UCAT Quantitative Reasoning

Question 1)

Number of lollies eatenFrequency
140
260
3100
430

The owner of a lolly shop wants to know the mean number of lollies eaten by their customers. The mean is:

  • A. 1
  • B. 1.5
  • C. 2
  • D. 2.5
  • E. 3

Question 2)

The mean number of lollies eaten each year per person is 372 in 2018, this is expected to grow by 6% in 2019. What is the average daily number of lollies eaten per person in 2019?

  • A. 1
  • B. 1.1
  • C. 1.2
  • D. 1.3
  • E. 1.4

Question 3)

A car park for the lolly shop is designed so that it can fit 200 cars. The designers want 50% to be covered by cars and the area 1 car covers is 2 m by 3 m. What are the dimension of the car park?

  • A. 60 m by 60 m
  • B. 8 m by 8 m
  • C. 30 m by 20 
  • D. 100 m by 100 m
  • E. 20 m by 12 m

Question 4) 

The compound growth in lolli consumption is continued to continue, which graph represents this?

  • D.
  • E.

Question 5)

A woman left her house at 10 am. She drove at 60 km/h for 5 km then drove at 20 km/h for 15 km. How long was she driving for?

  • A. 40 mins
  • B. 60 mins
  • C. 20 mins
  • D. 50 mins
  • E. 35 mins

Question 6)

She drove on the highway for 3 hours. 60 % of the time she was driving 90 km/h and the remainder she was driving at 110 km/h. How far did she drive

  • A. 394 km
  • B. 274 km
  • C. 374 km
  • D. 294 km
  • E. 400 km

Question 7)

The woman entered a tunnel starting from rest; she uniformly accelerated to 120 km/h in 8 seconds and continued at this speed for the remaining 2 km of the tunnel. How long did she spend in the tunnel?

  • A. 60 seconds
  • B. 62 seconds
  • C. 64 seconds
  • D. 66 seconds
  • E. 68 seconds

Question 8)

The woman wanted to see how many times she could travel in the tunnel so she decided to drive for 10 mins at 160 km/h, 40 seconds at 180 km/h and 3 mins at 110 km/h. How many times did she drive up and back in the tunnel?

  • A. 15 times
  • B. 16 times
  • C. 17 times
  • D. 18 times
  • E. 19 times

Question 9)

A farmer is undecided about a particular tractor model. The fuel consumption for the two models are as shown.


Tractor Model
Tractor 1Tractor 2
Fuel consumption up hill (L/10 km)10.211.2
Fuel consumption down hill (L/20 km)5.27.1
Fuel consumption level ground (L/10 km)8.410.1
CO2 emissions (gm per km)210194
Fuel Cost/ L$1.52$1.35

The tractor model 1 was used to drive 4 km up hill and 2 km on level ground How much fuel was burnt in the process?

  • A. 3.4 L
  • B. 4.2 L
  • C. 4.0 L
  • D. 3.8 L
  • E. 3.2 L

Question 10)

The farmer typically uses the tractor 5 times a week. In an 8 week period what would be the difference in fuel consumption between model 1 and 2 if he drove 15 km on level ground every time he used the tractor?

  • A. 170 L
  • B. 160 L
  • C. 150 L
  • D. 140 L
  • E. 130 L

Question 11)

The farmer decides he wants to take his tractor on a road trip which is 40 km long and made of level ground. What will be the difference in price if he uses the second tractor model instead of the first?

  • A. $3.47 less
  • B. $3.47 more
  • C. $4.47 less
  • D. $4.46 more
  • E. $3.97 More

Question 12)

If both tractors were to drive a total of 1040 km this year what would be the difference in CO2 emissions between them?

  • A. 17640 gm
  • B. 18650 gm
  • C. 18655 gm
  • D. 16640 gm
  • E. 15640 gm

Question 13)

An airplane travels 8000 miles travelling at 600 km/hour. How many minutes did it take to travel this distance? (1.6 mile = 1 km)

  • A. 500 mins
  • B. 450 mins
  • C. 400 mins
  • D. 350 mins
  • E. 0.138 mins

Question 14)

The pilot wants to get home quicker for his son’s birthday. If he drives at 20% more than the plane’s normal speed. What percentage tie reduction will there be in the plane’s travel time?

