I just chose numbers that satisfied the given information:

X = 4 (factor of y and multiple of z)
Y = 8
Z = 2

In the answer choices you have A and C the same, but the answer should be B.

(8 + 2) / 4
10/4 is not an integer

Given, x is a factor of y i.e y=x*m.......(1)
x is a multiple of z i.e x=z*n...........(a)
we can also write (1) as y=z*s........(b)
Lets now use (a) & (b) on given options...
(x+y)/z = (z*n +z*s)/z ...... it is an integer ,
similarly for C) (x+y)/z D) xy/z E) yz/x ...so all these options r integers except B) (y+z)/x .... NOT integer

Is plugging in the best method for this question ? or is there any logical mathematical approach to this problem?

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2009wish wrote:Is plugging in the best method for this question ? or is there any logical mathematical approach to this problem?

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plugging in would be the simplest method to solve this particular question

i picked
x = 8
y = 32
z = 2

(y+z)/x = (32+2)/8 = 34/8 (not an integer) therefore, choice B

IMO uing numbers should be the last option.
No offence, only my personal views


acorra,
A and C are same.
I think you missed something.
may be sign is different


x is a factor of y
means
y contains x [ie y=x or y is integer multiple of x]
hence
y/x is integer


x is a multiple of z
so
x/z is an integer


y/x is an integer and
x/z is an integer
multiply both
so we have
y/z also an integer

now all option other than B will turn out to be some / multiplication on integers.

remember Qn says x, y, z are integers...

You can try yourself

Hope it helps!!