Mathematical Conventions

for the Quantitative Reasoning Measure of the GRE® revised General Test

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Overview The mathematical symbols and terminology used in the Quantitative Reasoning measure of the test are conventional at the high school level, and most of these appear in the Math Review. Whenever nonstandard or special notation or terminology is used in a test question, it is explicitly introduced in the question. However, there are some particular assumptions about numbers and geometric figures that are made throughout the test. These assumptions appear in the test at the beginning of the Quantitative Reasoning sections, and they are elaborated below. Also, some notation and terminology, while standard at the high school level in many countries, may be different from those used in other countries or from those used at higher or lower levels of mathematics. Such notation and terminology are clarified below. Because it is impossible to ascertain which notation and terminology should be clarified for an individual test taker, more material than necessary may be included. Finally, there are some guidelines for how certain information given in test questions should be interpreted and used in the context of answering the questions—information such as certain words, phrases, quantities, mathematical expressions, and displays of data. These guidelines appear at the end.

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Numbers and quantities • All numbers used in the test questions are real numbers. In particular, integers and both rational and irrational numbers are to be considered, but imaginary numbers are not. This is the main assumption regarding numbers. Also, all quantities are real numbers, although quantities may involve units of measurement. • Numbers are expressed in base 10 unless otherwise noted, using the 10 digits 0 through 9 and a period to the right of the ones digit, or units digit, for the decimal point. Also, in numbers that are 1,000 or greater, commas are used to separate groups of three digits to the left of the decimal point. • When a positive integer is described by the number of its digits, e.g., a two-digit integer, the digits that are counted include the ones digit and all the digits further to the left, where the left-most digit is not 0. For example, 5,000 is a four-digit integer, whereas 031 is not considered to be a three-digit integer. • Some other conventions involving numbers: one billion means 1,000,000,000, or 109 (not 1012 , as in some countries); one dozen means 12; the Greek letter p represents the ratio of the circumference of a circle to its diameter and is approximately 3.14. • When a positive number is to be rounded to a certain decimal place and the number is halfway between the two nearest possibilities, the number should be rounded to the greater possibility. For example, 23.5 rounded to the nearest integer is 24, and 123.985 rounded to the nearest 0.01 is 123.99. When the number to be rounded is negative, the number should be rounded to the lesser possibility. For example, -36.5 rounded to the nearest integer is -37. • Repeating decimals are sometimes written with a bar over the digits that repeat, as in
25 = 2.083 12

and

1 = 0.142857. 7

• If r, s, and t are integers and rs = t , then r and s are factors, or divisors, of t; also, t is a multiple of r (and of s) and t is divisible by r (and by s). The factors of an integer include positive and negative integers. For example, -7 is a factor of 35, 8 is a factor of -40, and the integer 4 has six factors: -4, -2, -1, 1, 2, and 4. The terms factor, divisor, and divisible are used only when r, s, and t are integers. However, the term multiple can be used with any real numbers s and t provided r is an integer. For example, 1.2 is a multiple of 0.4, and -2p is a