  • A. 16 % reduction
  • B. 17% reduction
  • C. 18 % reduction
  • D. 19% reduction
  • E. 20% reduction

Question 15)

The below graph shows the percentage of people people 20,000 who walk to walk to vs drive to three different regions. 

How many more people walk to region B then those who walk to region A?

  • A. 7000
  • B. 6000
  • C. 6500
  • D. 7500
  • E. 3500

Question 16)

What is the total number of people who visit the regions A and/or B and/or C by walking?

  • A. 35000
  • B. 20000
  • C. 40000
  • D. 75000
  • E. 30000

Question 17)

What is the difference in people who walk to region A then region B and C by walking or driving?

  • A. 1000
  • B. 2000
  • C. 3000
  • D. 4000
  • E. 5000

Question 18)

What is the difference in people who walk to region A then region B and C?

  • A. 2500
  • B. 5000
  • C. 1000
  • D. 12500
  • E. 15000

Question 19)

The below chart shows the percentage composition by mass of a house which is made of sustainable materials.

If the house weighs 2.2 tones, how many kg does the brick and glass weigh?

  • A. 0.959
  • B. 959
  • C. 0.80
  • D. 800
  • E. 0.850

Question 20)

Concrete is 50% sand and the rest a mixture of cement and aggregate. What is the total mass of sand in the 2.2 tone house?

  • A. 0.959 Ton
  • B. 959 kg
  • C. 0.80 Ton
  • D. 800 kg
  • E. 0.850 Ton

Question 21)

If the total mass of brick was reduced by 20%, what would be the new mass of the sustainable house?

  • A. 1.9 Ton
  • B. 2 Ton
  • C. 2.15 Ton
  • D. 2.12 Ton
  • E. 2.2 Ton

Question 22)

The owners decide they don’t want any brick any more so every other material must be increased by 50%, what is the new mass of the house?

  • A. 1.90 Ton
  • B. 2.22 Ton
  • C. 2.15 Ton
  • D. 2.12 Ton
  • E. 2.24 Ton

Question 23)

The house owner finds a discount hardware shop. How much will the materials for the house cost if brick costs $2000/Ton, glass costs $5000/ Ton, concrete costs $1500/ Ton and sand costs $500/Ton

  • A. $2000
  • B. $3000
  • C. $4000
  • D. $5000
  • E. $6000

Question 23)

The average number of schools in 5 cities is 432. In four of the 5 cities there are 500, 431, 300 and 370 schools in the cities. How many school in the fifth city?

  • A. 559
  • B. 673
  • C. 350
  • D. 400
  • E. 432

Question 24)

The medical industry is composed of 35% doctors which accounts for 342000 people, how many people are in the medical industry?

  • A. 950 002
  • B. 900 201
  • C. 974 143
  • D. 984 534
  • E. 900 012

Question 25)

The following graph represents the average yield of grapes for 100 hundred different farms in Tasmania over a 10 year period.

What was the approximate percentage growth in grapes grown per vineyard for NSW over the 10 years.

  • A. 50%
  • B.100%
  • C. 200%
  • D. 30
  • E. 30000

Question 26)

What year did Tasmania expect the largest drop in grapes grown per vineyard?

  • A. Year 1
  • B. Year 2
  • C. Year 3
  • D. Year 4
  • E. Year 5

Question 27)

What year did NSW expect the largest drop in grapes grown per vineyard?

  • A. Year 1
  • B. Year 2
  • C. Year 3
  • D. Year 4
  • E. Year 5

Question 28)

What is the largest percentage growth in grape production for vineyards in either state?

  • A. 100%
  • B. 200%
  • C. 300%
  • D. 400%
  • E. 500%

Question 29)

Jenny and Russel want to go shopping in Australia, however, Jenny is from the US and Russel is from the UK. The exchange rate of $US 1 = $AUS .66 and € 1 = $AUS .5.

Jenny has 320  € and Russel has $US 430, how many Aus$ do they have combined?

