SBOTS Quantitative Reasoning Syllabus

Quantitative Reasoning syllabus — full chapter and topic list

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

1. 1

   Arithmetic Fundamentals

   4 topics

   • Number System & Fractions
   • HCF & LCM
   • Decimals & Simplification
   • Square Roots & Powers
2. 2

   Ratio, Proportion & Percentage

   4 topics

   • Ratio & Proportion
   • Percentages
   • Profit & Loss
   • Discount & Marked Price
3. 3

   Interest & Banking Math

   3 topics

   • Simple Interest
   • Compound Interest
   • Partnership & Shares
4. 4

   Time, Work & Distance

   3 topics

   • Time & Work
   • Time, Speed & Distance
   • Pipes & Cisterns
5. 5

   Averages, Mixtures & Allegation

   3 topics

   • Averages
   • Mixtures & Allegation
   • Age Problems
6. 6

   Data Interpretation

   4 topics

   • Tables
   • Bar Charts & Line Graphs
   • Pie Charts
   • Caselet Data Sets
7. 7

   Basic Algebra & Geometry

   3 topics

   • Linear & Quadratic Equations
   • Mensuration
   • Probability & Permutations

Quantitative Reasoning flashcards for SBOTS

25 of 50 cards from the Quantitative Reasoning deck — real questions with worked answers.

1. What are the four main types of numbers in the number system: natural, whole, integers, and rational/irrational?

   Natural numbers (1, 2, 3...); Whole numbers (0, 1, 2, 3...); Integers (...-2, -1, 0, 1, 2...); Rational numbers (expressible as p/q, q≠0); Irrational numbers (non-terminating, non-repeating decimals like √2, π).

2. What is a prime number, and what is the only even prime number?

   A prime number is a natural number greater than 1 divisible only by 1 and itself. 2 is the only even prime number.

3. How do you add or subtract two fractions with different denominators?

   Find the LCM of the denominators (least common denominator), convert each fraction to an equivalent fraction with that denominator, then add or subtract the numerators while keeping the denominator the same.

4. How do you divide one fraction by another (e.g., a/b ÷ c/d)?

   Multiply the first fraction by the reciprocal of the second: a/b ÷ c/d = a/b × d/c = (a×d)/(b×c).

5. What is the HCF (Highest Common Factor) of two numbers?

   The HCF is the largest number that divides both numbers exactly without leaving a remainder. It is also called the GCD (Greatest Common Divisor).

6. What is the LCM (Least Common Multiple) of two numbers?

   The LCM is the smallest positive number that is a multiple of both numbers (i.e., divisible by each of them).

7. What is the fundamental relationship between HCF and LCM of two numbers?

   HCF × LCM = Product of the two numbers. So for numbers a and b: HCF(a,b) × LCM(a,b) = a × b.

8. How do you find the LCM and HCF using prime factorization?

   HCF = product of the lowest powers of all common prime factors. LCM = product of the highest powers of all prime factors appearing in any of the numbers.

9. What is the rule for the number of decimal places in the product of two decimals?

   Multiply the numbers ignoring decimal points, then place the decimal point in the product so that the number of decimal places equals the total number of decimal places in both factors combined.

10. How do you convert a recurring (repeating) decimal like 0.333... into a fraction?

    For a pure recurring decimal, place the repeating digits over as many 9s as there are repeating digits. So 0.333... = 3/9 = 1/3, and 0.272727... = 27/99 = 3/11.

11. What is the order of operations (BODMAS/BIDMAS) used in simplification?

    Brackets, Orders (powers/roots), Division and Multiplication (left to right), then Addition and Subtraction (left to right).

12. How do you divide a number by a decimal (e.g., dividing by 0.25)?

    Convert the divisor to a whole number by multiplying both dividend and divisor by the same power of 10, then divide. Dividing by 0.25 equals multiplying by 4.

13. What is the value of √2, √3, and √5 approximately (to memorize)?

    √2 ≈ 1.414, √3 ≈ 1.732, √5 ≈ 2.236.

14. How do you find the square root of a number by prime factorization?

    Express the number as a product of primes, pair the identical prime factors, take one factor from each pair, and multiply them together. For example, √144 = √(2²×2²×3²) = 2×2×3 = 12.

15. What are the basic laws of exponents: product, quotient, and power of a power?

    a^m × a^n = a^(m+n); a^m ÷ a^n = a^(m−n); (a^m)^n = a^(m×n); a^0 = 1; a^(−n) = 1/a^n.

16. How do you express a square root as a fractional exponent?

    The nth root of a number equals that number raised to the power 1/n: ⁿ√a = a^(1/n). So √a = a^(1/2) and ³√a = a^(1/3).

17. What is a ratio, and how is the ratio a:b expressed as a fraction?

    A ratio is a comparison of two quantities of the same kind by division. The ratio a:b is expressed as the fraction a/b, where a is the antecedent and b is the consequent.

18. What is a proportion, and what is the rule of cross-multiplication?

    A proportion states that two ratios are equal: a:b = c:d (or a/b = c/d). By cross-multiplication, the product of extremes equals the product of means: a × d = b × c.

19. In the proportion a:b = c:d, what are the extremes, means, and the fourth proportional?

    a and d are the extremes; b and c are the means. d is the fourth proportional, found by d = (b×c)/a.

20. What is the difference between direct proportion and inverse proportion?

    In direct proportion, two quantities increase or decrease together (a/b = constant). In inverse proportion, one increases as the other decreases (a × b = constant).

21. How do you convert a fraction or ratio into a percentage?

    Multiply the fraction by 100 and add the % sign. For example, 3/4 = (3/4 × 100)% = 75%.

22. How do you find x% of a value N?

    x% of N = (x/100) × N. For example, 20% of 250 = (20/100) × 250 = 50.

23. How do you calculate the percentage increase or decrease between two values?

    Percentage change = (Change in value / Original value) × 100. Use increase when new value is higher, decrease when lower, always dividing by the original value.

24. If a value increases by x% and then decreases by x%, what is the net effect?

    There is a net decrease of (x²/100)%. The net change formula for two successive changes a% and b% is: a + b + (ab/100)%, where decreases are negative.

25. What is the formula for Profit and Profit Percentage?

    Profit = Selling Price (SP) − Cost Price (CP). Profit% = (Profit / CP) × 100. Profit percentage is always calculated on the cost price.

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