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NTS NAT-IA Quantitative Reasoning Syllabus

The Quantitative Reasoning syllabus for NTS NAT-IA in full: 6 chapters and 25 topics, every one listed below, plus 50 Quantitative Reasoning flashcards with answers.

6Chapters
25Topics
50Flashcards

Quantitative Reasoning syllabus: all 6 chapters

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

  1. Arithmetic

     6 topics
    • Number Systems
    • Fractions and Decimals
    • Ratio and Proportion
    • Percentages
    • Profit and Loss
    • Average

  2. Algebra

     4 topics
    • Linear Equations
    • Algebraic Expressions
    • Exponents and Roots
    • Sequences and Series

  3. Geometry

     5 topics
    • Lines and Angles
    • Triangles and Polygons
    • Circles
    • Area and Perimeter
    • Coordinate Geometry

  4. Word Problems

     4 topics
    • Time, Speed and Distance
    • Time and Work
    • Ages
    • Mixtures and Alligation

  5. Data Interpretation

     3 topics
    • Tables
    • Bar and Line Graphs
    • Pie Charts

  6. Basic Statistics

     3 topics
    • Mean, Median and Mode
    • Probability
    • Permutations and Combinations

NTS NAT-IA Quantitative Reasoning flashcards — 50 questions with answers

  1. What is a rational number?

    A number that can be expressed as a fraction p/q where p and q are integers and q is not zero (e.g., 1/2, -3, 0.75).

  2. What is an irrational number? Give an example.

    A number that cannot be written as a ratio of two integers; its decimal is non-terminating and non-repeating. Examples: pi, square root of 2, e.

  3. Define a prime number and give the only even prime.

    A natural number greater than 1 with exactly two factors: 1 and itself. The only even prime is 2.

  4. What are composite numbers?

    Natural numbers greater than 1 that have more than two factors (i.e., divisible by a number other than 1 and itself), e.g., 4, 6, 9.

  5. State the divisibility rule for 3 and for 9.

    A number is divisible by 3 if the sum of its digits is divisible by 3; divisible by 9 if the digit sum is divisible by 9.

  6. State the divisibility rule for 4 and for 8.

    Divisible by 4 if the last two digits form a number divisible by 4; divisible by 8 if the last three digits form a number divisible by 8.

  7. How are HCF (GCD) and LCM of two numbers related?

    For two numbers a and b: HCF x LCM = a x b.

  8. What is the difference between a terminating and a recurring (repeating) decimal?

    A terminating decimal ends after a finite number of digits (e.g., 0.25); a recurring decimal has one or more digits repeating infinitely (e.g., 0.333...).

  9. How do you convert a fraction to a decimal?

    Divide the numerator by the denominator using long division.

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

    Find the LCM of the denominators, convert each fraction to an equivalent fraction with that common denominator, then add or subtract the numerators.

  11. How do you divide one fraction by another?

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

  12. What is a proper fraction versus an improper fraction?

    A proper fraction has numerator less than denominator (value < 1); an improper fraction has numerator greater than or equal to denominator (value >= 1).

  13. How do you compare two fractions a/b and c/d?

    Cross-multiply: compare a x d with b x c. If a x d > b x c then a/b > c/d (for positive denominators).

  14. What is a ratio and how is it written?

    A ratio is a comparison of two quantities of the same kind by division, written as a:b or a/b.

  15. What is a proportion?

    A statement that two ratios are equal, written a:b = c:d (or a/b = c/d).

  16. State the rule of cross-multiplication in a proportion a:b = c:d.

    The product of the means equals the product of the extremes: b x c = a x d (i.e., a x d = b x c).

  17. What is direct proportion?

    A relationship where two quantities increase or decrease together so their ratio stays constant: y = kx (y/x is constant).

  18. What is inverse proportion?

    A relationship where one quantity increases as the other decreases, keeping their product constant: xy = k.

  19. How do you divide a quantity Q in the ratio a:b?

    First part = Q x a/(a+b); second part = Q x b/(a+b).

  20. How do you convert a fraction or decimal to a percentage?

    Multiply by 100 and add the percent sign (e.g., 0.25 = 0.25 x 100 = 25%).

Show the other 30 Quantitative Reasoning flashcards

  1. How do you find x% of a number N?

    Compute (x/100) x N.

  2. What is the formula for percentage increase or decrease?

    Percentage change = (change in value / original value) x 100, where change = new value minus original value.

  3. If a value increases by p% then decreases by p%, what is the net effect?

    There is a net decrease of (p^2/100)% from the original value.

  4. Define Cost Price (CP) and Selling Price (SP).

    Cost Price is the price at which an item is bought; Selling Price is the price at which it is sold.

  5. State the formulas for profit and loss.

    Profit = SP - CP (when SP > CP); Loss = CP - SP (when CP > SP).

  6. How is profit percentage and loss percentage calculated?

    Profit% = (Profit/CP) x 100; Loss% = (Loss/CP) x 100. Both are calculated on the cost price.

  7. Given CP and a profit of p%, how do you find SP?

    SP = CP x (100 + p)/100.

  8. What is a discount and on which price is it calculated?

    A discount is a reduction in the marked (list) price; it is calculated on the marked price: Discount = Marked Price x Discount%/100.

  9. What is the formula for the average (arithmetic mean) of n values?

    Average = (sum of all values) / (number of values).

  10. If the average of n numbers is A, what is their sum?

    Sum = A x n (average multiplied by the count).

  11. How does adding a new value equal to the current average affect the average?

    The average stays unchanged, because the new value equals the existing mean.

  12. What is the average of the first n natural numbers (1 to n)?

    (n + 1) / 2.

  13. What is a linear equation in one variable?

    An equation of the form ax + b = 0 where a is not zero; it has degree 1 and exactly one solution, x = -b/a.

  14. What does the solution of a system of two linear equations in two variables represent graphically?

    The point of intersection of the two straight lines (the (x, y) value satisfying both equations).

  15. When does a system of two linear equations have no solution or infinitely many solutions?

    No solution when the lines are parallel (same slope, different intercepts); infinitely many when the lines are identical (coincident).

  16. What is the slope-intercept form of a line?

    y = mx + c, where m is the slope and c is the y-intercept.

  17. What is the difference between a term, a coefficient, and a constant in an algebraic expression?

    A term is a single part separated by + or -; a coefficient is the numerical factor of a variable; a constant is a term with no variable.

  18. State the identity for (a + b)^2.

    (a + b)^2 = a^2 + 2ab + b^2.

  19. State the identity for (a - b)^2.

    (a - b)^2 = a^2 - 2ab + b^2.

  20. State the identity for a^2 - b^2.

    a^2 - b^2 = (a + b)(a - b).

  21. State the laws of exponents for a^m x a^n and a^m / a^n.

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

  22. What do a^0 and a^(-n) equal (a not zero)?

    a^0 = 1; a^(-n) = 1/a^n.

  23. What is the power-of-a-power rule and how is a fractional exponent a^(m/n) interpreted?

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

  24. What is the difference between an arithmetic progression (AP) and a geometric progression (GP)?

    In an AP each term is obtained by adding a constant common difference d; in a GP each term is obtained by multiplying by a constant common ratio r.

  25. What is the formula for the n-th term of an arithmetic progression?

    a_n = a + (n - 1)d, where a is the first term and d is the common difference.

  26. What is the formula for the sum of the first n terms of an AP?

    S_n = (n/2)[2a + (n - 1)d], or equivalently (n/2)(first term + last term).

  27. What is the formula for the n-th term of a geometric progression?

    a_n = a x r^(n-1), where a is the first term and r is the common ratio.

  28. What are complementary and supplementary angles?

    Complementary angles sum to 90 degrees; supplementary angles sum to 180 degrees.

  29. State the angle sum property of a triangle and the exterior angle theorem.

    The three interior angles of a triangle sum to 180 degrees; an exterior angle equals the sum of the two non-adjacent (remote) interior angles.

  30. What is the formula for the sum of the interior angles of a polygon with n sides?

    Sum of interior angles = (n - 2) x 180 degrees.

NTS NAT-IA Quantitative Reasoning FAQ

What is in the NTS NAT-IA Quantitative Reasoning syllabus?

NTS NAT-IA Quantitative Reasoning is split into 6 chapters: Arithmetic, Algebra, Geometry, Word Problems, Data Interpretation and Basic Statistics. Together they contain 25 topics.

How many chapters are in NTS NAT-IA Quantitative Reasoning?

6 chapters, containing 25 topics. The largest chapter is Arithmetic, with 6 topics.

Are there flashcards for NTS NAT-IA 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.