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# Numerical Reasoning Explanation

## Explanation Numerical Reasoning Easy

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1. The graph shows that with every minute 2 l of water flows from the tap. Also at 4 minutes 10 liters has run from it.
4 min + 6 min = 10 min
2 l/min*6 min=12 l
10 l + 12 l = 22 l

2. The graph is a linear curve so it has formula y=ax+b whereas y is the amount of water and x is the time in minutes.
b can be found by checking the value for x=0 min, which gives 2 l at o min so b = 2
a can be found by filling in the formula with a random point and the found b value, using the point at 4 minutes this gives: 10 = a*4 + 2, which gives a = 2
So the correct formula is y = 2x + 2

3. There was 2 l of old water in the barrel.
When the barrel reaches 10 l there is 10 l – 2 l = 8 l of fresh water in there. so the ratio fresh water / old water = 8 l / 2 l = 4.

4. The tap runs with 2 l/min.
So in 60 minutes 60 min * 2 l/min = 120 l
120 l * \$0,25 = \$30

5. Loda Cola sales = 12%
Total sales = 3200
3200/100% * 12% = 384

6. Market share of Orange Fruity in March 2012 is 35%, so its market share in January is 35% – 20% = 15%
2500 sales January gives 2500/100% * 15% = 375

7. You cannot answer this since you have only information on March 2012, so the correct answer is Cannot say.

8. Current market share 6-Down = 23%
Current market share Orange Fruity = 35%
Total sales = 3200.
6-down sales = 3200/100% * 23% = 736
Orange Fruity sales = 3200/100% * 35% = 1120
Total sales – Orange Fruity sales = 3200 – 1120 = 2080 sales
6-Down sales / 2080 sales * 100% = 736 / 2080 * 100% = 35,38%
So 35% is the correct answer

## Explanation Numerical Reasoning Medium

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1. The total amount of seats is 43 + 22 + 112 + 28 + 76 + 15 + 40 + 9 = 345
2/3 * 345 = 230 seats
230 seats with 2 parties is impossible since the two biggest GADER(112 seats) and JHG(76 seats) add up to 112 + 76 = 188
230 – 188 = 42 the only other party with more than 42 seats is PVW with 43 seats.

2. Total seats = 345
JHG seats = 76
76 / 345 * 100% = 22%

3. New total seats = old total seats – GADER seats = 345 – 112 = 233 seats
2/3 * 233 = 155,3 so 156 is a 2/3 majority
The two biggest parties now are JHG(76 seats) and PVW(43 seats)
156 – (76 + 43) = 37 seats the only party left with more than 37 seats is Dem Front
So still 1 combination is possible(JHG+PVW+Dem Front)

4. New total seats = old total seats – GADER seats = 345 – 112 = 233 seats
JHG seats = 76
76/233 * 100% = 32,6 so 33%

5. % increase = (new – old)/old * 100%
old = 112 – 80 = 32
% increase = (112 – 32)/32 * 100% = 250%

6. For the actual value in Japanese Yens(JPY) you don’t have to take a transaction fee into account.
According to the table 1 euro is worth 114,96 JPY
So 730 euro * 114,96 Yen = 83920,80 yen

7. Again for the actual value in Australian dollars(AUD) you don’t have to take a transaction fee into account.
1 euro = 16,66 Mexican Pesos
173/16,66 = 10,384 euro
1 euro = 1,25 Australian Dollar
10,384 * 1,25 = 12,98 Austalian Dollar

8. This is an exchange at the bank so a transaction fee has to be paid.
1 euro = 7,30 Norwegian Krone
200 / 7,30 = 27,397 euro
Transaction costs are 2 euro + 2%
27,397 – (0,02 * 27,397) – 2 = 24,85 euro

