Answers to questions 26 - 40
Question 26
Total man km in 2010 is 300 million
Total man km in 2015 is 450 million
 difference is 150 million, that is 50% of 300 million (answer d)
Comment: this is a simple operation!
Question 27
Recommendation: start off by calculating the approximate percentages to see if any
of them is different from the others.
Increase in private cars
260 minus 175 equals 85  85 into 100 divided by 175 or approximately 50%
Two times 85 is 170, so that is approximately 50%, if you need to calculate
further, you are going wrong somewhere. The operations must be possible by mental
reckoning.
Increase in bus
90 minus 50 equals 40
 40 into 100 divided by 50 equals 80%
4/5th is 80%. It is good to know that by heart, but in any case when the denominator
is 5, you only need to multiply by two above and below to get the percentage directly.
4 into 2 over by 5 into 2 equals 4 into 2 x 10 over 5 into 2 x 10 equals 80 over 100
Increase in rail
100 minus 75 equals 25  25 into 100 divided by 75 is approximately 33%
(25 is a third of 75 and a third is 33%)
The approach pays as the bus percentage is clearly different (answer b).
Question 28
The difficulty lies in understanding the question, which is incorrectly translated. What
we are looking for is the number of km covered by the trains.
In 2010, all the people who took the train covered 75 million km.
The average of 250 people per train means that each km covered by a train is equal
to 250 man kilometres.
That means that the trains have covered
75 million divided by 250 (i.e. the number of people per train/km)
I.e., after simplification by 10: 7.5 million divided by 25 or 300,000 (same calculation
– 75 divided by 25!)
(answer d)
Question 29
Calculation identical to question 28 for the number of km covered by trains and cars
in 2015:
No of km covered by trains:
100,000,000 divided by 200 or 1,000,000 divided by 2 or 500,000
No of km covered by cars:
260,000,000 divided by 1.3 or 2,600,000,000 divided by 13 or 200,000,000
Ratio = 200,000,000 divided by 500,000 or 2000 divided by 5 or 400 (answer a)
Question 30
Interpretation of stage 1:
Transport by bus/taxi 2015: 90,000,000 man kilometres.
If taxis account for 10% of the figure, 9,000,000 man kilometres by taxi.
Interpretation of stage 2: same principle as question 28
 number of km covered by taxis is 9,000,000 divided by 3 or 3,000,000 (answer b)
Question 31
Method:
To avoid working with figures with many zeros, it is simpler to express the revenue in
kilograms (divide the values of the revenue line by 100)
Fruit
Apples
Pears
Cherries
Bilberries
Peaches
Plums
 answer c
Harvested qty
(*10,000 kg)
100
20
60
20
10
40
Revenue for
1 kg
1
1.5
2
2.4
1.6
1.2
Revenue
100
30
120
48
16
48
Question 32
The answer is derived directly from the calculation of question 31, if you take away
cherries, plums and peaches, you are left with
- Apples, revenue 100
- Pears, revenue 30
- Bilberries, revenue 48.
 answer b
Question 33
Find a common multiple for the costs of picking and growing. In view of question 35,
it is preferable to select kg (divide the figures of the picking costs line by 100 and
those of the growing costs line by 1000)
Fruit
Apples
Pears
Cherries
Bilberries
Peaches
Plums
 answer a
Picking costs per Growing costs
kg
per kg
0.5
0.05
0.5
0.05
1
0.04
0.8
0.06
0.6
0.06
0.6
0.04
Total
0.55
0.55
1.04
0.86
0.66
0.64
Other way of reasoning (faster):
- For the picking costs, the answer can be read off the table directly
(cherries). Maximum value of line 100 (or 1 per kg).
- This answer could be affected by growing costs only if for any of the fruit,
you get 1 for 1 kg or 1000 for 1000 kg (unit of expression of the growing
costs line), which is never the case (far from it).
Question 34
There is a factor of 10 between the units of expression of the two types of cost. The
exact calculation of the growing costs in relation to the picking costs must therefore
be done with the following formula:
Growing costs into 10 divided by the picking costs
The factor of 10 is therefore not important, in that one of the answers is necessarily
correct.
That means you only have to focus on the result of the division of growing costs by
picking costs.
Pears (50 over 50) and Cherries (40 over 100) can be eliminated straight away.
You only need to calculate 60 over 80 (which is three-fourths or 0.75) and (for
checking) 40 over 60, which is two-thirds or 0.66.
Question 35
Arithmetic method
Fruit
Apples
Pears
Cherries
Bilberries
Peaches
Plums
Revenue for
1kg
1
1.5
2
2.4
1.6
1.2
Costs for 1
kg
0.55
0.55
1.04
0.86
0.66
0.64
Profit
0.45
0.95
1.96
1.54
0.94
0.56
Deduction method:
- Pears can be eliminated as their revenue is greater than that of apples for
the same costs.
Question 36
= calculate the average
Average habitable area per inhabitant: average habitable area by home divided by
the average number of people in a family
 15 divided by 3 or 5 square metres.
This is only true when each family has only one home.
Question 37
= calculate the average
Average housing costs per square metre: annual housing costs per family divided by
the average habitable area per home
 10,000 divided by 20 or € 200.
(housing costs are expressed in multiples of 10,000 euros).
Question 38
= calculate the percentage
Share of the average annual income devoted to housing:
Average annual housing costs per family divided by average annual income per
family multiplied by 100
 1.2 into 100 divided by 3 equals 120 divided by 3 or 40%.
Question 39 (cancelled)
Calculation of the share of the annual income that is not devoted to housing:
- country A: 3 minus 1.2 equals 1.8
- country B: 4 minus 1 equals 3
Calculate the share by family member:
- country A: 1.8 divided by 3 equals 0.6
- country B: 3 divided by 4 equals 0.75
Relation between the average amount between inhabitants of countries A and B:
Share per member in country A divided by share per member in country B
 = 0.6 divided by 0.75 is the result to be expressed as one of the answers.
0.6 divided by 0.75 equals 60 divided by 75 equals 4 divided by 5
(simplification by 15: 60 equals 4 times 15 and 75 equals 5 times 15).
Question 40
= calculate the weighted average
Average no. of rooms per home in country C:
No. of rooms in country A into no. of families in country A + no. of rooms in country B
into no. of families in country B divided by no. of families in country A plus number of
families in country B
The number of families of countries A and B are unknown. But we do know that the
no. of families in country A is twice that in country B. So the number of families in
country A is 2 and the no. of families in country B is 1.
 2.5 into 2 + 4 into 1 divided by 3 equals 5 plus 4 divided by 3 equals 3