Hi Sud21!sud21 wrote:
The easiest way to approach this problem is with a number line (well, 2 number lines actually).
We know that k and m are consecutive even numbers, but we don't know which is bigger. That means that we have one of the following 2 cases:
(a) <------- K ---- | ---- M --------> K is NOT larger than M (k<m)
(b) <------- M ---- | ---- K --------> K IS larger than M (k>m)
Now, all we need to do to answer the question is eliminate one of these 2 cases.
Statement (1) tells us that (k+2) and (m-2) are no longer consecutive even integers...so let's apply this to both number lines and see:
(a) <------- M-2 ---- | ---- K+2 -------->
these are still consecutive, so this cannot be the true case
(b) <------- M-2 ---- | ---- M ---- | ---- K ---- | ---- K+2 -------->
M-2 and K+2 are NOT consecutive, so this must be the true case
Statement 1 is [spoiler]SUFFICIENT![/spoiler]
Statement (2) tells us that (k-1) and (m+3) are consecutive odd integers...so let's apply this to both number lines and see:
(a) <------- (K-1) ---- K ---- | ---- M ---- | ---- | ---- (M+3) -------->
K-1 and M+3 are NOT consecutive odd numbers so this cannot be the true case.
(b) <------- M ---- (K-1) ---- K ---- (M+3) -------->
K-1 and M+3 are consecutive odds, so this must be the true case
Statement 2 is [spoiler]SUFFICIENT![/spoiler]
Therefore the answer is D.
Hope this helps!
Whit
