SSC CGL 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 SSC CGL, not a summary of it.

1. 1

   Number System

   4 topics

   • Divisibility & Remainder
   • Multiples & Factors
   • Integers
   • LCM & HCF
2. 2

   Algebra

   4 topics

   • Identities
   • Polynomials
   • Algebraic Equations
   • Graphs of Equations
3. 3

   Geometry

   4 topics

   • Triangles congruence
   • Circles
   • Coordinate geometry
   • Lines and angles
4. 4

   Trigonometry

   3 topics

   • Trigonometric ratios
   • Heights and Distances
   • Trigonometric identities
5. 5

   Mensuration

   3 topics

   • Area and Perimeter
   • Volume
   • Surface Area
6. 6

   Statistics

   3 topics

   • Mean, Median, Mode
   • Graphical representation of data
   • Measures of Dispersion

Quantitative Aptitude flashcards for SSC CGL

21 of 59 cards from the Quantitative Aptitude deck — real questions with worked answers.

1. What is the divisibility rule for 8?

   A number is divisible by 8 if the number formed by its last three digits is divisible by 8.

2. What is the divisibility rule for 11?

   A number is divisible by 11 if the difference between the sum of digits at odd positions and the sum of digits at even positions is 0 or a multiple of 11.

3. For any natural number n, what is the sum of the first n natural numbers, the sum of their squares, and the sum of their cubes?

   Sum = n(n+1)/2; Sum of squares = n(n+1)(2n+1)/6; Sum of cubes = [n(n+1)/2]^2.

4. State the relationship between HCF, LCM and two numbers a and b.

   HCF(a,b) x LCM(a,b) = a x b (product of the two numbers).

5. What is the BODMAS/order of operations used in simplification?

   Brackets, Of, Division, Multiplication, Addition, Subtraction — evaluated in that order (division and multiplication left to right, then addition and subtraction left to right).

6. What do the surd laws give for √(ab) and √(a/b)?

   √(ab) = √a x √b and √(a/b) = √a / √b (for a, b ≥ 0, b ≠ 0).

7. How do you rationalise the denominator of 1/(√a + √b)?

   Multiply numerator and denominator by the conjugate (√a − √b), giving (√a − √b)/(a − b).

8. State the three basic laws of exponents for multiplication, division, and power of a power.

   a^m x a^n = a^(m+n); a^m / a^n = a^(m−n); (a^m)^n = a^(mn).

9. What are the values of a^0 and a^(−n) (a ≠ 0)?

   a^0 = 1 and a^(−n) = 1/a^n.

10. How do you express a^(m/n) as a root?

    a^(m/n) = the n-th root of a^m = (n-th root of a)^m, i.e. ⁿ√(a^m).

11. How do you convert a fraction to a percentage and a percentage to a fraction?

    Fraction to percentage: multiply by 100 (add % sign). Percentage to fraction: divide by 100.

12. If a value increases by x% then decreases by x%, what is the net change?

    There is a net decrease of x²/100 percent.

13. Give the formulas for Profit% and Loss%.

    Profit% = (Profit/Cost Price) x 100; Loss% = (Loss/Cost Price) x 100.

14. What is the formula relating Selling Price, Cost Price and Profit% (or Loss%)?

    SP = CP x (100 + Profit%)/100, and for loss SP = CP x (100 − Loss%)/100.

15. How is Discount% defined, and how does Selling Price relate to Marked Price?

    Discount% = (Discount/Marked Price) x 100; SP = MP x (100 − Discount%)/100.

16. If two articles are sold at the same price, one at x% gain and the other at x% loss, what is the overall result?

    There is always a net loss of x²/100 percent.

17. If a:b = 2:3 and b:c = 4:5, what is a:b:c?

    a:b:c = 8:12:15 (make b common: a:b = 8:12, b:c = 12:15).

18. In a proportion a:b = c:d, what is the product relationship (rule of cross products)?

    a x d = b x c (product of extremes = product of means).

19. How is the average of a set of values calculated?

    Average = (Sum of all observations) / (Number of observations).

20. What is the average of the first n consecutive natural numbers?

    (n + 1)/2.

21. State the alligation rule for finding the ratio in which two ingredients are mixed.

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

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