D1 – Y5 – MATH – TT

Amy took a two-part test yesterday and she correctly answered 50 percent of all the questions in the test.

The first part of the test had 180 questions, of which she correctly answered 30 percent, and the second part of the test had 150 questions.

How many percent of the questions in the second part of the test did she correctly answer?

A group of four friends, Fred, George, Miriam, and Samantha, agreed to share the cost of renting a car.

Fred’s share was $9 more than 1/6 of the cost of renting the car, George’s share was $8 less than 2/5 of the cost of renting the car, Miriam’s share was $1 more than 1/12 of the cost of renting the car, and Samantha’s share was $40.

How much did it cost them to rent the car?

A jar only contains red, yellow, blue, and green marbles.

There is one-third as many red marbles as yellow marbles in the jar and one-half as many blue marbles as red marbles.

If there are as many green marbles as blue marbles in the jar, what percent of the marbles in the jar are yellow?

Two honeybees left the beehive at the same time and flew in opposite directions.

One honeybee flew at a rate of 25 metres per hour and the other honeybee flew at a rate of 30 metres per hour.

How much time did it take before the distance between the two honeybees were 110 metres?

When the students in Miss Anne’s class are divided into equal groups of 7 students, 5 students will be left out. 

When the students in Miss Anne’s class are divided into equal groups of 13 students, 6 students will be left out.

If there are less than 200 students in Miss Anne’s class, what is the greatest possible number of students in her class?

Twenty-four identical machines, each working at a constant rate, can make 10 items in 5 minutes. 

How many additional such machines are needed to make 20 items in 8 minutes?

In triangle PQR below, the length of QR is equal to the length of RS.

The degree measure of angle QSR is 70 degrees.

What is the degree measure of angle QPR?

Frank is twice as old as Jeffrey and three times as old as Quinn. 

If the sum of the ages of Frank, Jeffrey, and Quin equals 33, how old is the youngest of the three?

Two sides of a triangle have lengths of 16 centimetres and 19 centimetres. 

Which of the following could be the perimeter of the triangle?

I. 50 centimetres

II. 60 centimetres

III. 70 centimetres

In triangle PQR below, the lengths of OP, OQ, and OR are all equal.

What is the degree measure of angle ORP?

Brian bought a chair at a factory price of $90. 

He then sold the chair at a 10 percent discount off the selling price.

If Brian made a profit that is equivalent to 20 percent of the chair’s factory price, what was the selling price of the chair without the discount?

An inlet pipe fills an empty water tank at a rate of 1 litre every 30 seconds. 

If the water tank has a capacity of 512 litres, how much time will it take the inlet pipe to fill the water tank?

The lengths of the sides of the two rectangles below have integer values only (that is, the lengths of the sides are all whole numbers).

The ratio of the perimeter of the orange rectangle to the perimeter of the green rectangle is 8 to 7.

If the area of the orange rectangle and the area of the green rectangle are both equal to 48 square centimetres, what is the perimeter of the orange rectangle?

A bridge is 800 metres long. 

At what constant speed must Jeff walk to cross the bridge in 12 minutes?

In the figure below, the diagonals, AC and BD, of trapezium ABCD intersects at O.

The ratio of the length of OD to the length of BD is 2 to 5.

What is the ratio of the length of AD to the length of BC?

Ben and Dave are walking in the same direction on the same street. 

Ben is walking at a rate of 130 metres per hour while Dave is walking at a rate of 100 metres per hour.

At exactly 8:00 AM, Ben is 10 metres behind Dave.

What is the distance between Ben and Dave at exactly 11:00 AM?

A vendor reduced the current price of the refrigerator by 30 percent, and then further reduced the resulting price by 40 percent. 

The two reductions in the current price of the refrigerator are equal to which single reduction percentage?

The half-life of a certain radioactive substance is 3 hours, that is, if you start with 10 grams of the substance, you will have 5 grams remaining 3 hours later. 

If a chemist starts with a 40-gram sample of the radioactive substance, how much remains after 9 hours?

Carl bought an item online with a 10 percent discount off the regular price and paid a $12 shipping fee for the item.

Gene also bought the same item online at the same regular price but with a 15 percent discount and paid a $15 shipping fee for the item.

If both Carl and Gene paid the same net amount, including the discount and the shipping fee, for the item, what was the regular price of the item?

In the figure above, what is the value of ?

Solution A is 60 percent salt by volume while solution B is 20 percent salt by volume.

How many litres of solution A must be added to 50 litres of solution B to get a mixture that is 40 percent salt by volume?

A caterpillar is trying to crawl to the top of the branch that is 14 centimetres high.

The caterpillar crawls 2 centimetres up in the first two minutes but slides down 1 centimeter in every alternate minute.

If the caterpillar continues its progress this way, how long will it take the caterpillar to reach the top of the branch?

The recipe calls for 1 gram of pepper for every 800 grams of pork.

How many grams of pepper will you need if you use 3 kilograms of pork?

A bag contains an unknown number of candies.

If Michelle splits all the candies in the bag into equal groups of 35 candies, there will be 3 candies left over.

How many candies will be left over if Michelle splits them into equal groups of 7 candies?

Working alone at constant rates, John can finish the work in 10 hours, Pete can finish the same work in 12 hours, and Steve can finish the same work in 15 hours.

What is the ratio of the maximum and minimum time taken to finish the work if at least one person will work every hour?

A jar contains red and blue marbles only.

Half the number of red marbles in the jar is equal to one-fourth of the total number of marbles in the jar.

One-third of the number of blue marbles in the jar is equal to one-seventh of the total number of marbles in the jar.

What is the ratio of the number of red marbles in the jar to the number of blue marbles in the jar?

If a dragonfly is flying at a speed of 10 kilometres per hour, how many metres does it fly in 30 seconds? (1 kilometre = 1 000 metres)

The old and the new machine at the factory each work at constant rates.

The old machine can produce 1 000 widgets in 4 hours while the new machine can produce the same number of widgets in half the time.

What fraction of 1 000 widgets can the two machines make if both worked simultaneously for 40 minutes?

Margaret is three times as old as Sheryl and Sheryl is twice as old as Victoria.

If Margaret is Y years old, what is the average (arithmetic mean) age of the three women in terms of Y?

The store sells pens for $1.80 each and notepads for $13.90 each.

Emilia spent a total of $26.50 to buy at least one pen and at least one notepad from the store.

How many pens did Emilia buy from the store?

Peter, working at a constant rate, made 300 birdhouses in 30 days.

He spent the first 80 percent of the time making the first 20 percent of the birdhouses and made the rest of the birdhouses in the remaining 20 percent of the time. 

How many birdhouses did Peter make in the last two weeks?

Andrew, David, and Robert are all software programmers.

Andrew, working alone at a constant rate, can write 1 200 lines of a code in 3 hours.

David, working alone at a constant rate, can write 1 200 lines of a code in 2 hours.

Robert, working alone at a constant rate, can write 1 200 lines of a code in 6 hours.

If the three of them worked together at their respective constant rates, how many hours will it take them to write 3 600 lines of the code?

A pipe is filling bottles with oil at a rate of 80 millilitres per second.

Each bottle has a capacity of 2.4 litres.

At this rate, how many minutes will it take the pipe to fill 120 bottles?

A dog ran a distance of 100 metres at a constant speed.

Had the speed of the dog been 5 metres per hour faster, then it would have taken the dog one hour less to run that distance.

What was the original speed of the dog?

Ernie is currently 12 years younger than Bert.

Nine years from today, Bert will be twice as old as Ernie.

How old will Ernie be five years from today?