提问前请先搜索
新问题:
问题说明(可选):
我要悬赏(可选):
积分
>>>武汉申友GMAT编辑<<<
今天申友GMAT给大家解读GMAT数学高频考点之奇偶性,希望通过知识点和例题的讲解,大家能够掌握。
奇数(odd),又称单数,是整数中不能被2整除的数,奇数的个位为1,3,5,7,9。可用2k+1表示,这里k就是整数。偶数(even),又称双数,若某数是2的倍数,它就是偶数(双数),可表示为2k。
所有整数不是奇数(单数),就是偶数(双数);
奇数个奇数相加减=奇数;
偶数个奇数相加减=偶数;
奇数和偶数相加减=奇数;
任意个偶数相加减=偶数;
相乘时有一个偶数时结果是偶数,只有全部是奇数相乘结果才是奇数。
例题1:If n is an integer, is n even?
(1) n^2-1 is an odd integer.
(2) 3n + 4 is an even integer.
A Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
B Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
C BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
D EACH statement ALONE is sufficient.
E Statements (1) and (2) TOGETHER are NOT sufficient
【解析】D
条件1:n^2-1是奇数,n^2是偶数,n即为偶数(一个数的平方的奇偶性和这个数本身的奇偶性是一致的),充分;
条件2:3n + 4是偶数,3n是偶数,n即为偶数,充分。
例题2:If x、y is positive integer, is xy even?
(1)y=x+1
(2)y= x^2+1
A Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
B Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
C BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
D EACH statement ALONE is sufficient.
E Statements (1) and (2) TOGETHER are NOT sufficient
【解析】D
条件1:y=x+1,x和y就是连续的两个整数,那么x和y一奇一偶,xy是偶数,充分;
条件2:y=x^2+1,y和x^2就是连续的两个整数,因为x^2和x的奇偶性一致,就能得到y和x还是一奇一偶,xy是偶数,充分。
例题3:If A and B are positive integers such that A-B and A / B are both even integers, which of the following must be an odd integer?
(A)A/2
(B)B/2
(C)(A+B)/2
(D)(A+2)/2
(E)(B+2)/2
【解析】D
A-B是偶数:那么A和B都是奇数或都是偶数;
A/B是偶数:那么A=B*偶数,A一定是偶数;
所以A,B都是偶数,假设B=2N,A=B*偶数=2N*偶数=2N*2M=4MN;
带入选项:
A/2=2MN,偶数,排除;
B/2=N,奇偶性不确定,排除;
(A+B)/2=2MN+N,奇偶性不确定,排除;
(A+2)/2 =2MN+1,一定是奇数,正解;
(B+2)/2=N+1,奇偶性不确定,排除。
例题4:If x and y are integers, is y an even integer?
(1) 2y – x = x^2 – y^2
(2) x is an odd integer.
A Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
B Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
C BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
D EACH statement ALONE is sufficient.
E Statements (1) and (2) TOGETHER are NOT sufficient.
【解析】A
条件1:y(y+2)=x(x+1),x和x+1是连续的两个整数,所以x和x+1一奇一偶,x(x+1)是偶数,所以y(y+2)是偶数,y和y+2的奇偶性是一致的,所以只能是y和y+2同为偶数,充分;
条件2:x是奇数,x和y的奇偶性无关,y奇偶性未知,不充分。
申友张同学,6.5报名申友经典强化方法课,6.23出分710分,2周短时高效提分【650-710】!
申友GMAT王同学,今日一战出分750,在职党,从3月中旬开始咨询上课到今日出分750,仅用3个多月时间,超出目标分100分,太优秀了!
添加微信【thinkwithu002】免费获取GMAT 700+高分备考资料攻略,还可获取GMAT第一手换库资讯和GMAT机经课程,并且可参与申友GMAT 公开课、刷题团、单词团等GMAT提分活动。电话:027-87132585;网址:www.thinkwithu.com
>>>武汉申友GMAT编辑<<<
我要举报: