If $0<x<y<z$ integers

And $\frac{1}{x}+\frac{1}{y}+\frac{1}{z}=\frac{1}{4}$

So it asks the possible values of $z$.

Options goes as:

A)9 B)10 C)11 D)12 E)13

  • $\begingroup$ I have added that $x,y,z$ are integers. Next time, show that you have worked a little on the questions you are working on. $\endgroup$ – Jean Marie Apr 5 at 12:34
  • $\begingroup$ Since my native language isn't English, I have to translate everything myself. I will be more careful though. $\endgroup$ – terrestrian Apr 5 at 13:58
  • $\begingroup$ Welcome to Mathematics Stack Exchange! A quick tour will enhance your experience. Here are helpful tips to write a good question and write a good answer. For equations, use MathJax. $\endgroup$ – dantopa May 25 at 3:49

13 is the answer.

Since $1/x \gt 1/y \gt 1/z$

Hence $1/4 = 1/x+1/y+1/z \gt 1/z +1/z +1/z$

Hence $1/4 \gt 3/z$

Giving $z\gt 12$

  • $\begingroup$ I didn't get the second part. Why did you sum 1/z three times and how do you know that the total is smaller than 1/4? $\endgroup$ – terrestrian Apr 5 at 11:41
  • $\begingroup$ edited, $1/4 = 1/x+1/y+1/z \gt 1/z +1/z +1/z$ $\endgroup$ – L KM Apr 5 at 11:43
  • $\begingroup$ Typo on the fourth line: $1/4 > 3/z$. $\endgroup$ – NickD Apr 5 at 11:56

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