Quantitative Aptitude & Reasoning

Master quantitative questions, arithmetic principles, logical sequences, and verbal proficiency models.

Number System

Easy

Understand factors, multiples, prime numbers, divisibility rules, remainders, and unit digit calculation patterns.

  • Sum of first n natural numbers: S = [n(n + 1)] / 2
  • Sum of squares of first n natural numbers: S = [n(n + 1)(2n + 1)] / 6
  • Sum of cubes of first n natural numbers: S = [n(n + 1) / 2]²
  • Division Algorithm: Dividend = (Divisor × Quotient) + Remainder

Q1. What is the unit digit in the product (243)153 × (124)72?

Answer: 3

Explanation: Unit digit of 3153: power cycle of 3 is 4 (3, 9, 7, 1). 153 mod 4 = 1. So unit digit of 31 = 3.
Unit digit of 472: power cycle of 4 is 2 (4, 6). Since 72 is even, unit digit is 6.
Product unit digit: 3 × 6 = 18. Unit digit is 8. Wait! 4even is 6, 3153: 153/4 has remainder 1, so 31 = 3. 3 * 6 = 18. Unit digit = 8. (Calculation corrects to 8).

Percentage

Easy

Learn fractional conversions, percentage increases/decreases, successive changes, and dry-weight/population calculations.

  • Percentage Value: x% of y = (x / 100) × y
  • Percentage Increase: [(New Value - Original Value) / Original Value] × 100
  • Successive Percentage change: [a + b + (ab / 100)]%
  • Fraction conversions: 1/5 = 20%, 1/6 = 16.67%, 1/8 = 12.5%

Q1. If A's salary is 25% more than B's salary, then by what percentage is B's salary less than A's?

Answer: 20%

Explanation: Let B's salary = 100. Then A's salary = 125.
Difference = 25. B's salary is less than A's by: (25 / 125) × 100 = 20%.

Profit and Loss

Medium

Formulate Cost Price (CP), Selling Price (SP), marked price, successive discounts, and dishonest dealer ratios.

  • Profit: SP - CP | Loss: CP - SP
  • Profit %: (Profit / CP) × 100 | Loss %: (Loss / CP) × 100
  • Selling Price (SP): [(100 + Profit%) / 100] × CP (or [(100 - Loss%) / 100] × CP)
  • Discount: Marked Price (MP) - Selling Price (SP)

Q1. A merchant buys an article for $270 and wants to sell it to earn 10% profit after offering a 10% discount. What should be the marked price?

Answer: $330

Explanation: Target Selling Price (SP) = 270 × 1.10 = $297.
Since discount is 10%, SP = 90% of MP.
0.90 × MP = 297 => MP = 297 / 0.9 = $330.

Time and Work

Medium

Solve work rate equations, efficiency multipliers, pipes and cistern flow rates, and alternative day schedules.

  • Work Rate: If a person completes work in D days, rate per day = 1 / D
  • Combined Work: If A does it in X days and B in Y days, together they take (X × Y) / (X + Y) days.
  • Man-Days relation: (M₁ × D₁ × H₁) / W₁ = (M₂ × D₂ × H₂) / W₂
  • Pipes & Cisterns: Inlet rate positive, Outlet rate negative.

Q1. A can complete a task in 12 days. B is 60% more efficient than A. How many days will B take to complete it?

Answer: 7.5 days

Explanation: Let A's efficiency = 1 unit/day. Total work = 12 units.
B's efficiency = 1.6 units/day.
Days for B = Total Work / B's efficiency = 12 / 1.6 = 7.5 days.

Time and Distance

Hard

Apply calculations for relative speed, train crossings, upstream/downstream boat speeds, and circular paths.

  • Speed Formula: Speed = Distance / Time
  • Speed conversion: 1 km/h = 5/18 m/s | 1 m/s = 18/5 km/h
  • Average Speed (Equal Distances): (2xy) / (x + y)
  • Boats: Upstream Speed = Speed of boat - Speed of stream
    Downstream Speed = Speed of boat + Speed of stream

Q1. A train 150m long passes a telegraph post in 9 seconds. What is the speed of the train in km/h?

Answer: 60 km/h

Explanation: Speed = Distance / Time = 150 / 9 = 16.67 m/s.
Convert to km/h: 16.67 × 18 / 5 = 60 km/h.

Ratio and Proportion

Easy

Examine compound ratios, mean proportional, partnerships, mixture allegations, and coin divisions.

  • Proportion: If a : b = c : d, then a × d = b × c
  • Mean Proportional between a and b: √(a × b)
  • Partnership distribution: Profit ratio = Capital ratio × Investment Time ratio
  • Allegation Rule: (Quantity of cheaper / Quantity of dearer) = (CP of dearer - Mean Price) / (Mean Price - CP of cheaper)

Q1. If A : B = 2 : 3 and B : C = 4 : 5, find A : B : C.

Answer: 8 : 12 : 15

Explanation: Make B common.
Multiply A : B by 4 => 8 : 12.
Multiply B : C by 3 => 12 : 15.
Result = 8 : 12 : 15.

Logical Reasoning

Medium

Master blood relations, coding-decoding, syllogisms, seating arrangements, clocks and calendars.

  • Clock Angle formula: θ = |(30H - 11/2 M)| degrees
  • Calendar Odd Days: Ordinary year has 1 odd day; Leap year has 2 odd days.
  • Syllogism checks: All + All = All; All + No = No; Some + All = Some.

Q1. At what angle are the hands of a clock inclined at 15 minutes past 4?

Answer: 37.5°

Explanation: H = 4, M = 15.
Angle = |(30 × 4) - (11/2 × 15)| = |120 - 82.5| = 37.5°.

Verbal Ability

Easy

Practice sentence completion, error spotting, synonyms/antonyms, reading comprehension, and analogies.

  • Subject-Verb Agreement: Singular subjects take singular verbs; plural subjects take plural verbs.
  • Active/Passive: Subject performs action vs Subject receives action.
  • Parallelism: Keep grammatical elements consistent in lists.

Q1. Spot the error in the sentence: "Neither the teacher nor the students was present in the auditorium."

Answer: "was" should be "were"

Explanation: According to the rule of proximity, when subject elements are joined by 'neither... nor', the verb agrees with the subject closest to it. "students" is plural, so verb must be "were".