Day 3 Year 6 Math Trial Test

Macrosoft Company introduces a new early retirement program to all their employees.

For an employee to qualify for the early retirement program, the sum of the employee’s age and years of service must be at least 70 years. 

If Diane was Y years old when she joined the company, which of the following gives the minimum age, in years, at which she could qualify for early retirement?

Mickey Mouse has three pieces of rope.

The first piece is 1 metre 20 centimetres 65 millimetres long, the second piece is 2 metres 45 centimetres 35 millimetres long, and the third piece is 2 metres 75 centimetres 55 millimetres long. 

How much rope does Mickey Mouse have?

Best Ribs Restaurant had a total of W workers, consisting of only waiters and cooks, some of whom had college degrees and others did not.

Of these W workers, N were cooks and 5N/4 had college degrees.

If 3N/4 cooks had degrees, W/4 of the waiters did not have degrees, and 30 of the workers did not have degrees, how many workers were at the restaurant?

Water lily grows at such a rate that it covers double the surface that it covered the day before.

It takes 30 days for a water lily to cover the entire surface of the pond. 

How long would it take for two water lilies of the same size to cover the entire surface of the same pond?

Start Industries sells boxes holding d magnets each.

The boxes are shipped in crates, each holding b boxes. 

What is the price charged per magnet, in cents, if Start Industries charges m dollars for each crate?

During a class gathering at the auditorium, the female students are seated in 1/2 of the total seats, and the male students are seated in 2/3 of the remainder.

The male students are seated in what fraction of the occupied seats?

If the average (arithmetic mean) of 10 consecutive integers is 19.5, what is the value of the largest integer?

Two different candles burn at different constant rates, and one is 3 centimetres longer than the other.

The longer candle was lit at 6:00 PM, and the shorter candle was lit at 7:30 PM. 

At 10:00 PM, both candles were of the same length, and the longer candle burned out at 12:00 AM, while the shorter one burned out at 11:30 PM.

What was the original length of the shorter candle?

In the figure below, all the sides meet at a right angle.

If the perimeter of the figure is 32 centimetres, what is its area?

Planet Morax has a total population of 50 million, and they are distributed, in descending order, among District 1, District 2, District 3, District 4, District 5, and District 6.

District 4 has 21 percent of the total population, District 6 has a population of 2 million, and some districts can have the same population.

What is the greatest possible population of District 5?

Andrew bought 12 pepperoni and vegetarian pizzas for his study group.

Pepperoni pizzas cost $13 each, and vegetarian pizzas cost $17 each. 

If he spent a total of $184 on the pizzas, how many pepperoni pizzas did he buy?

On Saturday, Jodie sold a quantity of lemonade, all served in 600-millilitre glasses and sold the same total quantity of lemonade on Sunday, all served in 400-millilitre glasses.

If the price on Saturday was $9 per glass, and the revenue on Sunday was 3/4 that of the revenue on Saturday, what was the price per glass of lemonade on Sunday?

The price of a microwave oven was discounted by 10 percent on the first day of the sale.

On the second day of the sale, the microwave oven is discounted another 10 percent, and on the third day, it is discounted an additional 20 percent.

The price of the microwave oven on the third day of the sale was what percentage of the sale price on the first day of the sale?

The bar graphs below show the annual revenue growth rate of ACME Corporation and the tax rate as a percent of revenue for each year from 2019 to 2023.

If ACME Corporation’s revenue in 2019 was $98 million, which one of the following is closest to how much more the company paid in taxes in 2021 than in 2020?

A train trip begins at Riverdale, makes stops first at Sunnydale, then at Bellwood, and ends at Greendale.

The distance between Riverdale and Bellwood is four times the distance between Bellwood and Greendale, and the distance between Riverdale and Sunnydale is equal to half the distance between Sunnydale and Bellwood.

The distance between Riverdale and Bellwood is how many times the distance between Sunnydale and Greendale?

Currently, Homer is four times as old as Bart.

Eight years from today, Homer’s age will be two and a half times Bart’s age. 

What will be the ratio of Bart’s age to Homer’s age 32 years from today?

A bag contains tokens that are worth 3, 5, or 11 points.

During a turn, Jake selects up to 10 pieces at random from the bag. 

Jake’s score for the turn is found by taking the product of the point values of each selected token.

If Jake’s score for the turn was 12 375 points, how many total tokens did he select?

What is the total number of squares, each with a perimeter of 36 centimetres, into which a rectangle with a width of 36 centimetres and a length of 72 centimetres can be partitioned?

