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Top 50 Numerical Reasoning Questions

Numerical Reasoning Test

A numerical reasoning test is a form of psychometric assessment commonly used in the application stages of the recruitment process. It is specifically designed to measure a candidate’s numerical aptitude and their ability to interpret, analyze, and draw conclusions from sets of data.

They’re often used in conjunction with other psychometric tests, including verbal reasoning tests, personality tests, and situational judgment tests.

Unlike standardized maths tests, which demonstrate a student’s ability to learn and apply mathematical techniques based on a set syllabus, numerical reasoning tests reflect how successfully a candidate can apply numerical understanding in a realistic context.

General arithmetic, percentages, fractions, and averages are all common elements of a numerical reasoning test, but its main focus is statistical information. Candidates are required to work with graphs, tables, and charts to identify key facts and figures and apply the correct logic to form an answer in response to a worded question.

You may be required to sit a numerical reasoning test if you’re applying for a job in a numeracy-based sector, such as finance or insurance. That said, they are increasingly common for any role that involves a level of data interpretation or numerical analysis, including marketing and HR.

 

 

 

How to Pass Numerical Reasoning Job Test: Questions and Answers

Top 50 Numerical Reasoning Job Test: Questions and Answers

Jack’s phone provider charges him $30.00 for his first 45 minutes of calls each month, plus $0.75 for every additional full minute of calling after that. If Jack’s total bill last month was $41.25, approximately how many minutes did he spend calling?

A) 53
B) 57
C) 59
D) 60

 

The correct answer is: (D) 60

  • If Jack is charged more than $30.00, that means he spent at least 45 minutes calling.
  • To find the total amount of time, subtract $30.00 from the total $41.25 bill to get $11.25.
  • Then divide $11.25 by $0.75 (the cost of each additional minute after the 45-minute mark).
    • $11.25 ÷ $0.75 = 15, meaning 15 more minutes of calling after the initial 45 minutes.
    • 45 + 15 = 60.

Determine the next number in this sequence:

11, 19, 16, 19, 21, 19, __

A) 24
B) 26
C) 37
D) 42

The correct answer is: (B) 26

  • This sequence may seem impossible and completely illogical at first, with seemingly no pattern connecting the numbers. However, try looking at the sequence again but this time disregard the 19’s:
    • 11, 19, 16, 19, 21, 19, __
  • Do you see it now? The 19’s are just a red herring meant to distract you from the numbers in between, which are just increasing by five, and 21 + 5 = 26.

George left his house at 3:00 PM on Friday and traveled 867 miles before arriving at his desired destination at 8:00 AM the following day. Assuming that his home and destination are in the same time zone, what was George’s average speed, in miles per hour, over the course of his trip?

A) 47
B) 51
C) 53
D) 58

 

The correct answer is: (B) 51

  • Total distance traveled = 867 miles
  • Total time spent traveling:
    • 3:00 PM to 12:00 AM = 9 hours;
    • 12:00 AM to 8:00 AM = 8 hours.
    • 9 hours + 8 hours = 17 hours.
  • Average speed = miles per hour
  • Miles per hour = (total miles ÷ total time):
    • 867 miles ÷ 17 hours = 51 miles per hour

A) 4
B) 5
C) 6
D) 7

 

The correct answer is: (A) 4

  • During his first 10 minutes of jogging, Vincent went 6 MPH, meaning that he ran at a rate of 6 miles every 60 minutes, or 1 mile every 10 minutes (60 ÷ 6 = 10). Since we know he ran for 10 minutes, we also know that he covered 1 mile over this period.
  • During his next 20 minutes, Vincent walked at a rate of 3 MPH, or 3 miles every 60 minutes, or 1 mile every 20 minutes (60 ÷ 3 = 20).
  • If he walked at a rate where he would have covered a mile every 20 minutes and walked for a duration of 20 minutes, this means that he walked 1 mile.
  • 1 mile + 1 mile = 2 miles covered in 30 minutes
  • We are looking for his rate of miles per hour, and if Vincent went 2 miles in 30 mins, he would have traveled 4 miles in 60 mins.

A) 4
B) 5
C) 6
D) 7

The correct answer is: (A) 4

  • During his first 10 minutes of jogging, Vincent went 6 MPH, meaning that he ran at a rate of 6 miles every 60 minutes, or 1 mile every 10 minutes (60 ÷ 6 = 10). Since we know he ran for 10 minutes, we also know that he covered 1 mile over this period.
  • During his next 20 minutes, Vincent walked at a rate of 3 MPH, or 3 miles every 60 minutes, or 1 mile every 20 minutes (60 ÷ 3 = 20).
  • If he walked at a rate where he would have covered a mile every 20 minutes and walked for a duration of 20 minutes, this means that he walked 1 mile.
  • 1 mile + 1 mile = 2 miles covered in 30 minutes
  • We are looking for his rate of miles per hour, and if Vincent went 2 miles in 30 mins, he would have traveled 4 miles in 60 mins.

