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NTS NAT-ICOM Quantitative Reasoning Syllabus
The Quantitative Reasoning syllabus for NTS NAT-ICOM in full: 4 chapters and 22 topics, every one listed below, plus 50 Quantitative Reasoning flashcards with answers.
Quantitative Reasoning syllabus: all 4 chapters
Expand any chapter to see its topics and sub-topics.
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Arithmetic
8 topics- Number System
- Fractions and Decimals
- Ratio and Proportion
- Percentage
- Average
- Profit and Loss
- Simple and Compound Interest
- Time, Speed and Distance
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Algebra
5 topics- Algebraic Expressions
- Linear Equations
- Quadratic Equations
- Factorization
- Exponents and Radicals
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Geometry
5 topics- Lines and Angles
- Triangles
- Quadrilaterals and Polygons
- Circles
- Perimeter, Area and Volume
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Data Interpretation
4 topics- Tables
- Bar and Line Graphs
- Pie Charts
- Basic Statistics
NTS NAT-ICOM Quantitative Reasoning flashcards — 50 questions with answers
What are natural numbers?
Counting numbers starting from 1: 1, 2, 3, 4, ... (excludes 0).
What is the difference between whole numbers and natural numbers?
Whole numbers include 0 (0, 1, 2, 3, ...), while natural numbers start at 1.
Define a rational number.
A number expressible as p/q where p and q are integers and q is not 0 (e.g. 3/4, -2, 0.5).
Define an irrational number and give an example.
A number that cannot be written as a fraction of two integers; its decimal is non-terminating and non-repeating. Examples: pi, sqrt(2).
What is a prime number? Give the smallest one.
A natural number greater than 1 with exactly two factors: 1 and itself. The smallest prime is 2 (and it is the only even prime).
What is a composite number?
A natural number greater than 1 that has more than two factors (e.g. 4, 6, 9). Note: 1 is neither prime nor composite.
State the divisibility rule for 3.
A number is divisible by 3 if the sum of its digits is divisible by 3.
State the divisibility rule for 9 and for 11.
Divisible by 9 if the digit sum is divisible by 9. Divisible by 11 if the difference between the sum of digits in odd and even positions is 0 or a multiple of 11.
What is the relationship between LCM, HCF and two numbers a and b?
LCM(a,b) x HCF(a,b) = a x b.
How do you convert a fraction to a decimal?
Divide the numerator by the denominator (e.g. 3/4 = 3 divided by 4 = 0.75).
How do you add fractions with different denominators?
Find the LCM of the denominators, convert each fraction to that common denominator, then add the numerators.
How do you divide one fraction by another?
Multiply the first fraction by the reciprocal of the second: (a/b) / (c/d) = (a/b) x (d/c).
What does it mean for a fraction to be in its lowest terms?
Numerator and denominator have no common factor other than 1 (HCF = 1), e.g. 6/8 reduces to 3/4.
Convert 0.25 to a fraction in lowest terms.
0.25 = 25/100 = 1/4.
What is a ratio?
A comparison of two quantities of the same kind by division, written a:b or a/b.
What is a proportion?
A statement that two ratios are equal: a:b = c:d (i.e. a/b = c/d).
State the cross-multiplication property of a proportion a:b = c:d.
The product of the means equals the product of the extremes: a x d = b x c.
In a:b = c:d, which terms are the means and which are the extremes?
The means are b and c (inner terms); the extremes are a and d (outer terms).
How do you divide an amount in the ratio a:b?
Total parts = a + b. Each share = (its part / total parts) x amount, e.g. first share = a/(a+b) x amount.
What is direct proportion versus inverse proportion?
Direct: as one quantity increases, the other increases at the same rate (y = kx). Inverse: as one increases, the other decreases (xy = k).
Show the other 30 Quantitative Reasoning flashcards
What is the formula to convert a fraction to a percentage?
Percentage = (fraction) x 100% (e.g. 3/5 = 3/5 x 100 = 60%).
How do you express x% as a fraction or decimal?
x% = x/100 (e.g. 25% = 25/100 = 0.25).
