Math Trial Test

• When 4 000 liters of water are added into a tank that is already 3/4 full of its capacity, it fills the tank to 4/5 of its capacity.

The total capacity of the tank is how many litres?

The table below shows unemployment as a percentage of the total labour force from 2012 to 2017.

The total labour force in 2012 was 6 million workers, and the total labour force in 2017 was 400 000 workers more than total labour force in 2012.

What was the increase in the number of unemployed members of the workforce from 2012 to 2017?

• The population of Riverdale is 4 times the population of Greendale, which has a population twice as great as that of Sunnydale.

What is the ratio of the population of Riverdale to the population of Sunnydale?

What is the average (arithmetic mean) of 12, 13, 14, 510, 520, 530, 1 115, 1 120, and 1 125?

• Thirty percent of the members of the Book Club wear glasses.

Of those who do not wear glasses, 12 are females and 30 are males.

How many members does the Book Club have?

• A group of tourists can charter a small aircraft at a fixed total cost.

If 36 tourists charter the small aircraft rather than 40 tourists, the cost per tourist is greater by $12.

What is the fixed total cost to charter the small aircraft?

• Barbie took a student loan amounting to $12 000.

The bank offered a payment plan consisting of a $2 000 downpayment and 12 monthly payments of $1 000 each.

How much did Barbie pay in interest with this plan?

• The greatest common factor of 36 and 96 is N.

What is the sum of the digits of N?

• A cube of side 3 centimetres is painted red on all its faces.

If the cube is sliced into 1 cubic centimetre smaller cubes, how many of the smaller cubes will have exactly one of their sides painted red?

• A group of friends can rent a cabin for the weekend at a fixed total cost.

If 36 friends join the group rather than 40 friends, the cost per friend is greater

by $12.

What is the cost per friend if 40 friends will rent the cabin?

• In the recent election, with only three candidates, Huey got 4 more percent of the votes than Dewey, and Dewey got 5 more percent than Louie.

If Huey got 226 votes and none of the votes were spoiled, how many votes were cast altogether?

• In Mulan’s flower shop, there are 1/3 as many violets as carnations and 1/2 as many tulips as violets.

If there are an equal number of roses and tulips, what percent of the flowers in the shop are carnations?

• The current population of Bellwood is 2 million, and the population is expected to increase by 4 percent each year.

What will be the population of Bellwood after 3 years?

• In a group of 600 adults, 175 are men.

Among the men, 2/3 as many do not listen to the radio as do listen to the radio. 

How many men listen to the radio?

• A basket contains 43 red and yellow balls.

If one red ball is removed from the basket, one-seventh of the remaining balls will be red. 

How many yellow balls are in the basket?

• According to the recent study, there were an average (arithmetic mean) of 16 000 car accidents per day on weekends and an average of 40 000 per day on each of the other days of the week.

Which of the following is nearest to the total number of accidents in a year?

• The game of baseketball consisted of two rounds.

In each round, the 20 teams competing were divided randomly into 10 pairs, and each pair played a single match.

If none of the matches resulted in a tie, and of the teams that lost in the first round, seven also lost in the second round, how many teams won both of their matches?

Twenty-five percent of 30 equals 75 percent of what number?

• Cookie Monster made a total of 125 cookies for seven straight days, beginning on Saturday.

He made 3/5 of the cookies on the first day and 3/5 of the remaining cookies on the second day. 

If, each successive day, he made fewer cookies than the previous day, what is the greatest possible number of cookies he could have made on Wednesday?

• If Joseph gives Alfred 5 baseball cards and Alfred gives Fred 2 baseball cards, the three boys will have the same number of baseball cards. 

How many more baseball cards does Joseph have than Alfred?

• A symmetric number of another number is a number where the digits are reversed. 

For example, 1 234 is the symmetric number of 4 321. 

The difference between a number and its symmetrical number must be divisible by which of the following?

• Archie took three days to travel from Riverdale to Greendale. 

On the first day, he travelled 2/5 of the distance from Riverdale to Greendale, and on the second day, he travelled 2/3 of the remaining distance.

What fraction of the distance from Riverdale to Greendale did Archie travel on the third day?

• The population of Arendelle grew from 13 000 in 2000 to 191 000 in 2020. 

What was the approximate percent increase in the population of Arendelle from 2000 to 2020?

In the figure below, ABCD is a parallelogram.

The area of triangle APB is 10 square centimetres, and the area of triangle APD is also 10 square centimetres. 

If the length of AQ is 5 centimetres, what is the length of BC?

• In a survey of 600 respondents, 175 are men.

If the number of women that drink soda is 12/13 of the number of women that do not drink soda, how many women do not drink soda?

• At the local grocery store, an onion costs 3 times as much as a tomato. 

Which of the following sets of purchases would have the same cost?

I. 9 onions and 3 tomatoes

II. 7 onions and 5 tomatoes

III. 7 onions and 9 tomatoes

• Stark Industries has three factories that produce motherboards. 

Two of the factories can each produce 100 000 motherboards in 15 days, while the third factory can produce motherboards 30 percent faster. 

Approximately how many days would it take to produce a million motherboards with all three factories working simultaneously?

• A fruit salad dessert consists of apples, peaches, and grapes. 

There are 3 times as many kilograms of apples as grapes and 2.5 times as many kilograms of peaches as grapes. 

If a fruit salad dessert has an average (arithmetic mean) of 13 kilograms per fruit, how many kilograms of apples does the dessert have?

• Of the marbles in the box, 4/9 are red, 1/5 are blue, 1/6 are green, and the remaining 51 are yellow. 

How many marbles are in the box?

• Nails are sold in boxes of 256 for $9.75 and in boxes of 128 for $7.75. 

Elmo needs exactly 512 nails for a project and buys 4 boxes of 128 nails instead of 2 boxes of 256 nails.

Approximately how much more per nail did Elmo spend than he would have if he had bought the larger containers?

• Of the 1 260 members of the Homeowners Association, only 5/12 of the total members cast votes for president of the association in the last election. 

If the winning candidate received 60 percent of the votes cast, how many votes did the winning candidate receive?

The grid below is composed of identical squares, and each square has an area of 1 square centimetre.

What is the area of the yellow quadrilateral?

• Twenty-five percent of the 4 800 students at Hogwarts School of Magic ride their broomsticks to school. 

If 33 1/3 percent of those that ride their broomsticks to school transfer to a different school and no other changes occur, what fraction of the remaining students at Hogwarts School of Magic ride their broomsticks to school?

• A luxury liner is transporting several cats, along with a crew consisting of sailors, a cook, and a one-legged captain, to a nearby port. 

If these passengers collectively have 15 heads and 41 legs, how many sailors are on board the luxury liner?

• An appliance store ordered 50 countertop stoves to be sold for $144 each, which represents a 20 percent markup over the store owner’s initial cost for each stove. 

Of the countertop stoves ordered, 5 were never sold. 

These ovens were returned for a refund of 50 percent of the owner’s initial cost. 

What was the store’s gain or loss as a percent of the initial cost of the 50 countertop stoves?