If x,y and z are consecutive positive integers and if x

Question

If x, y and z are consecutive positive integers and if x < y < z, which of the following must be a positive even integer ?

A. x + y -z
B. x - y + z
C. yz - x
D. (x - z)y
E. None of these

CrackverbalGMAT · Answer

We know that Even + Even = E

O + O = E

O - E = E - O = O

E - E = E

E * O = E

O * O = O

If x < y < z and x, y and z are consecutive and positive, then we will have 2 E and 1 O (eg 2, 3, 4) or 2 Odd and 1 E (3, 4, 5)

Using the Options and the examples above

Option 1:   x + y - z = 2 + 3 - 4 = 1 (odd)

Option 2:   x - y + z = 2 - 3 + 4 = 3 (odd)

Option 3:   yz - x = (2 * 3) - 1 = 5 (odd)

Option 4:   (x - z)y = (1 - 3) * 2 = -4 (even) and using the second example (2 - 4) * 3 = -6 (even)

We get negative integers

Option E

Arun Kumar

chandan1405042 · Answer

CrackVerbalGMAT 
The question is which must be a  positive even integer.  
So the answer will be E

CrackverbalGMAT · Answer

Edited the same. Thank You.

dolvera10 · Answer

I am confused as why it can't be A. Following the rules of adding/subtracting odds/evens, if we use 3,4,5 (consecutive numbers) 
odd+even=(3+4=7 odd) then odd-odd=(7-5=2 even) which gives us an even result.

What am I doing wrong or not reading correctly?

Thanks in advance!

Bunuel · Answer

The question asks which of the following MUST be true, not which COULD be true. While each option  could  be a positive even integer for some specific sets of numbers, none of them is  always  a positive even integer. So, the answer is E.

If x,y and z are consecutive positive integers and if x<y<z which of

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