9. First calculate the total value in euros:
1 euro = 10,09 HKD = 1,25 AUD
12 / 10,09 HKD = 1,189 euro
17 / 1,25 AUD = 13,60 euro
15 euro + 1,189 euro + 13,60 euro = 29,789 euro
Now deduct the transaction costs:
29,789 – (0,02 * 29,789) – 2 = 27,193 euro
Now transfer this to NOK:
1 euro = 7,30 NOK
27,193 * 7,30 = 198,51 NOK

10. Rental price per m2 per month = \$50
100 m2 * \$50 * 12 months = \$60000
Yearly building management fee = \$400
Yearly taxes per m2 = \$90
90 \$/m2 * 100m2 = 9000\$
This leads to \$60000 + \$400 + \$9000 = \$69400

11. You can simply calculate the prices for all cities, but with some clever thinking you can reduce the amount of work:
You’ll have to see that with a house of 1000 m2 the yearly building management fee is neglegible since this fee is not dependant on the size of the house.
Of the rental price and taxes the rental price is the dominant factor since this is per month so you multiply it not only by the house surface but also by 12 for 12 months.
Taking this into account it seems that either Piras or Langel are the cheapest cities after Emor.
Now lets calculate this for both Piras and Langel:
Piras: (1000 m2 * \$45 * 12 months) + \$350 + (1000 m2 * \$120) = \$660350
Langel: (1000 m2 * \$50 * 12 months) + \$400 + (1000 m2 * \$90) = \$690400
This shows Piras is the cheapest place to live after Emor but since Emor is were Leonardo wants to move away from, he will have to move to Piras.

12. You cannot say this since it is dependant on the size of the house, so the correct answer is “Cannot say”.

13. First calculate the current costs for a 100 m2 house in Emor:
(100 m2 * \$40 * 12 months) + \$300 + (100 m2 * \$36) = \$51900 per year
\$51900 / 12 months = \$4325 / month
% increase = (new – old) / old * 100% = (\$4325 – \$150) / \$150 * 100% = 2783%

## Explanation Numerical Reasoning Hard

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1. This is a trick question, since you do not know how many flowers are in a bouquet you cannot answer this question, so the correct answer is “Cannot say”.

2. Since it is the biggest relative price fluctuation you should take the highest and lowest price of every flower and divide them. The highest number is the highest relative price fluctuation:
low/high = relative price fluctuation
Violets 5,00/1,59 = 3,14
Chrysanthemums 10,99/4,49 = 2,44
Christmas trees 63,00/20,00 = 3,15
Sunflowers 12,75/3,99 = 3,19
Tulips 9,99/2,99 = 3,34
So tulips are the right choice

3. Since all seasons are equally long You can just add up the flower prices of every season per flower. The second lowest number will be the correct choice. Christmas trees don’t count since this is no bouquet.
Violets 1,59 + 5,00 + 1,59 + 5,00 = 13,18
Chrysanthemums 10,99 + 10,99 + 4,49 + 10,99 = 37,46
Sunflowers 12,75 + 3,99 + 6,49 + 8,99 = 32,22
Tulips 2,99 + 9,50 + 9,99 + 4,99 = 27,47
So tulips is the right choice

4. bouquets * price = yield
Violets 433 * 1,59 = 688,47
Chrysanthemums 635 * 4,49 = 2851,15
Christmas trees 76 * 40,00 = 3040
Sunflowers 412 * 5,49 = 2261,88
Tulips 167 * 9,99 = 1668,33
So Christmas trees is the correct answer

5. spring sales/total sales * 100%
876/(876 + 158 + 167 + 478) * 100%
876/ 1679 * 100% = 52%

6. (new – old)/old * 100%
((433 + 635 + 76 + 412 + 167) – (158 + 967 + 126 + 112))/(158 + 967 + 126 + 112)
(1723 – 1363)/1363 * 100% = 26%

7. First you should see that you’ll have to exclude christmas trees since these are not sold as bouquets but a piece.
add up all other prices and divide by the number of prices added up.
(1,59 + 5 + 1,59 + 5,00 + 10,99 + 10,99 + 4,49 + 10,99 + 12,75 + 3,99 + 6,49 + 8,99 + 2,99 + 9,50 + 9,99 + 4,99)/16 = 6,90€

8. new year – old year/ amount of years
1990-1995 (200 – 500)/5 = -60
1995-1998 (400 – 200)/3 = 67
2002-2008 (250 – 450)/6 = 33
2008-2010 (350 – 250)/2 = 50
So 1995-1998 has the highest averaghe annual change.

