Working in Kent

Question

1

2

3

4

5

6

7

8

9

Answer

2: 10

5: Frying Tonight

3: July

3: June

1: 20

2: 2 km

3: 3 km

2: 24 kmph

2: 13

Question

10

11

12

13

14

15

16

17

18

Answer

5: 25

3: 7/8

4: 18

4: 30

4: 48 mph

5: 3534 m

2: £265

1: £11,592

5: £11,523

Question

19

20

21

22

23

24

25

26

27

Answer

1: £6

5: 64

2: 5

3: 585

1: 125

5: Can't say

3: May

2: 22%

5: £1,177,800

How to work out the answers

1) 83 -17 = 56 + ?
66 = 56 + ?
? = 66 - 56 = 10

2) Which company's sales were most consistent throughout the year?
Range of Frying Tonight is minimum 1 (e.g. January) to maximum 3 (e.g. May): a range of only 2.

3) In which month did the sales of Hole in Roof and Stones' Throw differ the most?
Sales of Hole in the Roof are 2 in July: sales of Stones' Throw are 9 that month: a difference of 7 which is the greatest difference.

4) Which month gave the largest number of sales for all the companies combined?
June: 3 + 6 + 6 + 7 + 8 = 30 sales in June

5) What was the percentage increase in sales for Hot House between July and August?
Hot House sales in July = 5. Sales in August = 6
a) Find the difference between the two numbers: 6 - 5 = 1
b) Take this difference (1) and divide by the original number: 1/5 = 0.2
c). Lastly, multiply this by 100: 0.2 x 100 = 20%

6) How far does the student walk in total?
One km from 8.00 to 8.10 and another km from 8.25 to 8.35 = 2 km total

7) How far is he from the university students' union at 8.20 am?
Students' union is at 6 km distance from home.
At 8.20 am student is at 3 km from home. Therefore he has 3 km still to travel to the union.

8) What is the average speed of the bus?
Student gets on bus at 8.15 am at 1 km from home.
Student gets of bus at 8.25 am at 5 km from home.
Therefore bus travels 4 km in 10 minutes
The bus would travel six times as far in one hour = 6 x 4 km in one hour = 24 kmph

9) What is the missing number? 56 / 7 = ? - 5
56/7 = 8
Therefore 8 = ? - 5
8 = 13 - 5

10) What is the missing number? 20 / 0.8 = ?
20 / 0.8 = 25 (NOT 16: try it on a calculator if you don't believe it. Dividing by a fraction always gives a larger number)

11) Which is the largest fraction: 3/4 7/8 4/5 7/9 7/10
3/4 = 0.75, 7/8 = 0.875, 4/5 = 0.8, 7/9 = 0.777..., 7/10 = 0.7

12) If oranges cost 5 for 75p how many can you buy for £2.70? (Assuming they can be bought singly)
5 oranges cost 75p, therefore one orange costs 75 divided by 5 = 15p
£2.70 is the same as 270p.
Therefore the amount of oranges you get for 270p
= 270 divided by the cost of one orange
= 270 divided by 15
= 18 oranges

13) A shed has a side wall of the dimensions shown. Calculate the area of the wall in square feet.
Area = area of square + area of triangle at top
Area of square = length x width = 6 x 4 = 24 square ft
Area of triangle = base x perpendicular height / 2 = 6 x (6 -4) / 2 = 6 sq ft
Total area = 24 + 6 = 30 sq feet
Or you can use the formula for the area of a trapezium.
Area = average of the length of the two different sides x length of base
= (6 + 4)/2 x 6 = 5 x 6 = 30

14) A car left Canterbury at 7.12 am and arrived in Birmingham, 180 miles distant at 10.57 am. What was its average speed in miles per hour?
Time taken = 3 hours 45m = 3.75 hours (15/4 hours if you prefer fractions).
Speed = distance / time taken = 180 / 3.75 = 48 mph

15) An aircraft flies 930 miles in 75 minutes. How many miles does it fly in 4 hours 45 minutes assuming a constant speed?
75 minutes = 75 / 60 hours = 1.25 hours (or 5/4 hours if you prefer fractions)
Speed of aircraft = 930 / 1.25 = 744 mph
4 hours 45 m = 4.75 hours (or 19/4 hours in fractions)
Therefore aircraft will fly 744 x 4.75 miles = 3534 miles

