vietst Wrote:Question 2. Data Sufficiency
If z is the median of any 3 positive integers x, y and z then
i) x<y+z
ii) y=z
a) i only is sufficient and ii is not
b) ii only is sufficient and i is not
c) i and ii together are sifficient
d) Both
e) none
Any thoughts ?
it seems as though this question should be rephrased as follows (it's not meaningful in its current phrasing):
"Is z the median of the three positive integers x, y, z?"
important note:
make sure that you understand that this is the direction of the logic in all data sufficiency questions. you are always trying to prove/disprove the prompt question, based on the evidence given in the 2 statements. you have written the question backwards - your 'if' and 'then' construct a logic that runs in precisely the opposite direction - which will make it essentially impossible for you to answer questions correctly.
--
treatment of the question:
rephrase of initial question:
this is the same as asking: is z equal to the middle number of the three numbers?
statement (1)
this statement tells nothing about the order of the three numbers. it could be true regardless of the order of the 3 numbers, and, more to the point, regardless of the position of z in the ordered list.
examples:
x = 1, y = 2, z = 3: z is not the median
x = 1, y = 3, z = 2: z is the median
insufficient
statement (2)
if y and z are equal, there are three possibilities:
--- they are the two largest #s in the list. in this case, both of them equal the median of the list.
--- they are the two smallest #s in the list. in this case, both of them equal the median of the list.
--- all three numbers in the list are the same. in this case, all of them equal the median.
in any of these cases, z is the median.
sufficient
answer = b