9. 2% increase for 2050 – 2010 = 40 years
1,0240 * 2010 sales
1,0240 * 350 = 772,814
house sales are x1000 so 772814 is the correct answer

10. 1% increase for 5 years and 2% increase for 5 years
1,015 * 1,025 * 350 = 406,14
housesales x1000 makes 406140 sales

11. This depends on the speed with which you are driving so since you have no information on this the correct answer is “Cannot say”.

12. distance / speed = travel time
speed is either the speed limit or the top speed of the car.
M3: 175 mph/100 mi = 1,75 hour
S12: 150 mph/70 mi = 2,14 hour
M6: 200 mph/130 mi = 1,54 hour
S7: 125 mph/40 mi = 3,125 hour
So the M6 will be the fastest

13. Leonardo wants to be at his destination as fast as possible and it says nowhere that he doesn’t want to cross the speed limit, so assume he will drive all roads at top speed. If he drives the same speed at all roads the correct answer has to be the shortest road which is the S7.

14. This will be the Hindah. It won’t reach 100 mph since its top speed is 90 mph but nowhere is mentioned that the drive has to be as fast as possible.

15. The car will have to drive up and down twice so first calculate the total distance per motorway:
M3: 4 * 175 mi = 700 mi
S12: 4 * 150 mi = 600 mi
M6: 4 * 200 mi = 800 mi
S7: 4 * 125 mi = 500 mi
Looking at fuel consumption the M6 is no option since the drivers want to drive as fast as possible. All cars use a lot of fuel when driving full speed and combined with the fact that this is the longest road leads to the conclusion that the M6 is not the right road to take.

Now calculate the minimum speed required to drive this distance within 8 hours:
M3: 700 mi/8 hours = 87,5 mph
S12: 600 mi/8 hours = 75 mph
S7: 500 mi/8 hours = 62,5 mph
This shows the S12 and the S7 are not valid options since the minimum required speed is above the maximum allowed speed.

So the best road to take is the M3. Now simply check the fuel usage table for the car that has the lowest fuel usage at 100 mi/hour, which is the Olfo.
So the Olfo on the M3 is the correct answer.

16. The correct answer is “Cannot say” since his speed is not mentioned anywhere.

17. The Ditch always uses 25 mpg so it is no problem that you don’t know its speed.
Gallons of gas = total distance/mpg
3250/25 = 130 gallons

18. Total Opal sales/total BMV Sales
(130 + 230 + 50 + 90 + 40)/(10 + 140 + 30 + 60 + 260)
540/500 = 1,08

19. Total amount of cars May 2012 = 540 + 500 = 1040
Total amount of cars April 2012 = 1040/2 = 520
Ratio Opal/BMV May 2012 = 1,08
Ratio Opal/BMV April 2012 = 2 * 1,08 = 2,16
Opal cars April = x
BMV cars April = 520 – x
Opal/BMV April = x/(520-x) = 2,16
1123,4 – 2,16x = x
1123,4 = 3,16x
x = 1123,4/3,16 = 355,5 Opal cars.
520 – x = 520 – 355,5 = 164,5
So 165 Opal cars is the correct answer

20. Ratio Opal/BMV in Cornercity = 230/140 = 1,64
Total cars sold in Signtown = 50 + 30 = 80
x/(80 – x) = 1,64
x = 131,2 – 1,64x
2,64x = 131,2
x = 49,69
So still 50 Opals would have been sold

21. Since you don’t know how the sales in Greendale will develop you cannot answer this question, so the correct answer is “Cannot say”.