Examius
🇮🇳 AILET · subject
AILET Quantitative Techniques Syllabus
The Quantitative Techniques syllabus for AILET in full: 4 chapters, 13 topics and 27 sub-topics, every one listed below, plus 51 Quantitative Techniques flashcards with answers.
Quantitative Techniques syllabus: all 4 chapters
Expand any chapter to see its topics and sub-topics.
-
Data Interpretation
3 topics- Tabular and Graphical Data
- Tables and data charts
- Bar graphs and line graphs
- Pie charts and combined data sets
- Calculations from Data
- Computing ratios, shares and totals
- Comparisons and growth rates
- Caselet and Mixed Data
- Interpreting data presented in passages
- Drawing conclusions from data sets
- Tabular and Graphical Data
-
Arithmetic
4 topics- Ratio, Proportion and Percentage
- Ratios and proportions
- Percentage increase and decrease
- Profit, Loss and Interest
- Profit, loss and discount
- Simple and compound interest
- Averages, Mixtures and Allegation
- Averages and weighted averages
- Mixtures and allegation
- Time, Speed and Work
- Time, speed and distance
- Time and work
- Ratio, Proportion and Percentage
-
Numbers and Algebra
3 topics- Number System
- Properties of numbers, factors and multiples
- HCF and LCM
- Basic Algebra
- Linear equations
- Simplification and approximation
- Sequences and Operations
- Arithmetic progressions
- Order of operations and surds
- Number System
-
Mensuration and Basic Geometry
3 topics- Areas and Perimeters
- Area and perimeter of plane figures
- Surface area and volume of solids
- Elementary Probability and Statistics
- Basic probability
- Mean, median and mode
- Lines, Angles and Triangles
- Properties of triangles and angles
- Basic coordinate geometry
- Areas and Perimeters
AILET Quantitative Techniques flashcards — 51 questions with answers
In a frequency table, what is the difference between 'frequency' and 'cumulative frequency'?
Frequency is the count of observations in a single class; cumulative frequency is the running total of frequencies up to and including that class.
Which graph type is best for showing how a whole is divided into parts (percentage shares), and how is each slice's angle calculated?
A pie chart. Each slice angle = (component value / total) x 360 degrees.
On a bar graph versus a histogram, what is the key structural difference?
Bar graphs have gaps between bars and represent categorical data; histograms have no gaps (bars touch) and represent continuous/grouped data, with area proportional to frequency.
In a line graph showing a trend over time, how do you read the rate of change between two points?
Rate of change = (change in y-value) / (change in x-value), i.e., the slope of the line segment between the two points.
When data is given in a table, how do you compute the percentage change of a value from year A to year B?
Percentage change = ((Value_B - Value_A) / Value_A) x 100.
From a data table, how do you find what percentage one category contributes to the total?
Contribution % = (category value / sum of all categories) x 100.
In a 'caselet' (paragraph-style data) question, what is the first step before calculating?
Translate the prose into a structured table or set of equations, extracting each given quantity and the relationship between them, before computing.
What does 'mixed data' (combination charts) typically require you to do, e.g., a table plus a graph together?
Cross-reference both sources: use values from one (table/graph) to fill gaps or verify the other, since neither alone gives the full answer.
Define a ratio and state the basic property of an equivalent ratio.
A ratio compares two quantities (a:b = a/b). An equivalent ratio is obtained by multiplying or dividing both terms by the same non-zero number, e.g., 2:3 = 4:6.
What is a proportion, and what is the rule of cross-multiplication?
A proportion states two ratios are equal: a:b = c:d. Cross-multiplication gives a x d = b x c (product of extremes = product of means).
How do you convert a fraction or decimal to a percentage, and a percentage to a fraction?
Multiply a fraction/decimal by 100 to get a percentage; divide a percentage by 100 to get a fraction/decimal.
If a quantity increases by x% then decreases by x%, what is the net percentage change?
A net decrease of (x^2/100)%. The result is always lower than the original value.
In a ratio a:b:c, how do you split a total amount T among three parts?
Each share = (its ratio term / (a+b+c)) x T. E.g., first part = a/(a+b+c) x T.
Define Profit, Loss, and the formula for Profit Percent (Gain %).
Profit = SP - CP (when SP > CP); Loss = CP - SP (when CP > SP). Profit % = (Profit / CP) x 100, computed on cost price.
Write the formula for Simple Interest and the amount.
SI = (P x R x T) / 100, where P=principal, R=rate% per annum, T=time in years. Amount = P + SI.
Write the Compound Interest amount formula (compounded annually) and the CI formula.
Amount A = P(1 + R/100)^T. Compound Interest = A - P = P[(1 + R/100)^T - 1].
How do you find Selling Price from Cost Price given a profit percentage?
SP = CP x (1 + Profit%/100). For a loss, SP = CP x (1 - Loss%/100).
What is the difference between marked price, discount, and selling price?
Marked price (MP) is the listed/tag price; discount is a reduction on MP; Selling Price = MP - Discount = MP x (1 - Discount%/100).
Define the arithmetic mean (average) of n numbers.
Average = (sum of all observations) / (number of observations) = Total / n.
If the average of n values is A, how do you find the new average when one value is added or removed?
New average = (old sum +/- changed value) / (new count). Always recompute the total first, then divide by the updated number of items.
Show the other 31 Quantitative Techniques flashcards
State the rule of alligation for mixing two ingredients of different values.
(Quantity of cheaper)/(Quantity of dearer) = (Price of dearer - Mean price)/(Mean price - Price of cheaper). It gives the ratio in which two items are mixed to reach a mean value.
