GMAT備考的奇偶性： 奇數(shù)（odd），又稱單數(shù)，是整數(shù)中不能被2整除的數(shù)，奇數(shù)的個位為1，3，5，7，9?？捎?k+1表示，這里k就是整數(shù)。
?偶數(shù)（even），又稱雙數(shù)，若某數(shù)是2的倍數(shù)，它就是偶數(shù)（雙數(shù)），可表示為2k。 所有整數(shù)不是奇數(shù)（單數(shù)），就是偶數(shù)（雙數(shù)）。
?奇數(shù)個奇數(shù)相加減=奇數(shù)，偶數(shù)個奇數(shù)相加減=偶數(shù)，奇數(shù)和偶數(shù)相加減=奇數(shù)，任意個偶數(shù)相加減=偶數(shù)，相乘時有一個偶數(shù)時結(jié)果是偶數(shù)，只有全部是奇數(shù)相乘結(jié)果才是奇數(shù)。
例： 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 條件1：n^2-1是奇數(shù)，n^2是偶數(shù)，n即為偶數(shù)（一個數(shù)的平方的奇偶性和這個數(shù)本身的奇偶性是一致的），充分； 條件2：3n + 4是偶數(shù)，3n是偶數(shù)，n即為偶數(shù)，充分。
?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 條件1：y=x+1，x和y就是連續(xù)的兩個整數(shù)，那么x和y一奇一偶，xy是偶數(shù)，充分； 條件2：y=x^2+1，y和x^2就是連續(xù)的兩個整數(shù)，因為x^2和x的奇偶性一致，就能得到y(tǒng)和x還是一奇一偶，xy是偶數(shù)，充分。
?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是偶數(shù)：那么A和B都是奇數(shù)或都是偶數(shù)； A/B是偶數(shù)：那么A=B*偶數(shù)，A一定是偶數(shù)； 所以A,B都是偶數(shù)，假設(shè)B=2N,A=B*偶數(shù)=2N*偶數(shù)=2N*2M=4MN； 帶入選項： A/2=2MN，偶數(shù)，排除； B/2=N，奇偶性不確定，排除； (A+B)/2=2MN+N，奇偶性不確定，排除； (A+2)/2 =2MN+1，一定是奇數(shù)，正解； (B+2)/2=N+1，奇偶性不確定，排除。
?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 條件1：y(y+2)=x(x+1)，x和x+1是連續(xù)的兩個整數(shù)，所以x和x+1一奇一偶，x(x+1)是偶數(shù)，所以y(y+2)是偶數(shù)，y和y+2的奇偶性是一致的，所以只能是y和y+2同為偶數(shù)，充分； 條件2：x是奇數(shù)，x和y的奇偶性無關(guān)，y奇偶性未知，不充分。
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