SNAP Quantitative Ability Syllabus

Quantitative Ability syllabus — full chapter and topic list

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

1. 1

   Arithmetic

   7 topics

   • Percentages
     • Successive percentage change
     • Applications in profit and population
   • Profit, Loss and Discount
     • Cost price, selling price and marked price
     • Successive discounts
   • Simple and Compound Interest
     • Difference between SI and CI
     • Equated installments
   • Ratio, Proportion and Variation
     • Direct and inverse proportion
     • Componendo and dividendo
   • Averages, Mixtures and Alligation
     • Weighted averages
     • Alligation rule
   • Time, Speed and Distance
     • Relative speed
     • Trains, boats and streams
     • Circular and linear races
   • Time and Work
     • Work efficiency and rate
     • Pipes and cisterns
2. 2

   Algebra

   6 topics

   • Linear and Quadratic Equations
     • Roots, nature and sum-product relations
     • Word problems on equations
   • Inequalities and Modulus
   • Functions and Graphs
     • Domain, range and composite functions
   • Logarithms
     • Laws of logarithms
   • Progressions
     • Arithmetic progression
     • Geometric and harmonic progression
   • Surds and Indices
3. 3

   Geometry and Mensuration

   5 topics

   • Lines, Angles and Triangles
     • Properties of triangles and congruence
     • Similarity and theorems
   • Polygons and Circles
     • Quadrilateral properties
     • Tangents, chords and arcs
   • Coordinate Geometry
     • Distance, section and midpoint formulae
     • Equation of a line and slope
   • Mensuration
     • Areas of 2D figures
     • Surface area and volume of solids
   • Trigonometry Basics
     • Trigonometric ratios and identities
     • Heights and distances
4. 4

   Number System

   5 topics

   • Classification of Numbers
     • Natural, integer, rational and real numbers
   • Factors and Multiples
     • HCF and LCM
     • Number of factors and their sum
   • Divisibility and Remainders
     • Divisibility rules
     • Remainder theorems and cyclicity
   • Unit Digit and Last Digits
   • Base System
     • Conversion between bases
5. 5

   Modern Mathematics

   4 topics

   • Permutations and Combinations
     • Arrangements and selections
     • Circular permutations
   • Probability
     • Classical probability
     • Conditional probability and events
   • Set Theory
     • Venn diagrams
     • Union, intersection and complement
   • Binomial Theorem

Quantitative Ability flashcards for SNAP

25 of 53 cards from the Quantitative Ability deck — real questions with worked answers.

1. How do you convert a percentage increase from value A to value B into a formula, and what is the result if a price rises from 80 to 100?

   Percentage change = ((B − A)/A) × 100. From 80 to 100: ((100−80)/80)×100 = 25% increase.

2. If a quantity increases by x% and then decreases by x%, what is the net percentage change?

   A net decrease of (x²/100)%. The two changes never cancel; the result is always lower than the original.

3. What is the formula for Profit %, and what does it tell you?

   Profit % = (Profit / Cost Price) × 100. It expresses gain as a fraction of the cost price (not the selling price).

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

   SP = MP × (1 − Discount%/100). Discount is always calculated on the Marked Price, not on the Cost Price.

5. A shopkeeper gives two successive discounts of a% and b%. What single equivalent discount do they represent?

   Equivalent discount = a + b − (ab/100) percent.

6. What is the Simple Interest formula, and what does each symbol mean?

   SI = (P × R × T)/100, where P = principal, R = rate % per annum, T = time in years.

7. What is the Compound Interest amount formula for annual compounding?

   A = P(1 + R/100)^T, and CI = A − P, where P = principal, R = annual rate %, T = years.

8. For 2 years, by how much does Compound Interest exceed Simple Interest on the same principal and rate?

   CI − SI (2 years) = P × (R/100)². This difference equals the interest earned on the first year's interest.

9. What does the ratio a : b mean, and how do you find the value of each part if a:b = 3:5 and the total is 64?

   a:b means a/b = 3/5. Total parts = 3+5 = 8; each part = 64/8 = 8, so a = 24 and b = 40.

10. State the relationship in a proportion a : b :: c : d and the property it satisfies.

    a/b = c/d, meaning the product of the means equals the product of the extremes: a × d = b × c.

11. Define direct variation and inverse variation.

    Direct: y = kx (y increases as x increases, ratio constant). Inverse: y = k/x (y decreases as x increases, product constant).

12. What is the formula for the average (arithmetic mean) of n quantities?

    Average = (Sum of all quantities) / (Number of quantities). Equivalently, Sum = Average × n.

13. State the alligation rule for mixing two ingredients to get a desired mean price.

    (Quantity of cheaper)/(Quantity of dearer) = (Price of dearer − Mean price)/(Mean price − Price of cheaper).

14. A vessel has milk and water in ratio. What is the formula for milk left after one of n repeated replacements of x from a volume V?

    Milk left = V × (1 − x/V)^n, after each operation removing x and replacing with water.

15. What is the basic relationship between speed, distance and time, including the unit conversion from km/h to m/s?

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

16. What is the formula for average speed when equal distances are covered at speeds u and v?

    Average speed = 2uv/(u + v), the harmonic mean of the two speeds (not the simple average).

17. For two trains crossing each other, how does relative speed differ for same vs opposite directions?

    Opposite directions: relative speed = sum of speeds. Same direction: relative speed = difference of speeds.

18. In Time and Work, if A completes a job in n days, what is A's one-day work, and how is combined work found?

    A's one-day work = 1/n. If A does 1/a and B does 1/b per day, together they do (1/a + 1/b) per day; time = 1/(1/a+1/b).

19. State the relationship between the roots and coefficients of ax² + bx + c = 0.

    Sum of roots = −b/a; Product of roots = c/a.

20. What is the quadratic formula and what does the discriminant indicate?

    x = (−b ± √(b²−4ac))/2a. Discriminant D = b²−4ac: D>0 two real distinct roots, D=0 equal real roots, D<0 complex roots.

21. When solving inequalities, what operation reverses the inequality sign?

    Multiplying or dividing both sides by a negative number reverses the inequality sign (e.g. −2x > 6 becomes x < −3).

22. How do you solve the modulus inequality |x| < a (a > 0) and |x| > a?

    |x| < a means −a < x < a. |x| > a means x < −a or x > a.

23. What is the definition of a function, and how do you determine if a graph represents one?

    A function maps each input to exactly one output. The vertical line test: any vertical line meets the graph at most once.

24. What do f(x) + k, f(x + k), and f(−x) do to the graph of f(x)?

    f(x)+k shifts up by k; f(x+k) shifts left by k; f(−x) reflects across the y-axis.

25. State the definition of a logarithm: what does log_b(x) = y mean?

    log_b(x) = y means b^y = x, where b > 0, b ≠ 1, and x > 0.

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Planning Quantitative Ability for SNAP

Quantitative Ability (SNAP) FAQ