In a mixture, if x litres are drawn out and replaced by water n times from an initial V litres, what is the remaining pure quantity?
Remaining pure quantity = V x (1 - x/V)^n.
State the relationship between speed, distance, and time.
Speed = Distance / Time; Distance = Speed x Time; Time = Distance / Speed.
How do you convert km/hr to m/s and vice versa?
km/hr to m/s: multiply by 5/18. m/s to km/hr: multiply by 18/5.
What is the relative speed of two objects moving (a) in the same direction and (b) in opposite directions?
Same direction: difference of speeds (S1 - S2). Opposite directions: sum of speeds (S1 + S2).
In time-and-work problems, if A finishes a job in 'a' days, what is A's one-day work, and the combined rate of A and B?
A's one-day work = 1/a. Combined one-day work of A and B = 1/a + 1/b; together they finish in ab/(a+b) days.
What is the average speed for a journey covering equal distances at speeds u and v?
Average speed = 2uv/(u+v), the harmonic mean of the two speeds (not the arithmetic mean).
Classify natural, whole, integer, rational, and irrational numbers briefly.
Natural: 1,2,3,...; Whole: 0,1,2,...; Integers: ...,-2,-1,0,1,2,...; Rational: expressible as p/q (q!=0); Irrational: non-terminating non-repeating decimals (e.g., sqrt2, pi).
State the divisibility rules for 3, 9, and 11.
Divisible by 3: digit sum divisible by 3. By 9: digit sum divisible by 9. By 11: difference between sums of alternate digits is 0 or divisible by 11.
What is the relationship between LCM and HCF of two numbers a and b?
LCM x HCF = a x b (product of the two numbers).
Define prime, composite, and co-prime numbers.
Prime: exactly two factors (1 and itself). Composite: more than two factors. Co-prime: two numbers whose HCF is 1 (no common factor besides 1).
State the algebraic identity for (a + b)^2, (a - b)^2, and (a + b)(a - b).
(a+b)^2 = a^2 + 2ab + b^2; (a-b)^2 = a^2 - 2ab + b^2; (a+b)(a-b) = a^2 - b^2.
Write the quadratic formula for solving ax^2 + bx + c = 0.
x = [-b +/- sqrt(b^2 - 4ac)] / (2a), valid when a != 0.
What does the discriminant (b^2 - 4ac) tell you about the roots of a quadratic?
If > 0: two distinct real roots; if = 0: two equal real roots; if < 0: no real roots (complex roots).
For ax^2 + bx + c = 0, state the sum and product of the roots.
Sum of roots = -b/a; Product of roots = c/a.
State the identity for a^3 + b^3 and a^3 - b^3.
a^3 + b^3 = (a + b)(a^2 - ab + b^2); a^3 - b^3 = (a - b)(a^2 + ab + b^2).
Define an arithmetic progression (AP) and give its nth term formula.
An AP has a constant common difference d between consecutive terms. nth term a_n = a + (n-1)d, where a is the first term.
Write the formula for the sum of the first n terms of an AP.
S_n = n/2 [2a + (n-1)d] = n/2 (first term + last term).
Define a geometric progression (GP) and give its nth term and sum formula.
A GP has a constant ratio r between terms. nth term = a r^(n-1); Sum of n terms = a(r^n - 1)/(r - 1) for r != 1.
What is the sum of the first n natural numbers, and the sum of their squares?
Sum = n(n+1)/2; Sum of squares = n(n+1)(2n+1)/6.
State the order of operations (BODMAS/PEMDAS) used to evaluate expressions.
Brackets, Orders (powers/roots), Division and Multiplication (left to right), then Addition and Subtraction (left to right).
Write the formulas for area and perimeter of a rectangle.
Area = length x breadth; Perimeter = 2(length + breadth).
Write the area and circumference formulas for a circle of radius r.
Area = pi r^2; Circumference = 2 pi r (= pi d, where d is diameter).
State the area of a triangle given base and height, and Heron's formula.
Area = 1/2 x base x height. Heron's: Area = sqrt[s(s-a)(s-b)(s-c)], where s = (a+b+c)/2.
Write the area and perimeter of a square, and the area of a parallelogram.
Square: Area = side^2, Perimeter = 4 x side. Parallelogram: Area = base x height.
What is the formula for the area of a trapezium?
Area = 1/2 x (sum of the two parallel sides) x (perpendicular distance between them).
Define probability of an event and give its range.
P(E) = (number of favourable outcomes) / (total number of equally likely outcomes). P(E) lies between 0 and 1 inclusive.
State the addition rule for probability and the rule for complementary events.
P(A or B) = P(A) + P(B) - P(A and B). Complement: P(not A) = 1 - P(A).
Define mean, median, and mode in statistics.
Mean: arithmetic average. Median: middle value when data is ordered (average of two middle values if even count). Mode: the most frequently occurring value.
State the angle sum property 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 opposite (remote) interior angles.
What are complementary, supplementary, and vertically opposite angles?
Complementary: two angles summing to 90 degrees. Supplementary: two angles summing to 180 degrees. Vertically opposite angles (formed by two intersecting lines) are equal.
AILET Quantitative Techniques FAQ
What is in the AILET Quantitative Techniques syllabus?
AILET Quantitative Techniques is split into 4 chapters: Data Interpretation, Arithmetic, Numbers and Algebra and Mensuration and Basic Geometry. Together they contain 13 topics and 27 sub-topics.
How many chapters are in AILET Quantitative Techniques?
4 chapters, containing 13 topics and 27 sub-topics. The largest chapter is Arithmetic, with 4 topics.
Are there flashcards for AILET Quantitative Techniques?
Yes — a 51-card Quantitative Techniques 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.