16) You get a wage increase of 4% plus an extra £5 per week. Your present wages are £250 per week. What will your new wage be?
Present wage = 250
4% of 250 = 4 x 2.5 = £10
Therefore new wage = 250 + 10 + 5 = £265

17) What is the total income of the taxi driver for the whole year?
Average fare = 4 x 90p = £3.60
Income per week = 70 fares at £3.60 each = 70 x 3.60 = £252
Income for 46 weeks work = £252 x 46 = £11,592

18) What is her total expenditure over the year to the nearest pound?
Car/Service/MOT/Repairs/ Insurance = £1250 p.a.
Mortgage costs = £250 per month = 250 x 12 per annum = £3000 p.a.
Other expenditure = £125 per week = £125 x 52 per annum = £6500 p.a.
Diesel fuel costs = 6p per mile.
Annual mileage = 4 miles x 70 fares per week = 280 miles per week
= 280 x 46 weeks worked each year = 12,880 miles
Therefore diesel cost = 12,880 x £0.06 = £772.8
Therefore total expenditure = £1250 + £3,000 + £6,500 + £772.8 = £11,522.8 = £11,523 to nearest pound

19) What is her average excess of income over expenditure per month to the nearest pound?
Income p.a. = £11,592 Expenditure p.a. = £11,523 (answers to previous two questions)
Therefore excess of income over expenditure = £69 p.a. = £69 / 12 per month = £5.75 = £6 per month to nearest pound

20) A cube has a volume of 8 cubic metres. If each side is doubled in length what will its new volume be in cubic metres?
Volume = length x width x height
8 = l x w x h but l, w and h are all equal as it is a cube
Therefore l = w = h = 2m
If each side is doubled in length l = w = h = 4m
Therefore new volume = 4 x 4 x 4 = 64 cubic metres
Or if you prefer the quicker method. If each side is doubled in length then the new volume must be 2 to the power 3 bigger = 8 x 8 = 64

21) A driver drives 8 km South then 6 km W. and 2 km S. again. She then drives 3 km E. to avoid a traffic jam before driving 6 km N. How many kilometres is she from her starting point?
Total distance driven South = 8 + 2 - 6 km = 4 km
Total Distance driven West = 6 - 3 km = 3 km
This makes a right angled triangle where the distance from her starting point is the hypotenuse.
Using Pythagoras Theorem: "In any right triangle, the area of the square whose side is the hypotenuse (is equal to the sum of the areas of the squares of the other two sides"
4 squared + 3 squared = hypotenuse squared
16 + 9 = 25 = hypotenuse squared
Therefore hypotenuse (distance from starting point) = square root of 25 = 5km
Or a simpler method is to see that the distances make a 3, 4, 5 triangle so the distance from start is 5 km

22) What was the largest number of students in any year that went on to further study?
2004 has the most students entering further study: 39% of 1500 students
39/100 x 1500 = 585 students in 2004

23) What was the decrease in the number of graduates in employment between 2002 and 2004?
Number of graduates in employment in 2002 = 1,700 x 40/100 = 680
Number of graduates in employment in 2004 = 1,500 x 37/100 = 555
Decrease = 680 - 555 = 125 graduates

24) In 2004 how many social science students were in employment after graduating?
Can't say: there is insufficient data.

25) Which month showed the largest total decrease in PC sales over the previous month?
Drop is from 3,400 + 3,800 + 2,900 in April (total 10,100) to 2,800 + 2,900 + 2,900 in May (total 8,600), a drop of 1,500.

26) What percentage of Manufacturer 2's sales were made in April (to the nearest percent)?
Manufacturer 2's Sales are March 4,100 April 3,800 May 2,900 June 3,100 July 3,500
Total Sales = 17,400
Sales in April = 3,800
Percentage of sales in April = 3,800 / 17,400 x 100 = 21.8% = 22% rounded to nearest percent

27) If the average profit made on each PC sold by Manufacturer 3 over all 5 months was £78 what was the total profit on all sales in this period by that manufacturer?
Total sales for Manufacturer 3 = 2,800 + 2,900 + 2,900 + 3,200 + 3,300 = 15,100
Profit per PC = £78, therefore total profit = 15,100 x £78 = £1,177,800

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