SSC CGL (Combined Graduate Level) 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 (Combined Graduate Level), not a summary of it.

1. 1

   Number System and Arithmetic Foundations

   4 topics

   • Number System
     • Divisibility, factors and multiples
     • HCF and LCM
     • Surds and indices
   • Simplification and Approximation
     • BODMAS and fractions
     • Powers and roots
   • Average
   • Ratio and Proportion
     • Proportion and variation
     • Mixture and alligation
2. 2

   Commercial Arithmetic

   6 topics

   • Percentage
   • Profit, Loss and Discount
     • Successive and equivalent discounts
     • Marked price and cost price relations
   • Simple and Compound Interest
     • Simple interest
     • Compound interest and installments
   • Partnership
   • Time, Speed and Distance
     • Trains, boats and streams
     • Relative speed and races
   • Time and Work
     • Work efficiency and wages
     • Pipes and cisterns
3. 3

   Algebra

   4 topics

   • Basic Algebraic Identities and Polynomials
   • Linear Equations in Two Variables
   • Quadratic Equations
   • Graphs of Linear Equations and Coordinate Geometry
4. 4

   Geometry and Mensuration

   5 topics

   • Lines, Angles and Triangles
     • Congruence and similarity
     • Centres of a triangle
   • Circles and Tangents
   • Polygons and Quadrilaterals
   • Mensuration 2D
     • Area and perimeter of plane figures
   • Mensuration 3D
     • Cube, cuboid, cylinder and cone
     • Sphere, hemisphere and prism
5. 5

   Trigonometry

   4 topics

   • Trigonometric Ratios and Identities
   • Heights and Distances
   • Complementary Angles and Standard Values
   • Circular Measure of Angles
6. 6

   Data Interpretation

   4 topics

   • Tables and Bar Graphs
   • Line Graphs
   • Pie Charts
   • Mixed and Caselet Data Interpretation

Quantitative Aptitude flashcards for SSC CGL (Combined Graduate Level)

21 of 50 cards from the Quantitative Aptitude deck — real questions with worked answers.

1. What is a prime number, and what are the prime numbers below 20?

   A prime number is a natural number greater than 1 having exactly two factors: 1 and itself. Primes below 20: 2, 3, 5, 7, 11, 13, 17, 19.

2. State the divisibility rules for 3, 9, and 11.

   Divisible by 3: sum of digits divisible by 3. Divisible by 9: sum of digits divisible by 9. Divisible by 11: difference between the sum of digits in odd places and even places is 0 or a multiple of 11.

3. What is the relationship between HCF, LCM, and two numbers?

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

4. How many prime numbers are there between 1 and 100, and what number is neither prime nor composite?

   There are 25 prime numbers between 1 and 100. The number 1 is neither prime nor composite.

5. What is the unit digit of a number raised to a power found using cyclicity (e.g. 7^n)?

   Unit digits repeat in cycles. For 7: cycle is 7, 9, 3, 1 (period 4). Divide the power by 4; the remainder gives the position (remainder 0 means take the last in the cycle, i.e. 1).

6. 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.

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

   Brackets, Orders (powers/roots), Division, Multiplication, Addition, Subtraction. Division and multiplication are done left to right, as are addition and subtraction.

8. In simplification, in what order are the four types of brackets solved?

   Innermost first: ( ) round/parenthesis, then { } curly braces, then [ ] square brackets. Also a vinculum (bar) is solved before others.

9. What does 'approximation' mean in Quantitative Aptitude, and a quick example?

   Approximation means replacing numbers with nearby round values to estimate an answer quickly. E.g. 49.8% of 199 is approximately 50% of 200 = 100.

10. How do you convert a recurring decimal like 0.bar(7) (0.777...) into a fraction?

    For a single repeating digit, place the digit over 9: 0.777... = 7/9. For 0.bar(ab), it equals ab/99, and so on (one 9 per repeating digit).

11. What is the formula for the average (arithmetic mean) of a set of values?

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

12. What is the average of the first n natural numbers, and the average of the first n consecutive odd numbers?

    Average of first n natural numbers = (n+1)/2. Average of first n consecutive odd numbers = n. (Average of first n consecutive even numbers = n+1.)

13. If the average of a group changes when one member is replaced, how do you find the new member's value?

    New value = Old value + (Change in average x Number of members). If the average increases by d when one of n members is replaced, the new member exceeds the old by n x d.

14. For a journey at speed x going and speed y returning over the same distance, what is the average speed?

    Average speed = 2xy/(x+y) (the harmonic mean of the two speeds), not the simple arithmetic mean.

15. What is a ratio, and how is the ratio a:b simplified or compared with c:d?

    A ratio a:b compares two quantities of the same kind by division. Simplify by dividing both terms by their HCF. To compare a:b and c:d, cross-multiply: a:b > c:d if ad > bc.

16. In proportion a:b = c:d, what are the means, the extremes, and the key product rule?

    b and c are the means; a and d are the extremes. Product of means = Product of extremes, i.e. b x c = a x d. d is the fourth proportional.

17. Define third proportional and mean proportional.

    Third proportional to a and b is c where a:b = b:c, so c = b^2/a. Mean (geometric) proportional between a and b is sqrt(ab).

18. How do you divide an amount A among three people in the ratio x:y:z?

    Total parts = x+y+z. Each share = (its ratio term / total parts) x A. E.g. first share = x/(x+y+z) x A.

19. How do you convert a fraction or decimal to a percentage and vice versa?

    Fraction/decimal to percent: multiply by 100. Percent to fraction: divide by 100 (remove % sign and put over 100). E.g. 0.45 = 45%; 30% = 30/100 = 3/10.

20. What is the formula for percentage increase and percentage decrease?

    Percentage increase = (Increase / Original) x 100. Percentage decrease = (Decrease / Original) x 100.

21. If a value is increased by x% and then decreased by x%, what is the net percentage change?

    There is a net decrease of x^2/100 percent. (Successive +x% then -x% gives -x^2/100 %, never zero.)

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