A) $35
B) $45
C) $50
D) $75

The correct answer is: (C) $50

  • Monthly salary = $1,500
  • Half of the monthly salary (1500 ÷ 2= 750) or $750, go towards bills.
  • A third of total bills ($750 ÷ 3 = $250) or $250 goes towards utility expenses.
  • A fifth of his total utility expenses ($250 ÷ 5 = $50) or $50 goes specifically towards heating bills.

A) $800
B) $1,200
C) $1,450
D) $1,650

The correct answer is: (B) $1,200

  • Hugh’s first option would have cost him $14,800.
  • On the other hand the second option, which he decided to use, cost him $600 up front + $15,400 in monthly payments ($350 per month x 44 months = $15,400). $600 + $15,400 = $16,000.
  • Hugh’s second option, $16,000, cost him $1,200 more than his first option, $14,800 ($16,000 - $14,800 = $1,200).

2, 4, 12, 48, 240, __

A) 1,200
B) 1,250
C) 1,360
D) 1,440

The correct answer is: (D) 1,440

  • Next Number Calculation Formula:
    • n = Position of number in sequence (e.g. 1,2,3 )
    • Next Number = Prev Number x (n+1)
  • The first number, 2, is multiplied by 2; the second number is multiplied by 3; the third number is multiplied by 4, and so on. For example:
    • 2 x (1+1) = 4
    • 4 x (2+1) = 12
    • 12 x (3+1) = 48
    • 48 x (4+1) = 240
    • 240 x (5+1) = 1,440

A) $101,200
B) $102,000
C) $103,333
D) $104,480

The correct answer is: (A) $101,200

  • Initial salary = $80,000
    • First raise increases her salary by 15%
    • $80,000 x 1.15 = $92,000
  • Second raise increases her new salary ($92,000) by 10%
    • $92,000 x 1.1 = $101,200

*Hint: 1 lb = 0.454 kg*

A) 18.879
B) 19.047
C) 20.412
D) 21.462

The correct answer is: (C) 20.412

  • On the first day, she bought 36 lbs of watermelon
    • On the second day, she purchased ¼ of the amount that she got on the first day.
    • 36 ÷ 4 = 9. This means that she purchased 9 lbs of watermelons on the second day
    • Therefore, she purchased 45 lbs of watermelons over the course of two days: 36 + 9 = 45 lb
  • 1 lb = 0.454 kg
    • 45 * 0.454 kg = 20.412 kg

1, 4, 9, 16, __

A) 21
B) 23
C) 25
D) 26

The correct answer is: (C) 25

  • Identify the pattern
    • Next Number – NN
    • Previous Number - PN
    • NN= Number Count 2
  • Calculating the Next Number
    • 1^2 = 1
    • 2^2 = 4
    • 3^2 = 9
    • 4^2 = 16
    • 5^2 = 25

A) 30%
B) 40%
C) 52%
D) 70%

The correct answer is: (C) 52%

  • Earnings 100% , Rent 30%
  • Cost of dishwasher purchase is 40% less than what was spent on the rent
    • 30% x (1 - 0.40) = 30% x 0.6 = 18 %
  • Spent on the rent and dishwasher total
    • 30% + 18% = 48%
    • 100% - 48% = 52%
  • John had leftover 52 % of his last month's earnings

1, 8, 22, 50, __

A) 96
B) 106
C) 116
D) 126

The correct answer is: (B) 106

  • Formula calculating next number
    • Next Number – NN
    • Previous Number - PN
    • NN= PN + 6 + PN = 2*PN + 6
  • Calculating the following number
    • 1 + 6 + 1 = 8
    • 8 + 6 + 8 = 22
    • 22 + 6 + 22= 50
    • 2 * 50 + 6 = 106

A) 10%
B) 40%
C) 43%
D) 140%

The correct answer is: (C) 43%

  • If original speed is 1, then
  • Initial speed increase
    • 1 x 1.3 = 1.3
  • The total increase in speed
    • 1.3 x 1.1=1.43

1, 5, 13, 29, ___

A) 51
B) 61
C) 73
D) 83

The correct answer is: (B) 61

  • Identifying the pattern:
    • Next Number – NN
    • Previous Number – PN
    • Number Count = Number in Pattern
    • NN= PN + 2 (Number Count)
  • Calculating the next number:
    • 1 + 22= 1 + 4 = 5
    • 5 + 23= 5 + 8 = 13
    • 13 + 24= 13 + 16 = 29
    • 29 + 25= 29 + 32 = 61

