## UKCAT Quantitative Reasoning Volume 1 Answers

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1. A small business needs 250 colour flyers for a promotion. How much will this cost?

A. £50 **B. £40** C. £30 D. £7.50 E. £10

Explanation: A simple multiplication of 16 x 250 = 4000pence = £40

2. A customer needs 160 retractable pens and 300 black and white flyers. They want their logo to be printed on the pens. How much will they have to pay?

A. £14.75 B. £15 C. £14.67 D. £14.66 **E. £66.60**

Explanation: 160 x (26 + 10) = 5760pence = £57.60

300 x 3 = 9000pence = £9

£9 + £57.60 = £66.60

Number of pens Basic pen cost per pen Retractable pen cost per pen Premium pen cost per pen Cost for logo per pen 0-99 25 30 45 15 100-9999 20 26 43 10 10000+ 12 20 38 5

3. A business has £600 available for advertising this month. How many basic pens with a logo can they buy to the nearest pen with this money?

A. 1200 B. 1400 **C. 2000** D. 2002 E. 1999

Explanation:

999 pens at (25p+15p) each = £399.60, but the business has a budget of more than this so we can buy more.

The next bracket to check would be for 1000-9999 purchases so

9999 x (20p+10p) = £2999.70 – which is over the budget, but we now know that the right amount in within the 1000-9999 bracket and these all cost 30pence each

Therefore £600 / £0.30 = 2000 pens.

4. The shop decides to offer an extra 15% discount to a regular customer on the price of their total purchase. The regular customer decides to buy 1000 colour flyers, 2000 black and white flyers, 150 Premium pens with colour logo and 400 retractable pens with colour logo. How much will they be charged?

A. £430 B. £425.50 C. £405.23 D. £380.50 **E. £325.98**

Explanation: (1000x3p)+(2000x2p)+(150x(43+10))+(400x(26+10))

=£120 + £40 + £79.50 + £144

=£383.50

There is a 15% discount on this so

85/100x383.5 = £325.98

5. In 2012 there was a price increase of 5p per logo, 2p on every premium pen and 3p added to every colour flyer across all quantities. In addition a new shipping charge was introduced – for order less than £99 the charge is £5 and for orders between £100-1000 the charge is £5. How much could a customer have saved in total by ordering the following items in 2012 rather than 2011 – 70 retractable pens with logo and 600 colour flyers?

A. £21.50 B. £21.40 C. £25 **D. £26.50 **E. £27

Explanation: An extra 5p on pens = 70x5p = £3.50

An extra 3p on flyers = 600x3p = £18

The actual cost of all would have meant the delivery charge would have been waived in 2011, but in 2012 at this price delivery is £5.

Therefore £3.50+£18+£5 = £26.50

6. The total cost of producing a colour flyer to the shop is 8.5p per colour flyer. If a customer orders 3500 colour flyers in 2011, what percentage of income is profit?

A. 30% B. 24.56% C. 29.18% **D. 29.17%** E. 29.71%

Explanation: 3500x12p = £420 = cost to customer

3500x8.5p = £297.50 = cost to shop

£420-£297.50 = £122.50 = profit

Therefore 122.5/420 = 29.17%

7. In 2011 the company made a gross profit of £424,250 which was an increase of 1.2% on 2010. What was the gross profit in 2010 to the nearest pound?

A. £419219.37 B. £419218 **C.£419219** D. £419217 E.£419216

Explanation: Note the questions asks for the answer to the nearest pound

101.2/100 x “2010 gross profit” = 424,250

Therefore “2010 gross profit” = 424250/1.012 = 419219.27 which to the nearest pound is £419219

8. The company had to pay 12.5% tax on gross profit in 2011. How much money was left after taxation to the nearest pound?

A. £371218 B. £371217 C. £371216** D.£371219** E. £371220

Explanation: note the question asks for the answer to the nearest pound

12.5% tax is paid therefore

87.5/100 x 424250 = £371218.75 which to the nearest pound is £371219

9. How long does it take to get from the Old shopping Centre to East lane

A. 22 B. 23 C. 24** D.25** E.27

Explanation: This question requires basic maths – e.g. the bus leaves old shopping centre at 05.50am and arrives at east lane at 6.15am which is a 25 minute difference

10. Mr. Jenkins arrives at Market Hall bus stop at 4.06PM, how many minutes does he have to wait for the bus?

**A. 4** B. 6 C. 8 D. 9 E.12

Explanation: At this stop buses come every 10mins from 07.30 until 10.30 so he will have to wait 4 minutes until 4.10pm for the next bus

11. The bus sets off from the City Centre at 2.22PM. Due to traffic the bus is progressively later by 2mins at each bus stop it comes to. At what time will it reach Bedley Road?

A. 3.12PM B. 2.51PM **C. 3.22PM** D. 2.33PM E. 2.20PM

Explanation: use the information in the table and the question. Adding 2 minutes on to each stop means that the bus will be 10 mins late by the time it gets to Bedley road. It should have arrive at 3.12pm but will now arrive at 3.22pm

12. Daniel has an appointment at the General Hospital. What is the time of the last bus he can get from Market Hall in order for him to arrive at the Hospital before 4.40PM, assuming no traffic?

A. 3.40PM B. 3.32PM C. 3.33PM **D.3.30PM** E. 3.39PM

Explanation: Bus comes every 10minutes, and takes 50minutes to get to the hospital. Therefore the last bus he can get to arrive BEFORE 4.40pm is the 3.30pm, as the 3.40pm will get him there AT 4.40PM.

13. If Dr. Peterson arrives at the Royal Infirmary bus stop at 1.13PM how many minutes will it be before he arrives at the General Hospital?

A. 61 B. 62 **C.67** D.51 E.54

Explanation: Royal informing to general hospital takes 61 mins. Dr Peterson has arrived at the bus stop 6 mins early, so it will take him 67 mins.

14. The bus travels at 23 miles per hour on average, between the City centre and Bedley Road – what is the distance in miles between the two stops?

A. 17.62 B. 17.64 C.17.65 D.17.61 **E.17.63**

Explanation: It takes 46 mins to compete this part of the journey. 23 mph for 46 mins gives 23x46/60 = 17.63 miles

15. On the journey from the city centre to the General Hospital the bus has an average speed of 27 mph. The bus uses 0.56L of fuel per mile –How many litres of fuel does it use?

A. 11.58 **B. 11.59** C. 11.56 D.11.60 E. Can’t tell

Explanation: The journey takes 54 minutes. 54/60 x 23 = 20.7miles

20.7x0.56 = 11.59L

16. Mr. Davies reaches the Old Centre bus stop at 9.21PM - how many minutes ago did the last bus leave the stop?

A. 4 **B. 5** C. 6 D. 7 E.8

Explanation: from 7.16am this bus comes every 10 mins, therefore the last bus left at 9.16pm, which was 5mins before Mr Davies arrives.

17. The bus company decides to run a later bus from the City centre at 22.30PM. What time will this bus reach East Lane?

**A. 22.59** B. 21.59 C. 23.00 D. 22.29 E. 23.59

Explanation: from city centre to east lane takes 29 minutes. If the bus leaves at 22.30 it will arrive at 22.59

18. In 2008 how much money was earned selling red ceramic cups?

A. £1450 B. £1400 C. £1350 D. £1250 **E. £1359**

Explanation: 302 cups sold at £4.50 = £1359

19. In 2010 what percentage of total money earned from selling ceramic cups was due to blue ceramic cups?

A. 48% **B. 47.5%** C.47% D. 40% E. 49%

Explanation: 245redcupsx£5 = £1225.

301bluecupsx£4.50 = £1354.5

Added together = 2579.5

Therefore 1225/2569.5 x 100 = 47.5%

20. If in 2011 27% of plastic printed logo cups were sold to customers in USA and Canada, and of these one out of nine were 3 colour logo prints, how much money was earned selling 1 colour logo printed cups to USA and Canada customers?

A. £340 B. £320 C. £49.50 **D.£396** E. £54

Explanation: In 2011 300 plastic cups sold

27% to USA and Canada = 27/100 X 300 = 81 Cups

1/9 were 3 colour logo so 8/9 were 1 colour logo

8/9 x 81 = 72 plastic 1 colour logo cups

@2011 price = £4.50 + £1.00 = £5.50

72 x £5.50 = £396

21. In 2007 340 Red ceramic cups were sold for £4.20 each. In which year was the most money earned from Red ceramic cups?

A. 2007 B. 2008 C. 2009 D. 2010 **E. 2011**

Explanation: 2011 sales = 290 x 5 = £1450

2009 = 321 x 4.5 = 1444.5 – this is the most of 2008-2010 all at same price sp others can be discounted.

2007 = 340 x 4.2 = 1428

22. In 2008, 20% of blue ceramic cups were shipped to the USA and Canada. In 2009 the number of blue ceramic cups shipped to the USA and Canada fell by 14.3%. How many blue ceramic cups were sold to USA and Canada in 2009, to the nearest whole number?

