Overview: Quantitative Reasoning

Table of Contents
1. What is Quantitative Reasoning?
2. Skills Required to Solve Quantitative Reasoning Questions
3. Examples
4. Arithmetic Reasoning Formulas
5. Types of Arithmetic Reasoning
6. Arithmetic Reasoning Tips and Tricks
View more

What is Quantitative Reasoning?

Quantitative reasoning is the ability to understand, interpret and solve problems that involve numerical data using the four basic arithmetic operations: addition, subtraction, multiplication and division. It combines calculation skills with an understanding of underlying concepts, recognition of patterns and logical decision-making based on numerical information.

Quantitative reasoning questions appear often in aptitude and reasoning tests. Such questions require the candidate to identify numerical relationships defined by the problem, select relevant facts, and apply appropriate methods to reach a correct result. Success in this area depends on both accurate computation and sound reasoning.

Arithmetic reasoning assesses the candidate's facility with numbers and basic mathematical operations. Many problems are numerical in nature and include calculation steps; however, clear concepts and regular practice make this section manageable for all candidates.

Example:

A man would like to take a new health insurance. An officer taking care of these matters says to the man, "Please tell me how many children you have." The man answers, "I have three of them." The officer, "What are the ages of your children?" The man answers, "The product of the ages is equal to 36." The officer replies, "This is not enough information, Sir!" The man replied, "Sorry that I was a little bit unclear, but the sum of the ages is equal to the number of shops in front of your office." The officer: "This still isn't enough information, Sir!" The man replies, "My oldest child loves chocolate." The officer: "Thanks for your cooperation, I now know the ages." Are you as smart as the officer? Then, give the sum of the ages of the children.

1. 13

2. 22

3. 36

4. 38

Solution:

The product of the ages is 36. Possible sets of three positive integer ages whose product is 36 are:

1, 1, 36 → sum = 38

1, 2, 18 → sum = 21

1, 3, 12 → sum = 16

1, 4, 9 → sum = 14

1, 6, 6 → sum = 13

2, 2, 9 → sum = 13

2, 3, 6 → sum = 11

3, 3, 4 → sum = 10

When told the sum (equal to the number of shops), the officer still could not determine the ages - this implies the sum must be ambiguous (can arise from more than one combination). The only ambiguous sum from the list is 13 (it arises from 1,6,6 and 2,2,9). The final clue, "My oldest child loves chocolate," indicates there is a distinct oldest child, so the ages cannot be 1,6,6 (which would have two oldest children of same age). Therefore the ages are 2, 2 and 9 and the sum is 13.

Hence, option (1) is the correct answer.

Skills Required to Solve Quantitative Reasoning Questions

• Understanding specific logic: Grasp the particular numerical or logical pattern presented in the question.
• Ordering clues correctly: Arrange and use given clues in the correct sequence and recognise which clues are essential.
• Knowledge of basic maths: Be familiar with percentages, averages, ratios, speed-time-distance, LCM/GCD, simple and compound interest, and elementary algebra.
• Creating symbolic representations: Translate words and conditions into equations or symbolic expressions to combine and analyse information efficiently.
• Timing and patience: Recognise when an indirect clue is being given and wait for enough information before making conclusions; manage time for different question types.

Examples

Q1: 5, 11, 24.2, 53.24, ?, 257.6816

Sol:

5 × 2.2 = 11

11 × 2.2 = 24.2

24.2 × 2.2 = 53.24

53.24 × 2.2 = 117.128

117.128 × 2.2 = 257.6816

Hence, the correct answer is 117.128.

Q2: 71 : 42 :: 98 : ?

Sol:

71 - 29 = 42

98 - 29 = 69

Hence, 69 will replace the question mark.

Q3: 71 : 42 :: 98 : ?

Sol:

71 - 29 = 42

98 - 29 = 69

Hence, 69 will replace the question mark.

Q4: 67 : 76 :: 42 : ?

Sol:

67 + 9 = 76

42 + 9 = 51

Hence, 51 will replace the question mark.

Q5: 49, 121, 169, ?, 361

Sol:

49 = 7²

121 = 11²

169 = 13²

Next square in the pattern is 17² = 289

361 = 19²

Hence, the correct answer is 289.

