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IIFT Entrance Exam Quantitative Aptitude Syllabus
The Quantitative Aptitude syllabus for IIFT Entrance Exam in full: 5 chapters, 30 topics and 44 sub-topics, every one listed below, plus 51 Quantitative Aptitude flashcards with answers.
Quantitative Aptitude syllabus: all 5 chapters
Expand any chapter to see its topics and sub-topics.
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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
- Percentages
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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
- Linear and Quadratic Equations
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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
- Lines, Angles and Triangles
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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
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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
- Permutations and Combinations
IIFT Entrance Exam Quantitative Aptitude flashcards — 51 questions with answers
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)%.
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.
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.
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.
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.
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).
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).
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).
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).
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.
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.
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.
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.
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.)
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.
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.
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.
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.
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.
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.
Show the other 31 Quantitative Aptitude flashcards
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.
Give the quadratic formula and the discriminant's meaning.
For ax^2 + bx + c = 0: x = [-b +/- sqrt(b^2 - 4ac)]/(2a). Discriminant D = b^2 - 4ac: D>0 two real distinct roots, D=0 two equal real roots, D<0 complex conjugate roots.
State the relationship between roots and coefficients of a quadratic ax^2 + bx + c = 0.
Sum of roots = -b/a; Product of roots = c/a. A quadratic can be written as x^2 - (sum)x + (product) = 0.
How do you solve an inequality involving multiplication/division by a negative number?
When you multiply or divide both sides of an inequality by a negative number, you must reverse the inequality sign. Adding/subtracting any number, or multiplying by a positive, keeps the direction.
What does |x| < a and |x| > a mean (for a > 0)?
|x| < a means -a < x < a. |x| > a means x < -a OR x > a. |x| represents the distance of x from 0 on the number line.
Define a function and what makes it one-to-one and onto.
A function maps each input to exactly one output. One-to-one (injective): distinct inputs give distinct outputs. Onto (surjective): every element of the codomain is an output. Both = bijective (invertible).
How do the graphs of f(x)+c, f(x+c), and -f(x) transform from f(x)?
f(x)+c shifts up by c; f(x+c) shifts left by c; f(x)-c down; f(x-c) right. -f(x) reflects across the x-axis; f(-x) reflects across the y-axis.
State the key logarithm rules.
log(mn) = log m + log n; log(m/n) = log m - log n; log(m^k) = k log m; change of base: log_b a = log a / log b; log_b b = 1; log_b 1 = 0; a^(log_a x) = x.
How do you simplify and rationalize surds like 1/(sqrt(a)+sqrt(b))?
Multiply numerator and denominator by the conjugate (sqrt(a)-sqrt(b)): 1/(sqrt(a)+sqrt(b)) = (sqrt(a)-sqrt(b))/(a-b). Surd rules: sqrt(a)xsqrt(b)=sqrt(ab), sqrt(a)/sqrt(b)=sqrt(a/b).
Give the nth term and sum formulas for an arithmetic progression (AP).
nth term: a_n = a + (n-1)d. Sum: S_n = n/2[2a + (n-1)d] = n/2(a + l), where a = first term, d = common difference, l = last term.
Give the nth term and sum formulas for a geometric progression (GP).
nth term: a_n = a r^(n-1). Sum of n terms: S_n = a(r^n - 1)/(r - 1) for r != 1. Sum to infinity (|r|<1): S = a/(1 - r).
State the formulas for the sum of the first n natural numbers, their squares, and their cubes.
Sum = n(n+1)/2; Sum of squares = n(n+1)(2n+1)/6; Sum of cubes = [n(n+1)/2]^2 (the square of the sum).
State the standard algebraic identities for (a+b)^2, (a-b)^2, a^2 - b^2, and (a+b)^3.
(a+b)^2 = a^2 + 2ab + b^2; (a-b)^2 = a^2 - 2ab + b^2; a^2 - b^2 = (a+b)(a-b); (a+b)^3 = a^3 + 3a^2b + 3ab^2 + b^3; a^3 + b^3 = (a+b)(a^2 - ab + b^2).
What is the identity for a^3 + b^3 + c^3 - 3abc?
a^3 + b^3 + c^3 - 3abc = (a + b + c)(a^2 + b^2 + c^2 - ab - bc - ca). If a + b + c = 0, then a^3 + b^3 + c^3 = 3abc.
State the angle-sum properties of a triangle and the exterior angle theorem.
Interior angles of a triangle sum to 180 degrees. An exterior angle equals the sum of the two remote (non-adjacent) interior angles. The largest angle lies opposite the longest side.
State the Pythagorean theorem and the triangle inequality.
In a right triangle, hypotenuse^2 = sum of squares of the other two sides. Triangle inequality: the sum of any two sides exceeds the third; the difference of any two sides is less than the third.
Give the sum of interior and exterior angles of an n-sided polygon.
