Graduate Management Admission Test (GMAT)

In the course of working this out you will, of course, have to calculate the answer to the question and understand which, if any, of the statements give the required information.

Example

What is the value of x?

1.3x + y = 20

2.y = 2

Tip

You can narrow down the choices after reading Statement 1. If A gives enough information to answer the question, the final answer must be A or D from the list above. Now read statement 2 and decide whether the answer is A or D.

If statement 1 does not give you enough information to answer the question, the final answer must be B, C or E. Read statement 2 and then decide which it is.

This method will help on harder questions, or when an element of guesswork is involved, by narrowing down the number of statements that you have to choose from.

Background Study

This section breaks down the general topics that you are required to know into logical groups, and gives details of the elements of each topic. It does not attempt to teach you the math fundamentals required. See the How to Study for The GMAT section for advice on how to study the basic concepts.

Arithmetic

Properties of Integers

Basics: whole numbers, divisors, quotients, remainders, even and odd integers, factors, products, and prime numbers.

Tip

Remember that 0 is an even number.

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Graduate Management Admission Test (GMAT)

Fractions

Basics: numerators and denominators, greatest common divisor (gcd), addition and subtraction of fractions, least common multiple (lcm).

Proper fraction: when the numerator is less than the denominator; e.g., 23

Improper fraction: when the numerator is greater than the denominator; e.g., 75

Mixed fractions: when an integer and a proper fraction make up the number; e.g.,

2 23

Equivalent fractions: both 24 and 168 are equivalent to 12

Simplest form: when all common factors are cancelled from the numerator and denominator, so: 324 in its simplest form is: 18

Addition and subtraction of fractions: need the same denominator first (use lowest common multiple), then add/subtract numerators. Eg. 124 + 83 = 248 + 249 = 1724

Multiplication of fractions: multiply numerators and denominators together and simplify the result: 107 x 74 = 107 xx47 = 7028 = 52

Division of fractions: invert one of the fractions and multiply as above

Decimals

Basics: scientific notation, exponents, addition and subtraction of decimals, multiplication and division of decimals.

Significant figures - the degree of accuracy to which a number is expressed; e.g., 67,800 to 2 significant figures is 68000 as it is the closest number that can be written with 2 non-zero digits.

Decimal places - the degree of accuracy after the decimal point that a number is expressed to. If asked to write a number to 3 decimal places, look at the 4th digit after the decimal place, and round the third digit up or down as required; e.g., 0.5672 to 3 dp is .0567 and 0.458 to 2 dp is 0.46.

Rounding up/down: if the digit is >=5, round up, and round down for 4 and below.

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Graduate Management Admission Test (GMAT)

Real Numbers

Basics: 'the number line' and the properties of numbers on it.

Properties of real numbers, such as:

x + y = y + x

(x + y) + z = x + (y + z)

x + y = y + x and x ( y + z)= xy + xz

If both x and y are positive, x + y and xy are both positive.

If both x and y are negative, x + y is negative while xy is positive.

If both x is positive and y is negative, xy is negative.

If xy = 0 then either x = 0 or y = 0 (or both)

Absolute value: the distance from 0 of a number. For example, the number 3 has an absolute value of |3|, as does the number -3.

Tip

All absolute values are positive, and are written |x|, where x is the distance from 0 to the number in question.

Ratio and Proportion

Be familiar with different ways to express ratio; e.g., 2:3 or 23 or 2 to 3.

A proportion is a statement that 2 ratios are equal; e.g., 2/4 = 8/16

Converting fractions to percentages: multiply the fraction by 100 and simplify the result eg. 164 as a percentage= 164 x 100 = 40016 = 25%

Ratio: another way of expressing fractions. For example, a ratio of 3:5 is the same

as 83 : 85

Converting fraction ratios to integer ratios: convert the fraction ratio above to whole numbers as they are easier to deal with, so multiply by 8 to give: 248 : 408 = 3:5

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Graduate Management Admission Test (GMAT)

Percentages

Percentages as both fractions and decimals; e.g., 10030 or 0.30 or 30%. Here’s how to

find a certain percentage of a number, dealing with percentages greater than 100% and less than 1%.

Percentage change = differenceoriginal x 100

Powers and Roots of Numbers

Factorization - the process of writing a number as its product; e.g., 12=3x4

Prime factorization - the process of writing a number as the product of prime numbers; e.g., 12=2x2x3

Highest Common Factor (hcm) - the largest number that is a factor in all the given numbers, found by prime factoring and multiplying the factors to find all factors and comparing; e.g., 20 and 15. Prime factoring gives: 20=2x2x5, 15=3x5, therefore hcm is 5.

Lowest Common Multiple (lcm) - the smallest number into which all the given numbers will divide exactly. Found by prime factoring the numbers and taking the highest number of 2’s, the highest number of 3’s etc. For example, lcm for 20 and 15. Prime factoring gives: 20=2x2x5, 15=3x5, therefore the lcm is 2x2x3x5=60

Squares and square roots: a number is squared when it is multiplied by itself. For example, the square of 3 is: 3 x 3 = 9 and is written 3 2

The square root of a number is the reverse, dividing the number by itself. For example, the square root of 16 is 4 and is written 16 .

Cubes and cube roots: a number is cubed is when it is multiplied by itself twice. For example, the cube of 3 is: 3 x 3 x 3 = 27 and is written 3 3 .

The cube root of a number is the reverse, dividing the number by itself and by itself again. For example, the square root of 343 is 7 and is written 3 343 .

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