If x, y, and z are positive integers, is x - y - z positive ?

E.....3,2,1 not possible

Algebraic approach

In order for X - Y - Z to happen you need the following condition to be met.

X - (Y + Z). You factor out the negative in Y and Z to make -(Y + Z)

The statement does not give you anything related to this.

It does give you X > Y > Z however this still has nothing to do with the above requirement.

Is x-y-z>0?

means, Is x>y+z OR x-y>z OR x-z>y?

St1 Or St2 not suff.

St1 And St2 means x>y>z. None of above. INSUFF

E

x-y-z positive? y/n translates into

x>y-z? y/n

1) x>y
insufficient, we don't know anything about z

2) y>z
insufficient, we don't know anything about x

1+2)
combine the inequalities
x+y>y+z
x>z
Insufficient, we don't know anything about y

Choice E

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!

takeaway: if x is greater than y and z does not mean x is greater than the sum.

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