Sum of interior angles = (n - 2) x 180 degrees. Sum of exterior angles = 360 degrees (always). Each interior angle of a regular polygon = (n-2)x180/n.
List the area formulas for square, rectangle, parallelogram, rhombus, and trapezium.
Square = side^2; Rectangle = length x width; Parallelogram = base x height; Rhombus = (1/2) x product of diagonals; Trapezium = (1/2) x (sum of parallel sides) x height.
State the key circle theorems about angles and tangents.
Angle at the center = twice the angle at the circumference on the same arc. Angle in a semicircle = 90 degrees. A tangent is perpendicular to the radius at the point of contact; tangents from an external point are equal in length.
Give the circumference and area of a circle, and arc length/sector area for angle theta degrees.
Circumference = 2(pi)r; Area = (pi)r^2. Arc length = (theta/360) x 2(pi)r; Sector area = (theta/360) x (pi)r^2.
State the distance, midpoint, and slope formulas in coordinate geometry.
Distance = sqrt[(x2-x1)^2 + (y2-y1)^2]; Midpoint = ((x1+x2)/2, (y1+y2)/2); Slope m = (y2-y1)/(x2-x1). Parallel lines have equal slopes; perpendicular slopes multiply to -1.
Give the equation of a line in slope-intercept form and the area of a triangle from vertices.
Line: y = mx + c (m = slope, c = y-intercept). Triangle area from vertices = (1/2)|x1(y2-y3) + x2(y3-y1) + x3(y1-y2)|.
State the surface area and volume formulas for a cube and a cuboid.
Cube (side a): Volume = a^3, Total surface area = 6a^2. Cuboid (l,b,h): Volume = lbh, TSA = 2(lb + bh + hl), diagonal = sqrt(l^2 + b^2 + h^2).
State volume and surface area formulas for a cylinder, cone, and sphere.
Cylinder: V = (pi)r^2h, CSA = 2(pi)rh. Cone: V = (1/3)(pi)r^2h, CSA = (pi)rl (l = slant height). Sphere: V = (4/3)(pi)r^3, Surface area = 4(pi)r^2.
State the basic trigonometric ratios and the fundamental identity.
sin = opposite/hypotenuse, cos = adjacent/hypotenuse, tan = opposite/adjacent = sin/cos. Identity: sin^2(x) + cos^2(x) = 1; also 1 + tan^2 = sec^2 and 1 + cot^2 = cosec^2.
In heights and distances, define angle of elevation and angle of depression.
Angle of elevation: the upward angle from the horizontal to an object above. Angle of depression: the downward angle from the horizontal to an object below. They are equal (alternate angles) for the same line of sight.
How do you find the number of factors and the sum of factors of a number N = p^a x q^b?
Number of factors = (a+1)(b+1). Sum of factors = [(p^(a+1)-1)/(p-1)] x [(q^(b+1)-1)/(q-1)]. The number of factors counts all combinations of prime powers.
State the relationship between HCF, LCM, and the product of two numbers.
HCF x LCM = product of the two numbers. HCF takes the lowest powers of common primes; LCM takes the highest powers of all primes appearing.
State divisibility rules for 3, 4, 8, 9, and 11.
By 3: digit sum divisible by 3. By 9: digit sum divisible by 9. By 4: last two digits form a multiple of 4. By 8: last three digits divisible by 8. By 11: difference of alternate-digit sums is 0 or a multiple of 11.
How do you find the number of trailing zeros in n! (factorial)?
Count factors of 5: trailing zeros = floor(n/5) + floor(n/25) + floor(n/125) + ... (sum until terms become 0). Zeros come from pairs of 2 and 5, and 5s are the limiting factor.
State the formulas for permutations nPr and combinations nCr, and the binomial theorem general term.
nPr = n!/(n-r)! (order matters); nCr = n!/[r!(n-r)!] (order doesn't matter); note nCr = nPr/r!. Binomial: (a+b)^n general term T(r+1) = nCr a^(n-r) b^r.
IIFT Entrance Exam Quantitative Aptitude FAQ
What is in the IIFT Entrance Exam Quantitative Aptitude syllabus?
IIFT Entrance Exam Quantitative Aptitude is split into 5 chapters: Arithmetic, Algebra, Geometry and Mensuration, Number System and Modern Mathematics. Together they contain 30 topics and 44 sub-topics.
How many chapters are in IIFT Entrance Exam Quantitative Aptitude?
5 chapters, containing 30 topics and 44 sub-topics. The largest chapter is Arithmetic, with 8 topics.
Are there flashcards for IIFT Entrance Exam Quantitative Aptitude?
Yes — a 51-card Quantitative Aptitude deck, printed in full in the flashcards section of this page and available in the Examius app with spaced repetition. The free plan covers one exam of your choice, including its flashcards; Examius Pro, a one-time purchase, unlocks every other exam and deck.