Q6: The position of how many digit(s) in the number 381576 will remain the same after the number is arranged in ascending order?

Sol:

Original number: 3 8 1 5 7 6

Ascending order: 1 3 5 6 7 8

Only the digit 7 remains in the same position (5th place).

Hence, the correct answer is One.

Q7: If 3x - 7 = 20, what is the value of x?

Sol:

3x - 7 = 20

3x = 20 + 7

3x = 27

x = 27 / 3

x = 9

Q8: A car travels 360 miles in 6 hours. What is its average speed?

Sol:

Average speed = Total distance / Total time

Average speed = 360 miles / 6 hours

Average speed = 60 miles per hour

Q9: What is 35% of 120?

Sol:

35% of 120 = (35/100) × 120

= 0.35 × 120

= 42

Q10: If the area of a rectangle is 180 square units and its length is 12 units, what is its width?

Sol:

Area = length × width

180 = 12 × width

width = 180 / 12

width = 15 units

Q11: Solve for y: 4y + 5 = 3y + 12

Sol:

4y + 5 = 3y + 12

4y - 3y = 12 - 5

y = 7

Q12: In a class of 40 students, 12 students are girls. What percentage of the class is made up of girls?

Sol:

Percentage = (Number of girls / Total students) × 100

Percentage = (12 / 40) × 100

Percentage = 30%

Q13: A store is offering a 25% discount on a jacket that originally costs $80. What is the sale price of the jacket?

Sol:

Discount = 25% of $80 = (25/100) × 80 = $20

Sale price = Original price - Discount

Sale price = $80 - $20 = $60

Q14: If a train travels at 75 miles per hour for 2 hours and 45 minutes, how far does it travel?

Sol:

Time = 2 hours + 45/60 hours = 2.75 hours

Distance = Speed × Time

Distance = 75 × 2.75 = 206.25 miles

Q15: What is the sum of the first ten positive odd numbers?

Sol:

First ten positive odd numbers: 1, 3, 5, 7, 9, 11, 13, 15, 17, 19

Sum = 1 + 3 + 5 + 7 + 9 + 11 + 13 + 15 + 17 + 19 = 100

Q16: A rectangular garden has a perimeter of 60 meters, and its width is 10 meters. What is its length?

Sol:

Perimeter = 2 × (length + width)

60 = 2 × (length + 10)

30 = length + 10

length = 20 meters

Q17: If the sum of three consecutive even numbers is 78, what is the largest number?

Sol:

Let the numbers be x, x + 2, x + 4

x + (x + 2) + (x + 4) = 78

3x + 6 = 78

3x = 72

x = 24

Largest number = x + 4 = 28

Q18: A fruit seller sold 120 kg of apples at $4 per kg and 80 kg of oranges at $5 per kg. How much money did he earn in total?

Sol:

Apples: 120 × $4 = $480

Oranges: 80 × $5 = $400

Total = $480 + $400 = $880

Q19: What is the smallest positive integer that is divisible by both 6 and 8?

Sol:

Prime factors: 6 = 2 × 3, 8 = 2³

LCM = 2³ × 3 = 8 × 3 = 24

Smallest positive integer = 24

Q20: Solve the following equation: 5(x - 3) = 4(x + 2)

Sol:

5(x - 3) = 4(x + 2)

5x - 15 = 4x + 8

5x - 4x = 8 + 15

x = 23

Q21: A car rental company charges $20 per day plus an additional $0.15 per mile driven. How much would it cost to rent a car for 3 days and drive 200 miles?

Sol:

Cost for days = 3 × $20 = $60

Cost for miles = 200 × $0.15 = $30

Total cost = $60 + $30 = $90

Q22: If 9 books weigh 36 pounds, how much would 15 books weigh?

Sol:

Weight of 1 book = 36 / 9 = 4 pounds

Weight of 15 books = 15 × 4 = 60 pounds

Q23: What is the average of the numbers 18, 24, and 30?

Sol:

Average = (18 + 24 + 30) / 3

Average = 72 / 3 = 24

Q24: If a square has a side length of 8 units, what is the length of its diagonal?

Sol:

Diagonal = side × √2

Diagonal = 8 × √2 = 8√2 units

Q25: A store sells packs of 6 pens for $4.50 per pack. How much would 3 packs cost?

