Hint for process of elimination: Since $latex y &s=1$ and $latex xy &s=1$ are both positive, $latex x &s=1$ is also positive. Therefore $latex y-x<y=15 &s=1$. This eliminates choice E, leaving you with four choices. Some awareness about how big or small the answer should be, for example noting that $latex x=8 &s=1$, may help you eliminate choice D for being too big, and choice A for being too small.
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Solution: Since $latex xy = 120 &s=1$ and $latex y = 15 &s=1$, it follows that $latex 15x = 120 &s=1$. Solving this equation gives $latex x = 8 &s=1$. Therefore $latex y-x = 15 – 8 = 7 &s=1$
A. $latex 5 = x – 3 &s=1$, not $latex y – x &s=1$
C. $latex 8 = x &s=1$, not $latex y-x &s=1$. A great deal of students solve for $latex x &s=1$ and do not bother to check whether the problem was asking for $latex x &s=1$ or simply something involving $latex x &s=1$. Don’t fall into this trap. Re-read the last sentence of every math problem before choosing your answer.
D. $latex 12 = y-3 &s=1$, not $latex y-x &s=1$.
E. $latex 23 = y+x &s=1$. Make sure you do the correct operation. Don’t let caught thinking every operation is addition.