5462 words - 22 pages

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 ...view middle of the document...

• 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 multiple of p . • The least common multiple of two nonzero integers a and b is the least positive integer that is a multiple of both a and b. The greatest common divisor (or greatest common factor) of a and b is the greatest positive integer that is a divisor of both a and b. • If an integer n is divided by a nonzero integer d resulting in a quotient q with remainder r, then n = qd + r , where 0 £ r < d . Furthermore, r = 0 if and only if n is a multiple of d. For example, when 20 is divided by 7, the quotient is 2 and the remainder is 6; when 21 is divided by 7, the quotient is 3 and the remainder is 0; and when -17 is divided by 7, the quotient is -3 and the remainder is 4. • A prime number is an integer greater than 1 that has only two positive divisors: 1 and itself. The first five prime numbers are 2, 3, 5, 7, and 11. A composite number is an integer greater than 1 that is not a prime number. The first five composite numbers are...

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