# UCAT Quantitative Reasoning Test #1

#### What fraction of the grid is not blacked out?

Correct answer: 2/3

We can count the total number of squares/cells in the grid and then deduct the number of blacked-out cells.

The total number of cells is 6.

Amount of cells Not covered in black: (3 whole cells + 2 half-cells)=4

4/6=2/3

#### A university has studied all 12 species of birds that are indigenous to a Pacific Ocean island group. The experiment needed a 72-hour monitoring of the birds' resting heart rate, which was measured via trackers. This graph depicts the relationship between a bird's resting heart rate and its wingspan in metres. What is the average length of a bird's wingspan?

Correct answer: 0.55 m

Find the'middle' number by counting the number of birds in the chart.

To get the median, multiply the number of birds by one and divide by 2 to get the middle value.

The median wingspan is 12 + 1 = 13 / 2 = 6.5 since there are 12 birds.

As a result, the median is located halfway between the 6th and 7th numbers.

The sixth is at 0.50m and the seventh is at 0.60m. 0.55 Is halfway between these.

#### The number of English counties pupils in two classes at a primary school who visited is listed above. Each class had a total of 30 students. What was the most number of counties visited by a Class 1 student?

Correct answer: 8

Determine the point at which the cumulative frequency equals the total class size:

Because there are 30 students in the class, this occurs in 8 counties for classes 1 through B.

#### A listed company's stock price is calculated over a single day.

The price is expressed as a number of pence per share.

A broker will pay a 'offer' price of 2p per share more than the price shown to buy shares, plus an additional £5 for stock transactions of 5000 or less shares.

There is a 0.5 percent charge above this level.

A broker will be paid a 'bid' price of 2p less than the price quoted to sell shares.

A broker will be paid a 'bid' price of 2p less than the price quoted to sell shares.

Any profit made from buying and selling stocks is subject to a 2.5 percent deduction.

The price at which all of a company's shares could be sold is termed its value.

The corporation has a total of 500,000 shares.

A dividend is a payment made to shareholders every quarter based on how many equities they own.

What is the largest change in the company's value over the course of one hour?

Correct answer: £10,000

Determine when the most significant price change occurs:

Between 10:00 and 11:00 a.m., this occurs.

The change is 176p to 174p – 2p.

Determine how this affects the company's worth.

The corporation has a total of 500,000 shares, so:

0.02 x 500,000 = £10,000 – C.

#### This is Mark's weekly schedule, which he has followed for the past six weeks while working from home. He has always skipped work on Saturdays and Sundays. He gets up at 7 a.m. and leaves the house at 8 a.m. What was his average speed during his 10-kilometer run, to the nearest 0.1 m/s?

Correct answer: 2.8 m/s

Calculate the average speed by converting the units to metres and seconds.

1 hour = 60 minutes = 60 x 60 seconds = 3600 s

10 km = 10,000 m

So in metres per second:

10000 / 3600 = 2.777… = 2.8 m/s

#### The table's figures are all in kilos.

1 ml water = 1g

What percentage of the total mass of coffee beans consumed in the country was consumed in cafés in 2013-14?

Correct answer: 67.80%

Calculate the percentage of coffee beans used in cafés as a percentage of total coffee beans used.

Beans in cafés: 242,000

Beans in total: 242000 + 50300 + 28341 + 36324 = 356965

242000/356965 = 0.6779… = 69.8%

#### The average rent per calendar month (PCM) in a popular South London neighborhood is depicted in this graph. There are 12 calendar months in a year.

In 2015, Simon rents a one-bedroom flat in this neighborhood for 75% of the average cost. Between 2015-16 and 2016-17, the price of the typical property increased twice as fast as the price of the average property. What is the difference between his new rent and the market average for 2016-17?

Correct answer: He pays £125 less

Calculate his rent over the years.

He paid 75% of the market average (£1000 PCM at the time).

0.75 x 1000 = 750

The average price went up from 1000 to 1250

Use the following formula to calculate the percentage increase:

New Value / Old Value = Multiplier

1250/1000 = 1.25 = 25%

His rent jumped by double the rate, or by 50%.

For a percentage increase, use the following formula:

New value = Old value x multiplier

50% increase = multiplier of 1.5

New rent = 750 x 1.5

New rent = £1125

Calculate the difference from the market rent.

According to the graph, the new average rent is £1250.

£1250 – £1125 = £125 so he pays £125 below the market rate.

#### What is the most common store-to-distribution-center distance?

Correct answer: 21 to 30 miles

The majority of the stores (26) are located between 21 and 30 kilometers from the center.

#### This is the revenue of an Australian medium-to-large business. All figures are in AUD$.

The corporation wants to figure out how much money it makes on a monthly basis, taking into account all three revenue streams. What is the average monthly total revenue for the three months listed in the table, rounded up to the closest $250?

Correct answer: $239,250

Calculate the monthly average by adding the incomes:

(120 + 145 + 130 + 15 +17.5 19 + 80 + 90 + 101) x 1000 = $717,500

To calculate the monthly average, multiply this by three.

$717,500/3 = $239,166… = $239,250 to the nearest $250.

#### The percentage of nickel in two coins is shown in the table.

What is the difference between the weight of copper present in Coin B and the weight of copper present in Coin A if both coins are made entirely of nickel and copper?

Correct answer: 0.675 g

The percentage of copper in Coin A is (100 – 25) = 75%.

The amount of copper in Coin A, which weighs 6.5 g, is 6.5 75/100 = 4.875 g.

The amount of copper in Coin B is 100 – 16 = 84%.

The amount of copper in Coin B, which weighs 5 g, is 5 84/100 = 4.2 g.

The difference in copper content between Coin B and Coin A is 4.875 - 4.2 = 0.675 g.

#### The temperature of Venus is in the middle of the temperature range between Earth and Mercury. What is Mercury's current temperature?

Correct answer: 940 °C

480 + (480 – 20) = 940.

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