Determine the value given conditions

Question

I am solving my exercise guide, I found this one and I answered it badly.

My logic was:

Yes $x$, is multiple of $3$, then:

$x = 3k$

And yes it is multiple of $4$, then:

$x = 4p$

And I did not know how to do it algebraically.

Then I thought more logically and if it is divisible by $3$ and $4$, then it has to be a multiple of $12$.

It can be $60$, but also $72$, then it can not be determined, so I answered the letter E.

But the correct letter was C, so it can be obtained with both data, but how? What am I doing wrong?

Answer 1

Your thinking is correct that if it is both a multiple of $3$ and $4$ it must be a multiple of $12$. Between should not include the endpoints, though it is used both ways. If $60$ is excluded, answer $C$ is correct because you know it must be $72$.

Answer 2

They were a bit unclear with the wording, where it mentioned "an integer between $60$ and $80$".

Instead of this, the problem could have said, "an integer being between $60$ and $80$ exclusive", or "$60<x<80$".

They probably have answer choice $C$ correct because $72$ is the only integer in the range of $60<x<80$ that is divisible by $3$ and $4$.