Quantitative Aptitude and Numerical Ability
Quantitative Aptitude and Numerical Ability tests arithmetic speed: percentage, ratio, profit and loss, interest, time-work, time-speed-distance, averages, mensuration, and data interpretation. Questions are short but designed to punish long division.
Core rules
- Percentage change: an increase and decrease of a% and b% gives net a + b - ab/100.
- Profit and loss are on cost price unless stated; marked price is not cost price.
- SI = PRT/100; CI = P[(1+r/100)^n - 1]; for two years the CI minus SI difference is P(r/100)^2.
- Time and work: take the LCM of days as total work; combined rate is the sum of rates.
- Trains: relative speed adds for opposite directions and subtracts for the same direction; distance is train length plus platform.
- Alligation gives the ratio of two mixtures from their strengths.
- Mensuration: volume of cylinder pi r squared h, cone one-third pi r squared h, sphere 4/3 pi r cubed; keep units consistent.
Worked example
A shopkeeper marks an item at 800 rupees and gives successive discounts of 20% and 10%. Selling price = 800 x 0.80 x 0.90 = 576 rupees. Single equivalent discount = 20 + 10 - (20 x 10)/100 = 28%. Check: 800 x 0.72 = 576 rupees.
Traps
Applying a single 30% discount instead of successive discounts; calculating profit on selling price when the question says cost; forgetting that half-yearly compounding halves the rate and doubles periods; mixing cm and m in mensuration; and over-rounding in data interpretation.