1、GRE（ QUANTITATIVE）练习试卷 17及答案与解析 1 A certain integer n is a multiple of both 5 and 9. Must n be a multiple of 15? 2 What are the common factors of 7 and 42? 3 What is the Greatest Common Factor of 48 and 72? 4 What is the Least Common Multiple of 30 and 40? 5 What is the greatest positive integer x s
2、uch that 2x is a factor of 1210? GRE（ QUANTITATIVE）练习试卷 17答案与解析 1 【正确答案】 The first step in solving this problem is to find the Least Common Multiple (LCM) of 5 and 9. Because a multiple of 5 must have either a 5 or a 0 in the digits place, and 95 is the first multiple of 9 with a 5 in the digits pla
3、ce, 95=45 must be the LCM. Therefore, n must be a multiple of 15, since 45 (one possible value of n) is a multiple of 15. 2 【正确答案】 Remember that common factors are all of the factors that two or more numbers share. The factors of 7 are 1 and 7 because 7 is a prime number. The factors of 42 include 1
4、 (421=42) and 7 (67=42), so the common factors of 7 and 42 are 1 and 7. 3 【正确答案】 The Greatest Common Factor (GCF) is the largest number that divides evenly into any two or more numbers. List the factors of 48 and 72, then select the largest factor that they have in common: Based on this list, the GC
5、F is 24. 4 【正确答案】 The Least Common Multiple is the smallest number that any two or more numbers can divide evenly into. One way to solve this problem is to determine the multiples of 30, stopping at the first one that is also a multiple of 40: 301=30 302=6O 303=90 304=120 Because 40 divides evenly i
6、nto 120, 120 is the Least Common Multiple of 30 and 40. 5 【正确答案】 To reach an answer, you first must find the smallest factors of 12, as follows: 1210=(322) 10 Remember that the exponent applies to every value within the parentheses; thus, (322) 10=3102 102 10. When multiplying powers with the same base, you add the exponents: 3102 (10+10) =(310)(220); 220is a factor of 1210.
