NTS NAT-ICS 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 NTS NAT-ICS, not a summary of it.

1. 1

   Arithmetic

   5 topics

   • Number Properties
   • Fractions, Decimals and Percentages
   • Ratio and Proportion
   • Average and Mean
   • Profit, Loss and Interest
2. 2

   Algebra

   5 topics

   • Linear Equations
   • Quadratic Equations
   • Exponents and Radicals
   • Logarithms
   • Algebraic Expressions and Factoring
3. 3

   Geometry

   5 topics

   • Lines and Angles
   • Triangles and Polygons
   • Circles
   • Area, Perimeter and Volume
   • Coordinate Geometry
4. 4

   Word Problems

   3 topics

   • Speed, Distance and Time
   • Work and Time
   • Mixtures and Allegations
5. 5

   Data Interpretation

   2 topics

   • Tables and Charts
   • Graphs and Reading Trends

Quantitative Reasoning flashcards for NTS NAT-ICS

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

1. What are integers, and how do they differ from whole numbers and natural numbers?

   Integers are the set {..., -3, -2, -1, 0, 1, 2, 3, ...} — all positive and negative whole numbers plus zero. Natural (counting) numbers are {1, 2, 3, ...}. Whole numbers are the natural numbers plus zero {0, 1, 2, ...}. Integers extend whole numbers by adding the negatives.

2. What is the difference between a prime number and a composite number?

   A prime number has exactly two distinct factors: 1 and itself (e.g. 2, 3, 5, 7). A composite number has more than two factors (e.g. 4, 6, 8, 9). The number 1 is neither prime nor composite, and 2 is the only even prime.

3. State the divisibility rules for 3, 4, 9, and 11.

   Divisible by 3 if the sum of its digits is divisible by 3. By 9 if the digit sum is divisible by 9. By 4 if the number formed by its last two digits is divisible by 4. By 11 if the difference between the sum of digits in odd positions and even positions is 0 or a multiple of 11.

4. What is the difference between the LCM and the HCF (GCD) of two numbers?

   The HCF (Highest Common Factor / GCD) is the largest number that divides both numbers exactly. The LCM (Least Common Multiple) is the smallest number that is a multiple of both. Key relation: for two numbers a and b, HCF × LCM = a × b.

5. How do you classify a number as even or odd, and what are the parity rules for addition and multiplication?

   An even number is divisible by 2; an odd number is not. Addition: even+even=even, odd+odd=even, even+odd=odd. Multiplication: even×anything=even; odd×odd=odd. A product is even if at least one factor is even.

6. What is the difference between a rational and an irrational number?

   A rational number can be written as a fraction p/q where p and q are integers and q ≠ 0 (its decimal terminates or repeats), e.g. 0.5, 1/3. An irrational number cannot be written as such a fraction; its decimal is non-terminating and non-repeating, e.g. √2, π.

7. How do you convert a fraction to a percentage, and a percentage to a fraction?

   To convert a fraction to a percentage, multiply by 100 and add the % sign (e.g. 3/4 = 0.75 × 100 = 75%). To convert a percentage to a fraction, divide by 100 and simplify (e.g. 40% = 40/100 = 2/5).

8. How do you convert a recurring decimal such as 0.333... into a fraction?

   Let x equal the decimal, multiply by a power of 10 to shift one full repeat block, subtract the original, then solve. For 0.333...: x = 0.333..., 10x = 3.333..., 10x − x = 3, so 9x = 3 and x = 1/3.

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

   Percentage change = (change in value ÷ original value) × 100. For an increase, change = new − old; for a decrease, change = old − new. The result is expressed as a percentage of the ORIGINAL value, not the new value.

10. If a quantity is increased by x% and then decreased by x%, what is the net effect?

    There is a net DECREASE, not zero change. The net percentage change is −(x²/100)%. For example, a 20% increase followed by a 20% decrease gives a net change of −(400/100)% = −4%.

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

    Find a common denominator (usually the LCM of the denominators), convert each fraction to an equivalent fraction with that denominator, then add or subtract the numerators while keeping the common denominator. Finally, simplify the result.

12. How do you divide one fraction by another?

    Multiply the first fraction by the reciprocal (inverse) of the second. That is, a/b ÷ c/d = a/b × d/c = (a×d)/(b×c). Then simplify the result.

13. What is a ratio, and how does it differ from a proportion?

    A ratio compares two quantities of the same kind by division, written a:b or a/b. A proportion is a statement that two ratios are equal, written a:b = c:d or a/b = c/d. A proportion is an equation built from two ratios.

14. State the cross-multiplication property of a proportion a:b = c:d.

    In any proportion a/b = c/d, the cross products are equal: a × d = b × c. The terms a and d are called the extremes, and b and c are called the means, so 'product of extremes = product of means'.

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

    In direct proportion, two quantities increase or decrease together so their ratio is constant (y = kx). In inverse proportion, when one increases the other decreases so their product is constant (xy = k, i.e. y = k/x).

16. How do you divide a quantity in a given ratio, e.g. divide 60 in the ratio 2:3?

    Add the ratio parts to get the total number of parts (2 + 3 = 5). Divide the quantity by the total parts to find one part (60 ÷ 5 = 12). Multiply by each ratio term: 2 × 12 = 24 and 3 × 12 = 36. So 60 splits into 24 and 36.

17. What is the formula for the arithmetic mean (average) of a set of numbers?

    Arithmetic mean = (sum of all the values) ÷ (number of values). Equivalently, Sum = Mean × Number of values, which is useful when the average and count are known but a total is required.

18. What is the difference between the mean, median, and mode?

    The mean is the sum of values divided by their count (the average). The median is the middle value when the data is arranged in order (the average of the two middle values if the count is even). The mode is the value that occurs most frequently.

19. How is the combined (weighted) average of two groups calculated?

    Combined average = (sum of all items from both groups) ÷ (total number of items). If group sizes are n1, n2 with means m1, m2, then combined mean = (n1·m1 + n2·m2) ÷ (n1 + n2). You cannot simply average the two means unless the groups are equal in size.

20. If the average of n numbers is A and one number is removed, how does the average change relationship work?

    The total sum is A × n. After removing a value v, the new sum is (A × n) − v and the new count is n − 1, so the new average = (A·n − v) ÷ (n − 1). Removing a value below the mean raises the average; removing one above the mean lowers it.

21. What is the formula for profit percentage and loss percentage?

    Profit% = (Profit ÷ Cost Price) × 100, where Profit = Selling Price − Cost Price. Loss% = (Loss ÷ Cost Price) × 100, where Loss = Cost Price − Selling Price. Both percentages are always taken on the COST PRICE.

22. How do you find the selling price when the cost price and profit percentage are known?

    Selling Price = Cost Price × (1 + Profit%/100). For a loss, Selling Price = Cost Price × (1 − Loss%/100). For example, CP = 200 at 10% profit gives SP = 200 × 1.10 = 220.

23. What is the formula for simple interest?

    Simple Interest (SI) = (P × R × T) ÷ 100, where P is the principal, R is the annual rate of interest in percent, and T is the time in years. The total amount returned is A = P + SI.

24. What is the compound interest formula, and how does it differ from simple interest?

    Compound interest amount A = P(1 + R/100)^T, and CI = A − P. Unlike simple interest, which is computed only on the original principal each period, compound interest is calculated on the principal PLUS the accumulated interest, so it grows faster.

25. What does 'discount' mean in commercial math, and on what value is it calculated?

    A discount is a reduction in the marked (list) price. Discount = Marked Price × (Discount%/100), and Selling Price = Marked Price − Discount. The discount percentage is always calculated on the MARKED price, not the cost price.

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