A) $1,700.00
B) $1,875.00
C) $2,250.00
D) $2,875.00

 

The correct answer is: (C) $2,250.00

  • Understanding the problem
  • First $1000.00 – 0% Import Tax, then 7%, Bob paid $87.5 of Import Tax
  • What amount was taxed
    • $87.5 / 7% = $x / 100%
    • x = $87.5 x 100% / 7%
    • x = $1,250.00
  • Total Value of the imported goods
    • $1000 + $1,250 = $2,250.00

2, 5, 8, 11, __

A) 12
B) 13
C) 14
D) 15

The correct answer is: (C) 14

  • Identifying the pattern
    • Next Number – NN
    • Previous Number - PN
    • NN= PN + 3
  • Calculating Next Number
    • 2 + 3=5
    • 5 + 3 = 8
    • 8 + 3 =11
    • 11 + 3 = 14

A) 5.0%
B) 7.2%
C) 8.1%
D) 145%

The correct answer is: (C) 8.1%

  • First Exchange Rate
    • EUR300=$580
    • ER1=EUR/$=580/300=1.93
  • Second Exchange Rate
    • EUR440=919.60
    • ER2=EUR/$=919.6/440=2.09
  • Percent change of the Exchange Rate
    • 2.09-1.93=0.1566
  • Percentage Increase in the exchange rate 0.1566/1.93 x 100=8.1

4, 12, 36, 108, __

A) 310
B) 314
C) 320
D) 324

The correct answer is: (D) 324

  • Identifying the pattern
    • Next Number – NN
    • Previous Number - PN
    • NN= PN x 3
  • Calculating Next Number
    • 4 x 3 = 12
    • 12 x 3 = 36
    • 36 x 3 = 108
    • 108 x 3 = 324

0, 1, 8, 27, 64, __

A) 85
B) 101
C) 115
D) 125

The correct answer is: (D) 125

  • Identify the patern
    • Next Number – NN
    • Previous Number - PN
    • NN= Number Count 3
  • Calculating the Next Number
    • 1^3 = 1
    • 2^3 = 8
    • 3^3 = 27
    • 4^3 = 64
    • 5^3 = 125

A) 5
B) 7
C) 8
D) 9

The correct answer is: (B) 7

  • The box can’t have more than one of the yellow marbles, because if there were two then there would’ve been 14 of the green.
  • There’s one yellow marble
  • There’re seven green marbles 1 x 7 = 7
  • The number of the orange marbles
  • 15 total – 1 yellow – 7 green = 7 orange marbles

The first and second bookshelves together have 80 books. The first and third bookshelves together have 60 books. The second and third bookshelves together have 40 books.

A) 1st - 40 2nd - 40 3rd - 20
B) 1st - 50 2nd - 30 3rd - 10
C) 1st - 30 2nd - 50 3rd - 10
D) 1st - 55 2nd - 25 3rd - 15

The correct answer is: (B) 1st - 50 2nd - 30 3rd - 10

  • The number of books on all three shelves doubled
    • 80 + 60 + 40 = 180
  • Then the number of books on all three shelves
    • 180 / 2 = 90
  • The number of books on the first shelf
    • 90 – 40 = 50
  • The number of books on the second shelf
    • 90 – 60 = 30
  • The number of books on the third shelf
    • 90 – 80 = 10

A) 1000
B) 2793
C) 2893
D) 2993

The correct answer is: (C) 2893

  •  First nine numbers have only one digit
    • 9 x 1 = 9
  • From 10 to 99 numbers have two digits
    • 90 x 2 = 180
  • From 100 to 999 numbers have three digits
    • 3 x 900= 2700
  • 1000 has four digits
  • Total number of digits to write
    • 9 + 180 + 2700 + 4 = 2893

A) 10 chickens 5 cows
B) 11 chickens 4 cows
C) 12 chickens 3 cows
D) 13 chickens 2 cows

 

The correct answer is: (C) 12 chickens 3 cows

  • If the farmer had only chickens then they’d have 30 legs altogether
    • 15 chickens x 2 legs/chicken = 30 legs
    • 36 legs – 30 legs = 6 legs
  • Cows have 4 legs, so extra 6 legs belong to cows
    • 6 / 2 = 3 cows
    • 3 x 4 legs = 12 legs belongs to 3 cows
  • 15 heads total – 3 cow’s heads = 12 chicken’s heads