A. 41 **B. 42** C. 43 D. 44 E. 50

Explanation: 2008 245 blue sold

20% of this = 20/100 x 245 = 49 sold to USA and Canada

This fell by 14.3% in 2009 so 14.3/100 = 7 cups

49-7 = 42

23. What was the average amount of money earned to the nearest pound for Red ceramic cups over the 4 years 2008-2011?

**A. £1402** B.£1403 C. £1602 D. £1399 E. £1401

Explanation: 2008- 302x4.5 =1359

2009- 321x4.5 = 1444.5

2010- 301x4.5 = 1354.5

2011- 290x5 = 1450

This adds up to £5608. 5608/4 = £1402

24. In the years 2008-2011, what was the average difference in money earned between blue ceramic cups and red ceramic cups, to the nearest whole pound?

A. £140 B. £141 C. £178 D. £176 **E. £177**

Explanation: simply work out how much money was made from the blue cups in each year and the red cups in each year, subtract the blue cups money from the red cups money for each year and then add up the total.

Blue Red Red-Blue

2008 245x5=1225 302x4.5=1359 134

2009 260x5 = 1300 321x4.5=1444.5 144.5

2010 245x5 = 1225 301x4.5 = 1354.5 129.5

2011 230x5 = 1150 290x 5* =1450 300

*Remember the price change for red cups in 2011 from £4.50 to £5

300+129.5+144.5+134 = 177

25. What area of land (meters squared) does the farmer own?

**A. 9850** B. 9840 C. 9745 D. 7650 E. 5907

Explanation: area of fields 1, 2, 3 + area of field 4 =

((60+25+20)x90) + (16x25) = £98503

26. The sheep pen has an area of 60 square meters, what total length of fence in metres was needed for it?

A. 4.63 **B. 4.62** C. 16.62 D17.62 E.17.61

Explanation: 60/13 = 4.62

27. The farmer wants to put up a new fence around the perimeter all his land. The fence costs £12 per meter, how much will this fence cost?

A. £5060 **B. £5064** C. £3552 D. £3554 E. £5544

Perimeter= 60+25+20+90+90+60+20+16+16+25=5064

28. The farmer decides to remove the sheep pen and decides to spray field 4 with fertiliser. He needs 2 Litres of fertiliser for each square metre. The fertiliser comes in solid granules which are then dissolved in water. To make 1 Litre of fertiliser the farmer needs 200g of granules. The fertiliser is only sold in 11kg bags, costing £7.50 each. How much will the farmer have to spend?

A. £110 B. £121.50 **C. £112.50** D.£211.50 E.£11.25

Explanation: 16x25 = 400 metres squared for field 4

400x400 (2 L per metre squared is needed and there is 400g per 2L)

=16000g = 160kg is needed

So 160/11 will give the amount of bags = 14.54 bags – round this up to 15 as you cant buy half a bag

Therefore 15 bags are needed @ £7.50 = £112.50

29. The farmer wishes to inspect his land and so walks the route ABCDE signified on the diagram by the red dots, each of which is assigned a letter. Walking at 0.8 metres per second, how many minutes will it take the farmer to walk this route?

**A. 238.75** B. 152.8 C. 255 D. 256 E.152.7

Explanation: 60+90+25+16 = 191

191/0.8 = 238.75

30. When walking back, he decides to walk the route EDFBA and walks at 1.2metres per second. How long does this take?

A. 161 B. 159.15 C. 160 **D. 159.17** E. 159.16

Explanation: The distance = 191/1.2 = 159.17

31. The farmer moves his sheep pen to field 4, and wishes to keep one side 13metres long and extend the other side to 10 metres long. What area will be left in field 4 outside the sheep pen after this is done?

A. 265 B.27.5 C.27 D.271 **E.270**

Explanation: field 4 area = 25x16 = 400 metres squared

Sheep pen area = 13x10 = 130 metres squared

Therefore area around sheep pen = 400-130 = 270 metres squared

32. The farmer builds a 7m by 40m barn at one end of field 3. How much land will be left around the barn in metres squared?

A. 152 **B. 1520** C. 1521 D.1519 E. 153

Explanation: 20mx90m = 1800 metres squared area for field 3

Barn area = 280 metres squared

1800-280 = 1520metres squared

33. From the remaining fields 1 and 2, the farmer hopes to grow wheat. He is able to grow 10 tonnes of wheat per hectare, how many tonnes can he grow? 1 hectare = 10,000 metres squared.

