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SBOTS Quantitative Reasoning Syllabus

The Quantitative Reasoning syllabus for SBOTS in full: 7 chapters and 24 topics, every one listed below, plus 50 Quantitative Reasoning flashcards with answers.

7Chapters
24Topics
50Flashcards

Quantitative Reasoning syllabus: all 7 chapters

Expand any chapter to see its topics and sub-topics.

  1. Arithmetic Fundamentals

     4 topics
    • Number System & Fractions
    • HCF & LCM
    • Decimals & Simplification
    • Square Roots & Powers

  2. Ratio, Proportion & Percentage

     4 topics
    • Ratio & Proportion
    • Percentages
    • Profit & Loss
    • Discount & Marked Price

  3. Interest & Banking Math

     3 topics
    • Simple Interest
    • Compound Interest
    • Partnership & Shares

  4. Time, Work & Distance

     3 topics
    • Time & Work
    • Time, Speed & Distance
    • Pipes & Cisterns

  5. Averages, Mixtures & Allegation

     3 topics
    • Averages
    • Mixtures & Allegation
    • Age Problems

  6. Data Interpretation

     4 topics
    • Tables
    • Bar Charts & Line Graphs
    • Pie Charts
    • Caselet Data Sets

  7. Basic Algebra & Geometry

     3 topics
    • Linear & Quadratic Equations
    • Mensuration
    • Probability & Permutations

SBOTS Quantitative Reasoning flashcards — 50 questions with 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).

Show the other 30 Quantitative Reasoning flashcards

  1. 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%.

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

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

  3. 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.

  4. 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.

  5. 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.

  6. What is the formula for Loss and Loss Percentage?

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

  7. How do you find the Selling Price (SP) given Cost Price (CP) and a profit percentage?

    SP = CP × (100 + Profit%)/100. For a loss: SP = CP × (100 − Loss%)/100.

  8. How do you find the Cost Price (CP) from the Selling Price (SP) and profit percentage?

    CP = SP × 100/(100 + Profit%). For a loss: CP = SP × 100/(100 − Loss%).

  9. What is Marked Price (MP), and how is Discount related to it?

    Marked Price (also list price) is the price labeled on an item before discount. Discount = MP − SP. Discount% = (Discount / MP) × 100. Discount is always calculated on the Marked Price.

  10. How do you find the Selling Price after a single discount on the Marked Price?

    SP = MP × (100 − Discount%)/100. For example, a 20% discount on MP gives SP = MP × 0.80.

  11. How do you find the single equivalent discount for two successive discounts of a% and b%?

    Equivalent single discount = a + b − (ab/100)%. For example, successive discounts of 20% and 10% equal a single discount of 20 + 10 − 2 = 28%.

  12. What is the formula for Simple Interest (SI)?

    SI = (P × R × T)/100, where P = Principal, R = Rate of interest per annum, and T = Time in years.

  13. How do you find the Amount (A) in Simple Interest?

    Amount = Principal + Simple Interest = P + (P×R×T)/100 = P(1 + RT/100).

  14. In Simple Interest, how do you find Principal, Rate, or Time given the other values?

    P = (100×SI)/(R×T); R = (100×SI)/(P×T); T = (100×SI)/(P×R).

  15. What is the formula for Compound Interest amount when compounded annually?

    A = P(1 + R/100)^n, where A = Amount, P = Principal, R = rate per annum, n = number of years. Compound Interest CI = A − P.

  16. How is the compound interest formula adjusted when interest is compounded half-yearly or quarterly?

    Half-yearly: A = P(1 + R/200)^(2n). Quarterly: A = P(1 + R/400)^(4n). The rate is divided and the period multiplied by the number of compounding times per year.

  17. What is the difference between Compound Interest and Simple Interest for 2 years on principal P at rate R?

    CI − SI (for 2 years) = P × (R/100)². This is a quick formula to find the difference over two years.

  18. In a partnership, how is profit divided when partners invest different amounts for the same time period?

    Profit is divided in the ratio of their investments (capitals). If A invests x and B invests y for equal time, profit is shared in ratio x : y.

  19. In a partnership, how is profit divided when both capital and time differ?

    Profit is divided in the ratio of (Capital × Time) for each partner. If A invests P₁ for t₁ and B invests P₂ for t₂, profit ratio = P₁t₁ : P₂t₂.

  20. What is the difference between a working partner and a sleeping partner?

    A working (active) partner manages the business and may receive a salary or commission in addition to a profit share. A sleeping (dormant) partner only invests capital and shares profit but does not participate in management.

  21. If A can do a piece of work in n days, how much work does A do in one day?

    A's one-day work = 1/n of the total work. Work done is the reciprocal of the time taken to complete the whole job.

  22. If A can do a work in x days and B in y days, how long do they take working together?

    Combined one-day work = 1/x + 1/y = (x+y)/(xy). Time taken together = xy/(x+y) days.

  23. What is the relationship between number of workers, days, and work done (the work equation)?

    M₁ × D₁ × H₁ / W₁ = M₂ × D₂ × H₂ / W₂, where M = men, D = days, H = hours/day, W = work. More workers means fewer days for the same work.

  24. What is the basic formula relating speed, distance, and time?

    Speed = Distance / Time; Distance = Speed × Time; Time = Distance / Speed.

  25. How do you convert speed from km/hr to m/s and from m/s to km/hr?

    km/hr to m/s: multiply by 5/18. m/s to km/hr: multiply by 18/5.

  26. What is the average speed for a journey covering equal distances at speeds x and y?

    Average speed = 2xy/(x+y) (the harmonic mean). It is NOT the simple arithmetic average of the two speeds.

  27. In boats and streams, what are the downstream and upstream speeds in terms of boat speed (b) and stream speed (s)?

    Downstream speed = b + s (with the current); Upstream speed = b − s (against the current). Also b = (downstream + upstream)/2 and s = (downstream − upstream)/2.

  28. In pipes and cisterns, how do inlet and outlet pipes affect the tank, and how is combined rate calculated?

    An inlet pipe fills (positive rate, e.g., +1/x per hour); an outlet pipe empties (negative rate, e.g., −1/y per hour). Combined rate = sum of individual rates; time to fill = 1/(net rate).

  29. What is the formula for Average (Mean), and how do you find the total from the average?

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

  30. What is the rule of Alligation for finding the ratio in which two ingredients are mixed?

    Ratio of cheaper to dearer = (Dearer price − Mean price) : (Mean price − Cheaper price). This gives the proportion in which two quantities at different prices are mixed to get the mean (average) price.

SBOTS Quantitative Reasoning FAQ

What is in the SBOTS Quantitative Reasoning syllabus?

SBOTS Quantitative Reasoning is split into 7 chapters: Arithmetic Fundamentals, Ratio, Proportion & Percentage, Interest & Banking Math, Time, Work & Distance, Averages, Mixtures & Allegation, Data Interpretation and Basic Algebra & Geometry. Together they contain 24 topics.

How many chapters are in SBOTS Quantitative Reasoning?

7 chapters, containing 24 topics. The largest chapter is Arithmetic Fundamentals, with 4 topics.

Are there flashcards for SBOTS Quantitative Reasoning?

Yes — a 50-card Quantitative Reasoning 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.