A) 1 day - 10, 2 day - 20, 3 day - 10
B) 1 day - 15, 2 day - 15, 3 day - 10
C) 1 day - 10, 2 day - 25, 3 day - 5
D) 1 day - 15, 2 day - 20, 3 day - 5

The correct answer is: (D) 1 day - 15, 2 day - 20, 3 day - 5

  • 3rd day they walked x miles
  • 1st day they walked 3x miles
  • 2nd day they walked (3x + x) miles
  • Total they walked 40 miles
    • 3x + (3x + x) + x =40
    • x = 40 / 8 = 5
  • First day 3 x 5 = 15 miles
  • Second day 15 + 5 = 20 miles
  • Third day 5 miles

A) 6
B) 8
C) 9
D) 12

 

The correct answer is: (C) 9

  • This problem needs to solved from the end
    • 6 x 4 / 3 + 2 – 1 = 9
  • Checking if it’s correct
    • (9 + 1 – 2) x 3 / 4 = 6

A) 74
B) 76
C) 82
D) 86

 

The correct answer is: (C) 86

  • Four people together are 70 years old
  • In four years each one of them would be four years older
  • Since the family has four members the total age increase of the family
  • 4 members x 4 years = 16 years
  • The total age of the family in four years
    • 70 + 16 = 86

A) 90
B) 55
C) 45
D) 25

 

The correct answer is: (D) 25

  • Both, first and second numbers can be 1, 3, 5, 7, 9
  • Five possibilities for each digit
  • The total possibilities of the two digits number where both digits are odd between 1 and 100
    • 5 x 5 = 25
  • Please look at the table diagram in the left top corner for a visual reference explaining this problem

A) 4, 8, 16
B) 3, 6, 13
C) 5, 10, 20
D) 2, 4, 8

 

The correct answer is: (A) 4, 8, 16

  • The sum of ages of all three sisters is 28 years
  • The age of the little sister is Y
  • The age of the middle sister is (2 x Y)
  • The age of the oldest sister is 2(2 x Y)
    • Y + 2 x Y + 2 x (2 x Y) = 28
    • 7 x Y = 28
    • Y = 28 / 7
    • Y = 4
  • The youngest sister is 4 years old
  • The middle sister is 8 years old
  • The oldest sister is 16 years old

A) 100
B) 105
C) 1000
D) 1050

The correct answer is: (D) 1050

  • There’re 20 numbers that end on 0 or 5 from 1 to 100
    • 5, 10, 15, 20, ….. 95, 90, 95, 100
  • The opposite numbers can be paired
    • 5 + 100 = 105
    • 10 + 95 = 105
    • 15 + 90 = 105
  • There’re ten pairs, so the sum of all the numbers
    • 10 x 105 = 1050

A) Sausage and Eggs
B) Burger
C) Chicken Salad
D) Soda

 

The correct answer is: (A) Sausage and Eggs

  • Revenue is calculated:
  • Price * Number of items sold
  • Complete calculations for the day in question
  • Sausage and Eggs have the largest revenue

A) older 50, younger 50
B) older 55, younger 45
C) older 60, younger 40

D) older 70, younger 30

 

The correct answer is: (D) older 70, younger 30

  • Since both brothers have the same number of baseball cards totaling 100 cards, then each brother has
    • 100 / 2 = 50
  • Initially, the older brother had
    • 50 + 20 = 70
  • The younger brother had
    • 50 – 20 = 30

The pitcher has three times more water than the coffeemaker, while the coffeemaker has 12 cups less water than the pitcher.

A) 12
B) 18
C) 20
D) 28

 

The correct answer is: (B) 18

  • The pitcher has three times more of water than the coffeemaker P = 3 x C
  • The coffeemaker has 12 cups less water than the pitcher
    • C = P - 12
    • P = C + 12
    • 3 x C = C + 12
    • C= 12 / 2 = 6
  • The coffeemaker has 6 cups of water
  • The pitcher has 12 + 6 = 18 cups of water

 

A) 5 years
B) 6 years
C) 9 years
D) 12 years

The correct answer is: (B) 6 years

  • A sum of ages of all three kids
    • 13 + 10 + 6 = 29
  • The difference of the father’s age and kids’ ages sum
    • 41 – 29 = 12
  • Every year the kid's age would increase by 3, while fathers’ age by 1
    • 3-1 = 2
  • The father’s age would be the same as the sum of his kid's ages
    • 12 / 2 = 6 years
    • (13+10+6)+3X=41+X, 29+2X=41, 2X=12, X=6