A factory calculated that on average, about 10 percent of the widgets produced are defective and must be rejected before shipment to the buyer.

The factory promised to supply 7 200 widgets priced at $10 each. 

It estimated that the overall profit on all the widgets produced will be 25 percent. 

How much did it cost the factory to produce one widget? (Profit = Revenue – Expenses)

Alice, Ben, and Carl are assigned to type a certain number of pages.

However, Carl left after 4 days when 40 percent of the job was complete. 

In this way, it takes a total of 13 days to finish the job. 

If Ben can type twice as fast as Alice, how much would the fastest of the three take to type the entire set of pages alone?

Elmo collects baseball cards and basketball cards.

He currently has 40 baseball cards and 25 basketball cards. 

Without changing the number of his basketball cards, what would the least number of baseball cards in his collection need to be so that the ratio of baseball cards to basketball cards would be at least 9:2?

Next year, sales of the new YBox 360 are expected to add 49 percent more revenue, bringing it to $73 606.

The current revenue of the store is double of what it was in the previous year. 

What was the previous year’s revenue?

A retailer sells products that belong to different categories, A to F, in alphabetical order.

The number of products sold in each category is distinct and in ascending order. 

If at least 2 products are sold in any category, and a total of 27 products were sold last week, what is the probability that a product sold last week belonged to category D?

The number of marbles of each of the four different colours in a box is in a ratio of 3:4:6:8.

If there are 24 marbles of one of the colours, which of the following cannot be the total number of marbles in the box?

The store gave away an average (arithmetic mean) of 92 candles per basket.

There was an average of 84 candles in the red baskets and an average of 96 candles in the white baskets. 

What was the ratio of the number of white baskets to the number of red baskets at the store?

A rectangular field is 500 metres long and 30 metres wide.

A rectangular hole 30 metres long, 20 metres wide, and 12 metres deep is excavated from the field, and the earth taken out is spread evenly over the field.

By how many centimetres will the level of the field be raised?

Big Bird decides to start a business making gift baskets.

He estimates that if he charges d dollars per gift basket, he will sell 65 – 5d gift baskets per day. 

If his estimate is accurate, which of the following best describes all values of d for which he will collect revenue in excess of $150 per day?

House of Java charges $3.25 for a cup of coffee that costs a total of $2.85 to make, while House of Mocha charges $2.80 for a cup that costs $2.65 to make.

If House of Java sells 55 000 cups of coffee, how many cups must House of Mocha sell to make at least as much in total profit as House of Java does? (Profit = Revenue – Expenses)

On the first week of showing of the new Avengers movie, 5 400 tickets were sold, all at reduced price.

During the remaining weeks of showing, five times as many tickets were sold at full price as were sold at reduced price. 

If the total number of tickets sold was 25 200, how many of those tickets were sold at full price?

In a certain economy, C represents the total amount of consumption in millions of dollars, Y represents the total national income in millions of dollars, and the relationship between these two values is given by the equation C = 90 + 9Y/11.

If the total amount of consumption in the economy increases by 99 million dollars, what is the increase in the total national income in millions of dollars?

The Book Club and the Cooking Club have the same number of members.

Both the ratio of men to women and the ratio of single women to married women in the Cooking Club is twice that of the Book Club. 

If there are 840 members in the Cooking Club in a ratio of 2 men for every woman, and the ratio of single women to married women in the club is 3:2, how many married women are in the two clubs?

A call centre has only two teams, headed by Bella and Edward.

Each member of Bella’s team was able to process 4/5 calls as compared to each member of Edward’s team. 

If Bella’s team has 5/8 as many agents as Edward’s team, what fraction of the total calls were processed by Edward’s team?

While on a trip in the Caribbean, Elmo calculated his non-hotel daily expenses as follows:

• on a frugal day, he could spend as little as $35 
• on an average day, he could spend $50
• on a splurge day, he could spend a minimum of $75

If Elmo has at most $300 to spend on non-hotel expenses during the five-day trip, what is the greatest possible number of splurge days he could have?

A car’s price decreased by 2.5 percent (from the original price) each year from 1996 to 2002.

During that time, the owner of the car invested in a new carburettor and a new audio system for the car, which increased the car’s price by $1 500.

If the price of the car in 1996 was $22 000, what was the car’s price in 2002?

The ratios of iron to chromium in two varieties of alloys, A and B, are 5:1 and 7:2, respectively.

Alloy C is produced by mixing alloys A and B at a ratio of 3:2. 

What is the ratio of iron to chromium in alloy C?