IIFT Entrance Exam Quantitative Aptitude Syllabus

Quantitative Aptitude syllabus — full chapter and topic list

Expand any chapter to see its topics and sub-topics. This is the whole examinable outline for Quantitative Aptitude in IIFT Entrance Exam, not a summary of it.

1. 1

   Arithmetic

   8 topics

   • Percentages
     • Percentage change and successive change
     • Applications in profit, population, and depreciation
   • Profit, Loss and Discount
     • Marked price, cost price and successive discounts
     • Dishonest dealer and false weights
   • Simple and Compound Interest
     • Annual, half-yearly and quarterly compounding
     • Difference between SI and CI
   • Ratio, Proportion and Variation
     • Componendo, dividendo and partnership
     • Direct, inverse and joint variation
   • Mixtures and Alligation
     • Rule of alligation
     • Repeated dilution / replacement
   • Time, Speed and Distance
     • Relative speed, trains and boats-streams
     • Circular tracks and races
   • Time and Work
     • Work-efficiency and pipes-cisterns
     • Work and wages
   • Averages and Ages
2. 2

   Algebra

   6 topics

   • Linear and Quadratic Equations
     • Nature of roots and sum-product relations
     • Equations reducible to quadratic form
   • Inequalities and Modulus
     • Linear and quadratic inequalities
     • Absolute value equations and graphs
   • Functions and Graphs
     • Domain, range and composite functions
     • Transformations and maxima-minima
   • Logarithms and Surds
     • Laws of logarithms and characteristic-mantissa
     • Rationalisation of surds
   • Progressions
     • Arithmetic and geometric progressions
     • Harmonic progression and special series
   • Polynomials and Algebraic Identities
3. 3

   Geometry and Mensuration

   7 topics

   • Lines, Angles and Triangles
     • Similarity and congruence
     • Pythagoras theorem and centres of a triangle
   • Polygons and Quadrilaterals
     • Interior-exterior angles
     • Properties of parallelograms and trapeziums
   • Circles
     • Tangents, chords and cyclic quadrilaterals
     • Angle subtended properties
   • Coordinate Geometry
     • Distance, section and area of triangle
     • Straight lines and slopes
   • Mensuration of 2D Figures
     • Area and perimeter of plane figures
     • Sectors and segments
   • Mensuration of 3D Solids
     • Cube, cuboid, cylinder, cone and sphere
     • Surface area and volume of frustum
   • Trigonometry and Heights-Distances
4. 4

   Number System

   5 topics

   • Factors, Multiples, HCF and LCM
   • Divisibility Rules and Remainders
     • Remainder and unit digit cyclicity
     • Fermat, Euler and Wilson theorems
   • Base System and Number of Trailing Zeros
   • Properties of Integers, Primes and Co-primes
   • Fractions, Decimals and Recurring Decimals
5. 5

   Modern Mathematics

   4 topics

   • Permutations and Combinations
     • Arrangements, selections and circular permutations
     • Distribution and grouping problems
   • Probability
     • Classical, conditional and Bayes' theorem
     • Probability with dice, cards and balls
   • Set Theory and Venn Diagrams
     • Two and three set formulae
     • Maxima-minima of overlapping sets
   • Binomial Theorem

Quantitative Aptitude flashcards for IIFT Entrance Exam

21 of 51 cards from the Quantitative Aptitude deck — real questions with worked answers.

1. What is the formula for percentage change, and how do you convert a fraction to a percentage?

   Percentage change = (Change / Original value) x 100. To convert a fraction to a percentage, multiply it by 100. A successive increase of a% then b% gives a net change of (a + b + ab/100)%.

2. If a value increases by x%, what single percentage decrease brings it back to the original?

   A decrease of [x / (100 + x)] x 100 %. For example, a 25% increase is reversed by a (25/125) x 100 = 20% decrease.

3. Define Cost Price (CP), Selling Price (SP), and the formulas for Profit% and Loss%.

   CP = price paid; SP = price sold. Profit = SP - CP; Loss = CP - SP. Profit% = (Profit/CP) x 100; Loss% = (Loss/CP) x 100. Both percentages are always calculated on CP.