  • A. $AUS 1285
  • B. $AUS 233
  • C. $AUS 750
  • D. $AUS 1750
  • E. $AUS 1455

Question 30)

Jenny and Russel want to go shopping, however, Jenny is from the US and Russel is from the UK. The exchange rate of $US 1 = $AUS .66 and € 1 = $AUS .5. They have decided they want to shop in the US now. Jenny has 320  € and Russel has $US 430, how many $US do they have combined?

  • A. $US 1285
  • B. $US 233
  • C. $US 650
  • D. $US 856
  • E. $US 650

Question 31)

Jenny and Russel want to buy matching pants, the UK store sells 55  € per pants but they currently have 20% off where as the Australian store is selling it for $Aus 80 for same pants. How much more/less would it cost to buy from the Aus shop then the UK store?

  • A. $US 5.35
  • B. $US 8.50
  • C. $US 13.79
  • D. $US 10.70
  • E. $US 4.25

Question 32)

A farmer evaluates his property to be worth $500 per hectare. His property is 70,000 Acre’s. If 1 hectare = 2.47 Acre, what is the value of his property?

  • A. $1.2 million
  • B. $1.3 million
  • C. $1.4 million
  • D. $1.5 million
  • E. $1.6 million

Question 33)

A beaver farm has the total number of bevers increasing by 5 % each year, how many beavers are there in 5 years if they started at 20 bevers but lost 5 at the end of the fifth year rounding to the nearest whole number?

  • A. 20 beavers
  • B. 21 beavers
  • C. 24 beavers
  • D. 25 beavers
  • E. 26 beavers

Question 34)

A child A is a quarter of the age of child B, in 10 years time, Child A is ½ the age of Child B, what is the difference in Age of the two children?

  • A. 3.75
  • B. 4
  • C. 3.5
  • D. 5
  • E. 0.8

Question 35)

Jenny earns 42, 000 a year, how much does she pay in tax?

Taxable incomeTax Rate
$0-37,000No tax
37,001-90,00015% on each dollar over 37,000
90,001-180,00030% on each dollar over 90,001 thousand and 15% on each dollar over 37,000
180,001 and over45% on each dollar over 180,001 and 30% on each dollar over 90,001 thousand and 15% on each dollar over 37,000
  • A. $750
  • B. $800
  • C. $850
  • D. $900
  • E. $950

Question 36)

Kevin earns 200,000 a year, how much does he earn after tax?

  • A. $119,000
  • B. $132,000
  • C. $143,000
  • D. $129,000
  • E. $68,000

Answers

  1. D (40 +2*60 +3*100 + 4*30)/(40+60+100+30) = 1.1 
  2. B (372*1.06)/365)= 1.1
  3. A (200*(2*3)*(1/.5))= 2400 m^2 = 60 m * 60 m
  4. E exponential growth not starting from 0
  5. D 60*((5/60)+(15/20))
  6. D 3 *(.6*90+.4*110)
  7. A (2-120*8/3600)*3600 + 8
  8. C (10/60*160+40/3600*180+3/60*110)/2
  9. D (10.2*.4+.2*8.4)/1.52
  10. A (10.1*25/10 – 8.4*25/10)*8*5
  11. B (4*4.8*1.52-4*10.1*1.35)
  12. D (1040(210-194))
  13. A (8000*(1/1.6)*(1/600)*60
  14. B (1-1/1.2)/1
  15. A 20000(.75-.4)
  16. A (.75+.4+.6)20000
  17. B ((.6+.2)-(.4+.3))*20,000
  18. B ((.3+.5)-.25)*20000
  19. B (.327*.109)2200
  20. E (.5*.345+.218)*2.2
  21. D 2.2 – (.1*.327*2.2)
  22. B (2.2-.327*2.2)*1.5
  23. C (.327*2000+.218*500+.345*1500+.109*5000)*2.2
  24. A 432*5 – 500 – 431 – 300 – 370
  25. C 60000/30000 * 100
  26. C
  27. B
  28. D 40000/10000 * 100
  29. A 320 * 2 + 430/2*3
  30. D 1285/3*2
  31. D (55*2*.8*2-80*2)*(⅔)
  32. C 500*7000/2.47
  33. B 20*1.05*1.05*1.05*1.05*1.05-5
  34. A
  35. A 5000*0.15
  36. B 20000-53000*.15-90000*.3-90000*.45

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