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The Point $A$ inside soccer field is closer to $x$ axis than to $y$ axis. Given that the coordinate of $A$ is given by $A(\log_2(17-x),3)$, determine the sum of the integer values of $x$.

The question comes down to solving, $$ 8>17-x \implies x>9 $$ At this point, many people take the sum of $10+11+12+13+14+15+16$, and arrive at $81$. It turns out that this is wrong because the question says the point is inside the field, but $\log1=0$ and that makes it on the $x$ axis.

(1) Do you think this is clear? (For one thing, in the rules of soccer, the line itself is considered inside the field.)

(2) Obviously, the question setters did not want to draw attention to the "inside the field" part, such as making it bold or underlining it. If you think that the current form is not clear, how would you put it, making it both clear but without drawing attention to it? (For example, not something like: The axes are not considered inside the field.)

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  • Problems : [1] Drawing misleading, as it suggests that point A is closer to the $y$-axis. [2] In $\Bbb{R^2},~$ a point $A$ has coordinates $(x,y)$. From that perspective, the statement "the coordinate of $A$" probably refers to "the coordinates of $A$". [3] The variable $A$ is overloaded, simultaneously referring to a point in $\Bbb{R^2}$ and a scalar associated with that point. [4] The issues that you discuss re the border is or is not inside the field. ...see next comment – user2661923 Sep 19 '21 at 07:19
  • [5] I followed your inference that $x \in {9,10,\cdots,16}$, but the idea that the problem solver is supposed to interpret "the sum of the integer values of $x$" to intend "the sum of the possible integer values of $x$" is bizarre. Point $A$ refers to a single fixed point, not a collection of points. This last item is another case of brevity is the soul of poorly worded math problems. Re all of the points: if I were this math problem's composer, I would be embarrassed that I was the author of this mishmash. – user2661923 Sep 19 '21 at 07:23
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    On the other hand, this problem could be an excellent cheating-detection device. The only way to solve this problem (assuming that the math class hasn't taught the rules of soccer, et al) is if you cheated, by somehow getting a copy of the intended solution in advance. – user2661923 Sep 19 '21 at 07:29

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