An effective approach in solving this question is to analyse till a particular stage and then use simple values to prove the statements/combination insufficient.
x, y and z are positive integers. To find out if x-y-z is positive, we have to find out if x-y-z>0. To do this, it’s sufficient to find out if x>y+z.
From statement I alone, x>y. This is insufficient to find out if x>y+z since we do not have any information about z.
For example, if x = 2, y = 1 and z = 1, x>y BUT x = y+z. On the other hand, if x = 5, y = 1 and z = 1, x>y AND x>y+z.
Statement I alone is insufficient to determine if x>y+z. Answer options A and D can be eliminated. Possible answer options are B, C or E.
From statement II alone, y>z. This is insufficient to find out if x>y+z since we do not have any information about x.
For example, if x = 3, y = 2 and z = 1, y>z BUT x = y+z. On the other hand, if x = 5, y = 2 and z = 1, y>z AND x>y+z.
Statement II alone is insufficient to determine if x>y+z. Answer option B can be eliminated. Possible answer options are C or E.
Combining statements I and II, we have the following:
From statement I, we have x>y; from statement II we have y>z. Therefore, x>y>z. This is insufficient to determine if x>y+z.
If x = 3, y = 2 and z = 1, x = y+z. But, if x = 5, y = 2 and z = 1, x>y+z. The combination of statements is insufficient to determine a unique YES or NO. Answer option C can be eliminated.
The correct answer option is E.
Hope that helps!
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