between 11:30 AM and 12:30 PM?

P and Q represent the single digits of the four-digit number 7 PQ8.

If 7 PQ8 is divisible by 12 and P = Q + 1, which of the following could be the value of P + Q?

A passenger train has 10 compartments, which carries an average (arithmetic mean) 20 passengers per compartment.

At least 12 passengers were staying in each compartment, and no compartment had an equal number of passengers. 

What was the greatest possible number of passengers that could stay in any compartment?

A factory uses two machines to fill an order for 3 360 batteries.

The first machine can produce 72 batteries every 24 minutes, and it can run for four hours before it must undergo a 3-hour recalibration procedure. 

The second machine can produce 48 batteries every 12 minutes, and it can run for four hours before it must undergo a 2-hour recalibration procedure. 

If both machines begin working at the same time and are working whenever they are not being recalibrated, how many of the 3 360 batteries are made by the second machine?

A drought decreased the amount of water in Bellwood’s water reservoir from 118 million litres to 96 million litres.

If the water reservoir were at 79 percent of total capacity before the drought began, approximately how many million litres were the reservoir below total capacity after the drought?

The supermarket sells small, medium, and large bottles of olive oil.

A large bottle costs $2.20, which is 25 percent higher than that of a medium bottle, while the cost of a small bottle is 75 percent of the cost of a medium bottle.

If the supermarket sells twice as many small bottles as medium bottles and four times as many medium bottles as large bottles, with a total revenue of $99, how many bottles of olive oil did the supermarket sell?

Equal volumes of water were poured into three empty containers, making one container 1/6 full, one container 1/8 full, and one container 1/12 full.

If half of the water from each of the two smallest containers is then poured into the largest container, what fraction of the largest container will be filled with water?