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RPurewal
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Is z the median of the 3 positive

by RPurewal Sun Jan 06, 2008 2:09 am

i've moved this question from another thread, on which it originally appeared in a post featuring 2 different questions.

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
taposh_dr
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Re: Is z the median of the 3 positive

by taposh_dr Wed Mar 03, 2010 3:18 pm

Thanks Ron for the explanation

I did this on my own and got "e".

I was struggling with statement 2, as it says that y=z, which means we will not
be able to determine which one is y or z. or in case all are equal which one is z.

Could you shed some light on how to change this thinking process, so that I get it right?
mschwrtz
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Re: Is z the median of the 3 positive

by mschwrtz Sat Apr 17, 2010 12:08 am

taposh_dr, I'm not sure that I understand your question, but I'll answer it as best I can.

You write that you missed the question because you misinterpreted Statement 2. I don't think that this is so. I think that you missed the question because you didn't invest the necessary time in rephrasing the question itself.

Note that if you had rephrased the question as Ron suggested--"Is z equal to the middle number of the three numbers?"--then the issue with Statement 2 would never have come up.

The best take-away for you here is that you ought to make that initial investment to rephrase the question.