Ratio and divisibility 
Given that $5x=3y=z$ where $x, y, z$ are integers, each choice given
  below must be integer except?  
A) $z/15 \quad\quad $ B) $z/5 \quad\quad$  C) $z/3 \quad\quad\\ $ D)
  $z/xy \quad\quad\\$  E) $x/3$

(Ans=D)  
How would I solve this problem any suggestions ?
 A: The best way to solve this type of problem is to plug some numbers in, and try to get a feel for WHY the various expressions either have to be integers, or don't have to be.  It shouldn't take very long to discover that $x$ must be a multiple of 3, $y$ must be a multiple of 5, and that we can write $x=3w$, $y=5w$ and $z=15w$ for some integer $w$.  
Since this is clearly a question in a quick-fire multiple choice test, a rigorous proof is unlikely to be needed.  In fact, we've already done enough to show that A, B, C and E are not the correct answers.  So circle D and move on to the next question.  If "none of the above" had been one of the options, then keep going - eventually you'll try $w=2$, and discover that D is indeed correct.
A: Why $15$ divides $z$ (meaning that $z/15$ is an integer): If a prime, in this case $3$, divides a product, in this case $5x$, then the prime must divide one (or both) of the terms. Since $3$ does not divide $5$, we conclude that $3$ must divide $x$. 
So $x=3t$ for some $t$, and therefore $x=15t$. We conclude that $15$ divides $z$.
The same kind of reasoning (but easier) shows that $z/5$, $z/3$, and $x/3$ are integers. In fact, we have already shown all these things in the process of showing that $15$ divides $z$. So by a process of elimination, the right answer must be D).
But we can see separately that $z/(xy)$ is not necessarily an integer. For example, let $x=6$, $y=10$, and $z=30$. Then your conditions are met, but $xy$, which is $60$, does not divide $z$. 
Note that $z/(xy)$ can be an integer, if $x=3$ and $y=5$. These are in fact the only positive cases when under our conditions, $z/(xy)$ is an integer.   
A: We have $5x=3y$, or $x \div y = 3\div 5$
Let their greatest common divisor be $k$, where $k$ is constant ;
So $x=3k$, $y=5k$,
we have $z=5x=5*3k=15k$;
so $z/xy =15k/(3k*5k)=1/k$;
and $1/k < 1$, as $k$ is constant
$1/k$ is not an integer
follow the same style for other options and you will found the answers are integer,
Thus and (d) $z/xy$ is correct;