A. 7 B. 7.64 C. 8.0 **D. 7.65** E. 7.66

Explanation: Area of fields 1 and 2: 85x90=7650metres squared

This is 0.765 Hectares, therefore the amount of wheat can be produced is 0.765x10 = 7.65

34. After using some wheat as feed for livestock, the farmer takes the remainder to Market where he has secured a price of £200 per tonne. He receives £1120 for the wheat he has brought to the market – how many tonnes did he use to feed the livestock?

**A. 2.05** B. 3.05 C. 4.50 D. 5 E. 6

Explanation: 1120/200 = 5.6 tonnes sold, 7.65 – 5.6 = 2.05 tonnes fed to the livestock

35. In 2008, what proportion of total ticket sales came from adult 2 day ticket sales?

A. 79% B. 80% **C. 80.26%** D. 80.25% E. 80.27%

Explanation: total 76000 tickets sold in 2008

61,000/76000 x 100 = 80.26%

36. What was the difference in number of tickets sold between 2009 and 2011?

A. 1600 **B. 1800** C.1900 D.2000 E. 2010

Total tickets sold in 2009=74000

Total tickets sold in 2011=75800

75800-74000= 1800

37. Between 2008 and 2009 there was a change in the number of tickets sold at the adult price. What was the percentage change in income from adult tickets between 2008 and 2009?

A. +12.50% B. +9.07% C. -6.25% **D. -9.07%** E. -12.50%

Explanation:

2008 = 1200+1300 x 80 = 200,000 add to 15,500x130 = £2215000

2009 = 1000+1100x80 = 168000 and 14200x130 = 184600 so added = 2014000

Therefore in 2008 £2215000earned

2009 £2014000 earned

2014000/2215000 = 0.9093

1-0.9093 = 0.0907 therefore as a percentage x100 =9.07% decrease i.e. -9.07%

38. Booking a ticket incurs a booking charge per ticket regardless of quantity bought at one time. In 2009 this charge was £10 for tickets ordered over the phone, and £5 when tickets were booked online. In 2010 these charges were raised by 15%. In 2010 84% of student tickets were bought online, the remainder by phone; in the same year 75% of adult tickets were bought online, the remainder by phone. What was the total income from booking charges in 2010?

**A. £485438** B. £475639 C. £422120 D.461346 E. £48913

Explanation: In 2010 total student tickets = 50000+3000+3400 = 56400. Of these 16% were by phone =16/100 x 56400 = 9024. 84/100x56400 = 47376 bought online.

In 2010 total adult sales = 11000+3000+1200 = 15,200. 75/100 x 15200= adult ticket sales online = 11400. 25/100x 15200 = 3800=adult sales on phone

Charges increased by 15% so online fee now = 5x115/100 = £5.75

Phone fee now = 10x115/100 = £11.50

Student online = 47376x5.75 = £272412

Phone = 9024x11.5 = £103776

Adult ticket online sales = 11400x5.75 = £65550

Phone sales = 3800x11.5 = £43700

Total = £485438

39. In 2011 a group of friends want to buy some tickets. In the group there are two students and three non-students. One of the students only wants to go one day, as do two of the non students. All the rest of the group wish to go for both days, with camping overnight. How much more will it cost the group as a whole to do this in 2011 compared to 2009?

A. £60 **B. £65** C. £70 D. £55 E. £40

Explanation: Student singles have increased by £5 and one bought

Student 2 day increased by £10 and one bought

Adult single day increased by £15 and 2 bought

Adult 2 day increased by £20 with one bought therefore total =£65

40. What percentage of ticket sales in 2011 were student tickets?

A. 75.53% B. 76.30% C. 76.33% **D. 76.32%** E. 77.48%

Explanation: 58000 – 18000 = 76000

58000/76000 x 100 = 76.32%

41. In 2012 the number of student tickets sold increased by 6.5% on 2011 figures, and constituted 70% of total ticket sales. How many adult price tickets were sold in 2012?

A. 88461 B. 89463 C. 89461 D. 88460 **E.89460**

Explanation:

Total number of tickets sold in 2011, 52000+3200+3600 = 58800

106.5/100 x 58800 = 62622 = 70% of total tickets

Therefore 62621/70 x 30 = 26838

26838+62622 = 89460

42. On average how many tickets were sold between 2009 and 2011?

A. 72800 B. 74800 C. 73820 **D. 73800** E. 73810

Explanation: 2009 – 74000 tickets

2010 – 71600

2011 – 75800

Total = 221400, divide this by three for the average = 73800

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