Day 3 Y5 Math Trial Test

Ruby took seven tests last week and had an average (arithmetic mean) score of 80 points per test.

If she scored 75, 69, 82, 90, and 72 points in the first five of the seven tests, what was her average score in the last two tests?

Katrina bought a microwave oven for $120.

If the total price she paid for the microwave oven was $133.50, which included the price of the microwave oven plus sales tax, which of the following is the best estimate of how many percent was the sales tax?

Roy placed a bowl of water under the hot, burning sun.

After the first hour, 3/4 of the water in the bowl had evaporated.

After the second hour, 3/4 of the remaining water in the bowl had evaporated.

If after two hours, only 0.5 litres of water was left in the bowl, how many litres of water was originally in the bowl?

Douglas has a piece of plywood that measures 8.5 metres by 10 metres.

He painted a black rectangle on the centre of the plywood, leaving a 1.5-metre margin around all four sides. 

What was the area of the rectangle that Douglas painted?

An insurance agent received a commission of 3 percent of the value of each of the first 10 insurance plans that he sold and 4 percent of the value of each insurance plan that he sold after the first 10.

If the value of each insurance plan was $100 000 and the insurance agent received a $42 000 commission, how many insurance plans did he sell?

A company employs a total of 1 500 workers and half of the workers employed by the company are aged 25 to 40 years old.

Next year, the number of workers aged 25 to 40 years old will increase by 1/3.

After this change, what percentage of the total 1 500 workers will the 25 to 40 years old represent?

Blue Skies Corporation’s total export in 2016 was $1.44 billion.

If Blue Skies Corporation’s exports in the first two months of 2017 were $288 million and continued to export at the same rate for the rest of the year, by how much would Blue Skies Corporation’s 2017 exports exceed those of 2016?

A factory packs the microchips it produced in boxes that measure 15 centimetres by 12 centimetres by 10 centimetres.

The boxes are stored in a warehouse that occupy 1.08 million cubic centimetres of space.

If the factory pays $0.25 per box per month for the storage of the boxes in the warehouse, how much does the factory pay each month for the storage space?

The speed of the turbines in the electric power plant was increased by 30 percent and then increased this speed again by 10 percent.

What percent of the original speed is the total increase in speed?

Four friends, Angela, Beth, Carol, and Diane, went on a cruise trip.

Beth spent $400 more than Carol on the trip, Diane spent $1 200 less than Angela on the trip, and Angela spent $400 more than Beth on the trip.

How many more dollars did Carol spend on the trip than Diane?

What is 150 percent of  of 720?

A box contains 12 000 solid-coloured balls.

One-third of the balls in the box were red, 1/4 of the remaining balls were green, and the rest were blue.

How many balls in the box were blue?

Jake invested $1 000 on bonds.

He invested part of the money on bonds that earned 5 percent annual interest and the rest on bonds that earned 6 percent annual interest.

If his total investment with interest at the end of one year was $1 053, how much did he invest on bonds that earned 5 percent annual interest?

A carpenter cuts a piece of wood into three smaller pieces in the ratio of 2:3:5.

If the shortest of the three smaller pieces is 30 metres long, what was the length of the wood before it was cut?

A prime property in the suburbs was priced at $12 000 in 2010.

In 2020, the price had increased to $18 000. 

By how many percent did the price of the property increase from 2010 to 2020?

Jenny made a vanilla butternut frosting composed of only three ingredients.

By mass, 1/3 of the frosting is butter, 3/5 is milk, and the remaining 12 grams is sugar.

What is the mass of the frosting that Jenny made?

Six bowls, labelled from 1 to 6, are filled with gumballs.

Ten students took turns picking gumballs from each bowl such that the number of gumballs picked by each student from each bowl is equal to the number marked on the bowl.

If the 6 bowls contain a total of 1 000 gumballs and the bowls were filled in such a way that none of the bowls became empty in the process, how many gumballs were left in the end?

A travel company will rent a boat for $8 000 going on a cruise to the Caribbean.

So far, 18 tourists have signed up for the cruise.

If the travel company charges $300 per tourist joining the cruise, how many more tourists must sign up for the cruise before the travel company can make any profit on the cruise?

A jeweller specializes in making gold and silver lockets.

He charges $650 for a gold locket and $325 for a silver locket.

If the jeweller made $15 925 in total from making gold and silver lockets last month, and he made five more gold lockets than silver lockets, what is the total number of gold and silver lockets the jeweller made last month?

Vince is three times as old as Axel, Jim is eight years younger than Vince, and Axel is seven years older than Leo.

If the sum of the ages of all four boys is 161, how old is Axel?

An appliance store marked up the price of a toaster by 40 percent and then offers a 15 percent discount on the marked price.

How many percent of profit does the appliance store make after the discount?

Last year a company spent 5 percent of their annual budget on advertisements.

This year, the annual budget of the company is 10 percent more than last year and they spent 8 percent of it on advertisements.

The amount spent on advertisement this year was what percent of the amount spent on advertisement last year?

Two bags of cement will be used on a construction project.

The combined mass of the two bags of cement is 100 kilograms.

If the smaller of the two bags is 5 kilograms less than half the mass of the larger bag, what is the mass of the smaller bag of cement?

A sales agent earns $10 per hour and a 15 percent commission for each sale he makes.

If he worked four 8-hour shifts this week and made an average of $40 of sales per hour, how much did the sales agent earn this week?

Josephine has 25 pairs of earrings.

If she loses 9 individual pieces of earrings, what is the greatest possible number of matching pairs she could have left?

A dog was 18 months old one year ago.

How many months old was the dog 4 months ago?

Twenty students, working together at a constant rate, can finish painting a house in 3 hours.

How many hours will it take 12 students, working at the same rate, to finish painting the same house?

A painter sold all his paintings for a total amount of $21 600.

If the painter made a profit of 8 percent of the cost on each painting, how much did it cost the painter to do all of his paintings?

A jar contains only black and white balls.

Ten percent of the balls in the jar are white and 90 percent of the rest have cracks.

What percent of the balls in the jar are both black and do not have cracks?

The train that travels from Melbourne to Sydney and back comes to Melbourne every 4 hours.

The train that travels from Melbourne to Adelaide and back comes to Melbourne every 6 hours.

If both trains are at Melbourne at 8:00 hours, at what time will they both be at Melbourne again?

This special dartboard has only two possible scores.

Which of the following scores could NOT be obtained by throwing one or more darts?

A machine worked for three straight hours making widgets.

If the machine made 132 widgets in the third hour, which was twice as many as it made in the second hour, and three times as many widgets as it made in the first hour, how many widgets did the machine make in all?

Bernice, Gale, and Lisa collect bottles for recycling.

The number of bottles that Bernice, Gale, and Lisa each collected are in the ratio of 10:6:5, respectively.

If altogether they collected 5 145 bottles, how many more bottles did Gale collect than Lisa?

An electric company charges 50 cents for the first kilowatt-hour consumed and $3 for each additional kilowatt-hour consumed until the customer reaches 4 kilowatt-hours.

After that, the electric company charges $1 per kilowatt-hour consumed.

If a certain customer consumed a total of 8 kilowatt-hours, how much is he going to pay?

An art gallery has a total of 112 watercolour and oil paintings.

The number of watercolour paintings is 1/3 the number of oil paintings, and 3/4 of the oil paintings are oil portraits.

How many oil portraits are there in the art gallery?