GMAT (Graduate Management Admission Test) Quantitative Foundations: Arithmetic & Number Properties Syllabus

Quantitative Foundations: Arithmetic & Number Properties syllabus — full chapter and topic list

Expand any chapter to see its topics and sub-topics. This is the whole examinable outline for Quantitative Foundations: Arithmetic & Number Properties in GMAT (Graduate Management Admission Test), not a summary of it.

1. 1

   Number Properties

   6 topics

   • Integers, factors, and multiples
     • Divisibility rules
     • Greatest common divisor (GCD)
     • Least common multiple (LCM)
   • Prime numbers and prime factorization
     • Counting factors from prime factorization
     • Primes in number-sense problems
   • Even, odd, positive, and negative behavior
   • Remainders and modular reasoning
     • Remainder patterns and cycles
     • Units-digit problems
   • Absolute value on the number line
   • Consecutive integers and number patterns
2. 2

   Fractions, Decimals & Percents

   5 topics

   • Operations with fractions
     • Common denominators and simplification
     • Complex/compound fractions
   • Decimal place value and conversions
   • Percent of, percent change, and successive percents
     • Percent increase vs decrease
     • Reversing a percent change
   • Fraction-decimal-percent equivalences
   • Estimation and benchmark values
3. 3

   Ratios, Proportions & Rates

   5 topics

   • Part-to-part vs part-to-whole ratios
   • Scaling ratios and the unknown multiplier
   • Direct and inverse proportion
   • Unit rates and unit conversions
   • Combining and splitting ratios across groups
4. 4

   Exponents, Roots & Order of Operations

   5 topics

   • Laws of exponents
     • Product, quotient, and power rules
     • Negative and zero exponents
   • Square roots and higher roots
     • Simplifying radicals
     • Rationalizing simple expressions
   • Fractional (rational) exponents
   • Scientific notation
   • PEMDAS and grouping

Quantitative Foundations: Arithmetic & Number Properties flashcards for GMAT (Graduate Management Admission Test)

22 of 51 cards from the Quantitative Foundations: Arithmetic & Number Properties deck — real questions with worked answers.

1. What is an integer, and which numbers are included?

   An integer is a whole number with no fractional or decimal part. The set includes negative whole numbers, zero, and positive whole numbers (..., -2, -1, 0, 1, 2, ...).

2. What is a factor (divisor) of an integer n?

   A factor of n is an integer that divides n with no remainder. For example, the factors of 12 are 1, 2, 3, 4, 6, and 12.

3. What is a multiple of an integer n?

   A multiple of n is the product of n and any integer (e.g., multiples of 4 are 4, 8, 12, 16, ...). Every integer is a multiple of itself and of 1.

4. How do you find the Greatest Common Factor (GCF) of two numbers using prime factorization?

   Take the prime factorization of each number, then multiply the lowest power of each prime common to both. The result is the GCF (largest factor shared by both).

5. How do you find the Least Common Multiple (LCM) using prime factorization?

   Take the prime factorization of each number, then multiply the highest power of every prime appearing in either number. The result is the LCM (smallest common multiple).

6. What is the relationship between GCF, LCM, and the product of two numbers a and b?

   GCF(a, b) x LCM(a, b) = a x b. So you can find one if you know the other and the two numbers.

7. What is a prime number, and what is the smallest one?

   A prime number is an integer greater than 1 with exactly two distinct positive factors: 1 and itself. The smallest prime is 2, which is also the only even prime.

8. Is 1 a prime number? Why or why not?

   No. 1 has only one positive factor (itself), but a prime must have exactly two distinct factors. 1 is neither prime nor composite.

9. What is prime factorization?

   Prime factorization is expressing an integer as a product of prime numbers (e.g., 60 = 2^2 x 3 x 5). Every integer greater than 1 has a unique prime factorization.

10. How do you count the total number of factors of an integer from its prime factorization?

    Add 1 to each exponent in the prime factorization and multiply the results. For 12 = 2^2 x 3^1, the count is (2+1)(1+1) = 6 factors.

11. What are the rules for the sign of a product/quotient of two numbers?

    Same signs give a positive result; different signs give a negative result. (+ x + = +, - x - = +, + x - = -, - x + = -).

12. What determines whether the product of several numbers is positive or negative?

    Count the negative factors. An even number of negative factors gives a positive product; an odd number gives a negative product (assuming no factor is zero).

13. State the parity rules for addition: even/odd + even/odd.

    even + even = even; odd + odd = even; even + odd = odd. (Same parity sums to even; different parity sums to odd.)

14. State the parity rules for multiplication: even/odd x even/odd.

    even x even = even; even x odd = even; odd x odd = odd. A product is odd only if every factor is odd.

15. How can any even integer and any odd integer be written algebraically?

    An even integer is 2n; an odd integer is 2n + 1 (or 2n - 1), where n is an integer.

16. In the division algorithm, what is the remainder, and what range must it fall in?

    For dividend a divided by divisor d, a = dq + r, where q is the quotient and r is the remainder satisfying 0 <= r < d.

17. When a is divided by d, how do you find the remainder using modular reasoning for a sum like (x + y) mod d?

    (x + y) mod d = ((x mod d) + (y mod d)) mod d. Remainders add (and you reduce mod d at the end). The same distribution works for products.

18. What is the remainder when an integer is divided by 10?

    It equals the units (ones) digit of the integer. For example, 347 divided by 10 leaves remainder 7.

19. Define the absolute value |x| and describe it on the number line.

    |x| is the distance of x from 0 on the number line, always non-negative. |x| = x if x >= 0, and |x| = -x if x < 0.

20. What does |a - b| represent geometrically?

    |a - b| is the distance between points a and b on the number line. It is the same as |b - a|.

21. How do you solve an equation of the form |x| = k (for k > 0)?

    Split into two cases: x = k or x = -k. If k = 0, then x = 0; if k < 0, there is no solution.

22. For n consecutive integers, when is their sum divisible by n?

    The sum of n consecutive integers is divisible by n when n is odd. (The average is the middle term, an integer.) When n is even, it is not.

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