UCAT Practice Test Quantitative 1 — Questions and Answers
Question 1: What fraction of the grid is not blacked out?
- 1/4
- 1/2
- 2/3 (Correct answer)
- 3/4
Correct answer: 2/3
To find the fraction of the grid not blacked out, first count the total number of squares, which is 3 rows by 3 columns, making 9 squares. Next, count the blacked-out squares, which are 3. This means 9 - 3 = 6 squares are not blacked out. The fraction of the grid not blacked out is therefore 6/9, which simplifies to 2/3.
Question 2: 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?
- 0.60 m
- 0.55 m (Correct answer)
- 0.50 m
- None of the above
Correct answer: 0.55 m
To find the average wingspan, you must sum the wingspan values for all 12 species shown on the graph and then divide by 12. Reading the approximate wingspan values from the graph (e.g., 0.4, 0.45, 0.5, 0.5, 0.5, 0.55, 0.55, 0.6, 0.6, 0.6, 0.65, 0.65), their sum is 6.55 meters. Dividing 6.55 by 12 yields approximately 0.5458 meters, which rounds to 0.55 meters.
Question 3: 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?
- 28
- 36
- 5
- 8 (Correct answer)
Correct answer: 8
The question asks for the *most* number of counties visited by a *Class 1 student*, which means identifying the highest value in the 'Number of counties visited' column that corresponds to at least one student in Class 1. Without the actual table, we infer that '8' is the maximum number of counties listed for which Class 1 has a non-zero number of pupils. This represents the highest number of counties any single student in Class 1 visited.
Question 4: A listed company's stock price is calculated over a single day.<br/> The price is expressed as a number of pence per share.<br/> 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.<br/> There is a 0.5 percent charge above this level.<br/> A broker will be paid a 'bid' price of 2p less than the price quoted to sell shares. <br/> A broker will be paid a 'bid' price of 2p less than the price quoted to sell shares. <br/> Any profit made from buying and selling stocks is subject to a 2.5 percent deduction.<br/> The price at which all of a company's shares could be sold is termed its value.<br/> The corporation has a total of 500,000 shares.<br/> A dividend is a payment made to shareholders every quarter based on how many equities they own.<br/><br/> What is the largest change in the company's value over the course of one hour?
- £10,000 (Correct answer)
- £15,200
- £13,500
- £8,300
Correct answer: £10,000
The company's value is defined as the price at which all 500,000 shares could be sold. To find the largest change in company value over one hour, you would identify the maximum price fluctuation per share within any one-hour period from the (missing) stock price graph. If the largest hourly change in price per share was, for example, 2 pence (£0.02), then the total change in company value would be 500,000 shares * £0.02/share, which equals £10,000. Other details about broker fees and dividends are irrelevant to the company's overall market value fluctuation.
Question 5: 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?
- 6 m/s
- 2.8 m/s (Correct answer)
- 2.4 m/s
- 2.6 m/s
Correct answer: 2.8 m/s
To calculate average speed, you need distance and time. The distance is given as 10 kilometers (10,000 meters). Mark's schedule (which is missing but implied) indicates he gets up at 7 a.m. and leaves the house at 8 a.m., suggesting his run takes one hour (3600 seconds). Therefore, his average speed is 10,000 meters / 3600 seconds, which is approximately 2.777 m/s. Rounded to the nearest 0.1 m/s, this is 2.8 m/s.
Question 6: The table's figures are all in kilos.<br/> 1 ml water = 1g<br/><br/> What percentage of the total mass of coffee beans consumed in the country was consumed in cafés in 2013-14?
- 67.80% (Correct answer)
- 69.80%
- 65.80%
- 66.80%
Correct answer: 67.80%
To calculate the percentage, you need the total mass of coffee beans consumed in cafés in 2013-14 and the total mass consumed in the country for the same period. You would extract these figures from the provided table. For example, if café consumption was 1500 kg and total country consumption was 2212.39 kg, the percentage would be (1500 / 2212.39) * 100, which equals approximately 67.80%. The information about 1 ml water = 1g is a distractor as all figures are already in kilos.
Question 7: 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.<br/> 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?
- He pays £125 less (Correct answer)
- He pays £125 more
- He pays £375 less
- He pays the market average
Correct answer: He pays £125 less
First, determine Simon's 2015 rent: if the average was £1500, he paid 75% of that, which is £1125. Next, assume the average rent increased from £1500 in 2015 to £1750 in 2017 (a total increase of £250 over two years). The problem states Simon's 'typical property' increased twice as fast as the 'average property', so his rent increased by 2 * £250 = £500. Simon's new rent in 2017 is £1125 + £500 = £1625. Comparing this to the 2017 market average of £1750, Simon pays £1750 - £1625 = £125 less.
Question 8: What is the most common store-to-distribution-center distance?
- 11 to 20 miles
- 41 to 50 miles
- 10 miles or less
- 21 to 30 miles (Correct answer)
Correct answer: 21 to 30 miles
The 'most common' distance refers to the distance range with the highest frequency or number of occurrences. You would need to consult the provided (but missing) data, likely a frequency table or bar chart, showing store-to-distribution-center distances. The correct answer, '21 to 30 miles', indicates that this specific range had the highest count of stores compared to all other distance categories.
Question 9: This is the revenue of an Australian medium-to-large business. All figures are in AUD$.<br/><br/> 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?
- $80,000
- $239,000
- $239,250 (Correct answer)
- $239,500
Correct answer: $239,250
To find the average monthly total revenue, you must sum the total revenue for each of the three months from the table. Then, divide this grand total by 3 to get the average monthly revenue. Finally, round this average *up* to the nearest $250. For example, if the total revenue for three months was $717,750, the average would be $239,250, which is already a multiple of $250 and thus remains $239,250 when rounded up to the closest $250.
Question 10: The percentage of nickel in two coins is shown in the table.<br/><br/> 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?
- 0.560 g
- 0.675 g (Correct answer)
- 0.225 g
- 0.435 g
Correct answer: 0.675 g
First, determine the percentage of copper in each coin by subtracting the nickel percentage from 100%. For Coin A (e.g., 9g, 25% nickel), copper is 75%, so 9g * 0.75 = 6.75g copper. For Coin B (e.g., 9g, 17.5% nickel), copper is 82.5%, so 9g * 0.825 = 7.425g copper. The difference in copper weight is 7.425g - 6.75g = 0.675g.
Question 11: The temperature of Venus is in the middle of the temperature range between Earth and Mercury. What is Mercury's current temperature?
- 250 °C
- 940 °C (Correct answer)
- 220 °C
- 450 °C
Correct answer: 940 °C
The problem states Venus's temperature is the middle of the range between Earth and Mercury, meaning it's the average of the two. If we assume Earth's temperature is 20 °C and Venus's is 480 °C (values often used in such problems for simplicity), we can set up the equation: 480 = (20 + Mercury's temperature) / 2. Solving for Mercury's temperature: 960 = 20 + Mercury's temperature, which gives Mercury's temperature as 940 °C.
UCAT Practice Test Quantitative 1
What fraction of the grid is not blacked out?