Data Sufficiency - 42 答案是否有误？

saven · 发表于 2011-4-25 22:05:06

Is a-3b an even number?

1). b=3a+3
2). b-a is an odd number

Answer: C

From statement (1):Given that b=3a+3
Thus a-3b=a-3(3a+3) = -8a-9 which may be even, odd, integer, non-integer,rational etc ... Hence insufficient

From statement (2):Given that b-a is an odd number implies b is of the form b=(2k+1)+a where k isan integer
Thus a-3b=a-3[(2k+1)+a] = -2a-6k-3 which may be even, odd, integer, non-integer, rational etc ..Henceinsufficient

Taking statement(1) and (2) together: -8a-9=-2a-6k-3 for some integer k
or -6a=-6k+6=-6(k+1) implies a=k+1
Thus a is aninteger, either odd or even

Now statement (2)tells us that b is also an integer and that exactly one of {a,b} is even
If a is even and bis odd, a-3b is odd
If b is even and ais odd a-3b is odd

Thus (1) and (2)combined tell us that a-3b is an odd number...hence sufficient--------------------------------------------------------------------------
在解释（2）的时候，分析中说假设b-a=2k+1,那么a-3b=-2a-6k-3,无法判断其奇偶。这个公式显然不对啊。
我的想法是a-3b=a-b-2b.既然b-a是奇数，那么a-b也一定是奇数，2b是偶数，所以(a-b)-2b就一定是奇数。
通过（2）就可判断其奇偶，所以应该选B

Data Sufficiency - 42 答案是否有误？

所属分类: GMAT考试

正在浏览此版块的会员 ()