4. How are Marked Price (MP), Discount, and Selling Price related?

   Discount is given on MP: Discount = MP - SP, and Discount% = (Discount/MP) x 100, so SP = MP x (1 - d/100). Profit/loss is still measured against CP.

5. What is the net effect of two successive discounts of x% and y%?

   Equivalent single discount = (x + y - xy/100)%. Successive discounts are always less in total than their simple sum because the second applies to a reduced price.

6. Give the Simple Interest formula and the amount formula.

   SI = (P x R x T)/100, where P = principal, R = rate% per annum, T = time in years. Amount A = P + SI = P(1 + RT/100).

7. Give the Compound Interest amount formula for annual compounding and for n compoundings per year.

   Annual: A = P(1 + R/100)^T, and CI = A - P. For compounding n times per year: A = P(1 + R/(100n))^(nT).

8. What is the difference between CI and SI for 2 years and for 3 years on principal P at rate R%?

   For 2 years: CI - SI = P(R/100)^2. For 3 years: CI - SI = P(R/100)^2 x (3 + R/100).

9. What does it mean to divide a ratio a:b into parts, and how is each share computed for total amount T?

   Shares are proportional: first part = T x a/(a+b), second part = T x b/(a+b). For ratio a:b:c, each share = T x (its term)/(a+b+c).

10. Distinguish direct, inverse, and joint variation.

    Direct: y = kx (y up as x up). Inverse: y = k/x (y down as x up). Joint: y varies as the product of two or more variables, e.g. y = kxz.

11. State the alligation (mean) rule for mixing two ingredients.

    (Quantity of cheaper)/(Quantity of dearer) = (Price of dearer - Mean price)/(Mean price - Price of cheaper). The cross-difference of the two prices from the mean gives the mixing ratio.

12. A container has pure liquid; x% is replaced by water each time over n operations. What fraction of pure liquid remains?

    Remaining pure liquid = Initial x (1 - x/100)^n. Used for repeated replacement/dilution problems.

13. State the basic relationship between Speed, Distance, and Time.

    Speed = Distance/Time; Distance = Speed x Time; Time = Distance/Speed. To convert km/h to m/s multiply by 5/18; m/s to km/h multiply by 18/5.

14. Give the formula for average speed when equal distances are covered at speeds a and b.

    Average speed = 2ab/(a+b), the harmonic mean. (Note: average speed = total distance / total time, NOT the arithmetic mean of speeds.)

15. How do relative speeds work for two objects moving toward each other vs. in the same direction?

    Opposite directions (or approaching): relative speed = sum of speeds. Same direction: relative speed = difference of speeds.

16. For a train of length L crossing a pole vs. a platform of length P, what distance is traveled?

    Crossing a pole: distance = L (the train's own length). Crossing a platform/bridge of length P: distance = L + P.

17. In boats and streams, give the downstream and upstream speeds.

    Downstream speed = boat speed + stream speed (b + s); Upstream = b - s. So b = (down + up)/2 and s = (down - up)/2.

18. If A does a job in a days and B in b days, how long do they take together?

    Combined time = ab/(a+b) days. Work rates add: 1/a + 1/b = 1/T. Generally, rate (work per day) is the reciprocal of time taken alone.

19. State the relationship between number of people, days, hours and work (chain rule for work).

    (M1 x D1 x H1)/W1 = (M2 x D2 x H2)/W2, where M = men, D = days, H = hours/day, W = work done. This balances man-hours against work.

20. Define arithmetic mean (average) and how a new average changes when an item is added.

    Average = (Sum of observations)/(Number of observations). Adding an item equal to the current average leaves it unchanged; adding one above/below shifts the average toward that value.

21. In ages problems, how do you express ages 'n years ago' and 'n years hence'?

    n years ago: subtract n from each present age. n years hence: add n to each present age. The difference between two people's ages stays constant over time.

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