Sol:

Cost = 3 × $4.50 = $13.50

Q26: A person invests $1000 in a savings account with an annual interest rate of 4% compounded annually. What is the balance in the account after 2 years?

Sol:

Use compound interest formula: A = P(1 + r/n)^(n t)

P = 1000, r = 0.04, n = 1, t = 2

A = 1000(1 + 0.04)²

A = 1000 × (1.04)²

A = 1000 × 1.0816

A = 1081.60

The balance after 2 years is $1081.60.

Arithmetic Reasoning Formulas

• Addition: a + b = c
• Subtraction: a - b = c
• Multiplication: a × b = c
• Division: a ÷ b = c
• Average: (a + b + c + ... + n) / n
• Percentage: (part / whole) × 100
• Ratio: a : b
• Proportion: a / b = c / d
• Distance: Distance = Speed × Time
• Speed: Speed = Distance / Time
• Time: Time = Distance / Speed
• Simple Interest: I = P × R × T / 100 (I = interest)
• Compound Interest: A = P(1 + r/n)^(n t)
• Profit or Loss: Profit = Selling Price - Cost Price; Loss = Cost Price - Selling Price
• Percent Change: (New - Old) / Old × 100
• Fraction addition: a/b + c/d = (ad + bc) / bd
• Fraction subtraction: a/b - c/d = (ad - bc) / bd
• Fraction multiplication: (a/b) × (c/d) = (a c) / (b d)
• Fraction division: (a/b) ÷ (c/d) = (a d) / (b c)
• Decimal → Fraction: Write decimal as numerator and denominator as appropriate power of 10, then simplify.
• Fraction → Decimal: Divide numerator by denominator.
• Fraction → Percentage: Fraction × 100
• Percentage → Fraction / Decimal: Percentage / 100
• Weighted average: (w1 x1 + w2 x2 + ... + wn xn) / (w1 + w2 + ... + wn)
• LCM (Least Common Multiple): Smallest number divisible by each given number.
• GCD (Greatest Common Divisor): Largest number that divides given numbers without remainder.
• Prime number: A number greater than 1 with exactly two factors: 1 and itself.
• Factor: A number that divides another number exactly.
• Square: a² = a × a
• Cube: a³ = a × a × a
• Square root: √a is a number which when squared equals a.
• Cube root: ∛a is a number which when cubed equals a.
• Permutations: nPr = n! / (n - r)!
• Combinations: nCr = n! / [r!(n - r)!]

Types of Arithmetic Reasoning

Puzzle

Puzzle problems present pieces of information from which you must select the relevant data, discard irrelevant facts and combine clues to obtain the required result.

Analogy

Analogy problems require you to identify relations between pairs of numbers or expressions and find a similar relation for another pair.

Series

Series questions ask you to identify the rule or pattern that generates a sequence and either find the next term or locate an incorrect term.

Inequality

Inequality questions test your understanding of comparison relations and symbols such as <, >, ≤, ≥, = and combinations of these in a logical chain.

Venn Diagram

Venn diagrams represent relationships between sets visually and help to count elements belonging to one or more sets using inclusion-exclusion principles.

Cube & Dice

Cube and dice problems require spatial reasoning to determine faces, opposite faces, development (net) patterns, or results after rotation and folding.

Arithmetic Reasoning Tips and Tricks

• Read carefully: Identify exactly what is asked and list given numerical data and constraints.
• Break down complex problems: Divide a problem into smaller parts and solve each part systematically.
• Choose the right formula or method: Match the problem to a known formula (e.g., averages, ratios, percentages, interest) or derive a simple equation.
• Organise data: Use a small table, diagram, or equation to keep information clear and avoid mistakes.
• Perform calculations accurately: Keep track of units and decimal places; simplify intermediate steps where helpful.
• Use elimination for multiple choice: Discard impossible answers quickly and test remaining options if necessary.
• Simplify the answer: If required, simplify your answer by expressing it in the most appropriate format, such as a fraction, decimal, or percentage.
• Check your work: Re-read the question and verify the result is reasonable in context.
• Practice pattern recognition: Series and analogy questions often rely on spotting arithmetic or positional patterns quickly.
• Manage time: Attempt easier questions first, mark time-consuming ones and return if time permits.