What is the formula for percentage increase?
Percentage increase = (increase / original value) x 100%.
What is the formula for percentage decrease?
Percentage decrease = (decrease / original value) x 100%.
If a price increases by 20% then decreases by 20%, is it back to the original? Why?
No. Successive percentage changes are not additive; net change = +20% then -20% gives a 4% overall decrease (e.g. 100 -> 120 -> 96).
What is the formula for the average (arithmetic mean) of a set of numbers?
Average = (sum of all values) / (number of values).
How do you find the total sum if you know the average and the number of items?
Sum = average x number of items.
What is the average of the first n natural numbers?
Average = (n + 1) / 2.
How is a new average affected when a value above the current average is added?
The average increases; adding a value below the current average decreases it; adding a value equal to it leaves it unchanged.
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.
What is the formula for profit and for loss?
Profit = SP - CP (when SP > CP); Loss = CP - SP (when CP > SP).
What is the formula for profit percentage?
Profit% = (Profit / CP) x 100% (profit and loss percentages are always calculated on cost price).
What is the formula for loss percentage?
Loss% = (Loss / CP) x 100%.
How do you find SP given CP and profit percentage?
SP = CP x (100 + Profit%) / 100.
What is the formula for simple interest?
Simple Interest = (P x R x T) / 100, where P = principal, R = rate per year, T = time in years.
What is the formula for the amount with compound interest?
Amount A = P(1 + R/100)^T; Compound Interest = A - P.
What is the key difference between simple and compound interest?
Simple interest is calculated only on the original principal each period; compound interest is calculated on the principal plus accumulated interest.
What is the compound interest formula when interest is compounded n times per year?
A = P(1 + R/(100n))^(nT), where n is the number of compounding periods per year.
What is the basic formula relating speed, distance and time?
Speed = Distance / Time (so Distance = Speed x Time, and Time = Distance / Speed).
How do you convert km/h to m/s?
Multiply by 5/18 (e.g. 36 km/h = 36 x 5/18 = 10 m/s).
What is the average speed for a whole journey?
Average speed = total distance / total time (NOT the simple average of the speeds).
For two objects moving in opposite directions, what is their relative speed?
The sum of their speeds; for the same direction, relative speed is the difference of their speeds.
What is the difference between a term and a coefficient in an algebraic expression?
A term is a part separated by + or - signs (e.g. 3x); a coefficient is the numerical factor of a term (e.g. 3 in 3x).
What are like terms?
Terms having the same variables raised to the same powers (e.g. 3x and 5x), which can be combined by adding/subtracting coefficients.
Expand (a + b)^2 and (a - b)^2.
(a + b)^2 = a^2 + 2ab + b^2; (a - b)^2 = a^2 - 2ab + b^2.
Factorize a^2 - b^2.
a^2 - b^2 = (a + b)(a - b) (difference of two squares).
What defines a linear equation in one variable, and how many solutions does it have?
An equation of the form ax + b = 0 (highest power of the variable is 1); it has exactly one solution: x = -b/a.
What is the standard (general) form of a quadratic equation?
ax^2 + bx + c = 0, where a, b, c are constants and a is not 0.
State the quadratic formula.
x = [-b plus or minus sqrt(b^2 - 4ac)] / (2a).
What does the discriminant b^2 - 4ac tell you about the roots of a quadratic?
If > 0: two distinct real roots; if = 0: one repeated real root; if < 0: no real roots (two complex roots).
NTS NAT-ICOM Quantitative Reasoning FAQ
What is in the NTS NAT-ICOM Quantitative Reasoning syllabus?
NTS NAT-ICOM Quantitative Reasoning is split into 4 chapters: Arithmetic, Algebra, Geometry and Data Interpretation. Together they contain 22 topics.
How many chapters are in NTS NAT-ICOM Quantitative Reasoning?
4 chapters, containing 22 topics. The largest chapter is Arithmetic, with 8 topics.
Are there flashcards for NTS NAT-ICOM 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.