A) 60, 20, 10
B) 55, 25, 10
C) 50, 30, 10
D) 55, 25, 15

The correct answer is: (C) 50, 30, 10

  • Three people are a grandfather who’s also a father G, a son who’s also a father F, and a son who’s also a grandson S
    Sum of all three ages twice
    • (G + F) + (F + S) + (G + S)= 80 + 40 + 60 = 180
  • Sum of all three ages
    • 180 / 2 = 90
  • Age of the grandson
    • 90 – (G + F) = 90 – 80 = 10
  • Age of the father
    • F + S = 40 F=40 – 10 = 30
  • Age of the grandfather
    • G + F = 80 G= 80 – 30 = 50

A) 2050
B) 3050
C) 4050
D) 5050

The correct answer is: (D) 5050

  • There are 50 pairs of numbers from 1 to 100
  • The sum of the first and the last number
    • 1 + 100 =101
  • The next additions
    • 2 + 99 = 101
    • 3 + 98 = 101
    • 4 + 97 = 101
  • The sum of all numbers for 50 pairs
    • 101 x 50 = 5050

A) 48.3%

B) 55.3%

C) 58.2%

D) 60.8%

Correct Answer is: (C) 58.2%

  • Environmental pollution of Chemical Industry is 34.5% and Cement Industry is 21.8%
  • hemical Industry pollution compared to Cement Industry = 34.5-21.8 = 12.7 Percentage value = (12.7 / 21.8) * 100% = 58.2%

A) Equatex

B) Entorix

C) Bantova

D) Alario

Correct Answer is: (A) Equatex

  • It seems Entorix, Bantova, and Alario have good stable profits. Therefore investing in those companies will be a good decision.
  • But Equatex is always increasing its profit from the first quarter to the end. Therefore Equatex has good possibility to increase the profit in long term Investing

A) 9:5

B) 3:2

C) 7:4

D) 5:3

The Correct Answer is: (A) 9:5

  • Percentage of the tax from IT sector is 27% and Agriculture sector is 15%
  • Ratio between IT and Agriculture = 27 : 15 = 27/3 : 15:3 = 9:5

A) Equatex and Entorix

B) Entorix and Bantova

C) Bantova and Alario

D) Alario and Equatex

Correct Answer is: (D) Alario and Equatex

  • We’ll calculate (profit/cost)% for all the 4 companies. Profit = Revenue - Cost
  • Equatex: {(15-10)/10} * 100% = 50%
  • Entorix: { (50-40)/40} * 100% = 20%
  • Bantova: {(25-20)/20} * 100% = 25%
  • Alario: {(40-25)/25} * 100% = 60%

A) 150%

B) 200%

C) 300%

D) 100%

The Correct Answer is: (D) 200%

  • Retail sale in 2018 = $20M and Online sale in 2018 = $60M
  • Growth of online sales in 2018 compared to retail sales = {(60 - 20)/20} * 100% = 200%

A) $250

B) $100

C) $200

D) $175

The Correct Answer is: (C) $200

  • Expense different between Rent and Food = 25% - 20% = 5%
  • Amount of the difference = (5 / 100) * $4000 = $200

A) $1500

B) $750

C) $1000

D) $500

Correct Answer is: (A) $1500

  • Half of the space is equal to (25 * 60) / 2 = 750
  • Rent for 750 squarefeet = 750 * $20 = $1500

A) $18000

B) $20000

C) $24000

D) $30000

The Correct Answer is: (C) $24000

  • Cost of Apple phones = (22 / 100) * $200000 = $44000
  • Cost for Samsung phones = (10 / 100) * $200000 = $20000
  • Cost difference = $44000 - $20000 = $24000

A) 50%

B) 75%

C) 80%

D) 85%

Correct Answer is: (B) 75%

  • Increment = 70M - 40M = 30M.
  • Percentage of the increment compared to 2012 = (30/40) * 100% = 75%
  • Revenue for Facebook in 2018 is $70M and in 2012 it is $40M.

A) 40%

B) 22%

C) 30%

D) 25%

Correct Answer is: (C) 30%

  • There is a total number of 50 companies in the chart. 11 + 4 = 15 companies provide their service to the both Agriculture and Chemical sectors.
  • Therefore the percentage = (15 / 50) * 100% = 30%

About the Author

Vadim Mikhailenko, MBA

Vadim lives in Milwaukee, Wisconsin and works as an Information Technology Consultant, Coach and Educator. Vadim is very passionate about Milwaukee community and teaches classes to underprivileged students at local community college to help them get employed. Throughout his consulting career Vadim studied a lot of tools and technologies and learned hiring process by helping organizations to hire candidates and also supported students to get prepared and to pass interview and assessment tests.

Vadim loves to share his knowledge with and enjoys teaching  new skills to help you get hired for your dream job.

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