Problem Solving

BTGmoderatorDC wrote:In the xy-coordinate system, line k has slope 1/2 and passes through point (0, 5). Which of the following points cannot lie on line k?

A. (-10, 0)
B. (8, 9)
C. (3, 6.5)
D. (-2, 2)
E. (-8, 1)

\[{\text{line}}\,\,:\,\,\,y = \frac{1}{2}x + 5\]
\[\boxed{\,\,{\text{?}}\,\,\,{\text{:}}\,\,\,{\text{point}}\,\,\left( {a,b} \right)\,\, \notin \,\,{\text{line}}\,\,\,\, \Leftrightarrow \,\,\,\,\,\,\,\,?\,\,\,\,:\,\,\,\,b \ne \frac{a}{2} + 5\,\,\,\,}\]

\[\left( A \right)\,\,\,0\,\,\,\mathop \ne \limits^? \,\,\frac{{ - 10}}{2} + 5\,\,\,\,\,\left\langle {{\text{NO}}} \right\rangle \]
\[\left( B \right)\,\,\,9\,\,\,\mathop \ne \limits^? \,\,\frac{8}{2} + 5\,\,\,\,\,\left\langle {{\text{NO}}} \right\rangle \]
\[\left( C \right)\,\,\,6.5\,\,\,\mathop \ne \limits^? \,\,\frac{3}{2} + 5\,\,\,\,\,\left\langle {{\text{NO}}} \right\rangle \]
\[\left( D \right)\,\,\,2\,\,\,\mathop \ne \limits^? \,\,\frac{{ - 2}}{2} + 5\,\,\,\,\,\left\langle {{\text{YES}}} \right\rangle \]

This solution follows the notations and rationale taught in the GMATH method.

Regards,
fskilnik.

P.S.: in this problem we don´t see any justifiable reason to start the choices evaluation from bottom to the top, with all respect to our colleague's different beliefs.
In short: we see no "scientific" (statistical, information available) arguments for the claim ("the correct answer is typically closer to the bottom than to the top").
(We read the link provided above and, with due respect, we believe the "statistical sample" mentioned there is not significant.)

Brent@GMATPrepNow wrote:

fskilnik wrote: P.S.: in this problem we don´t see any justifiable reason to start the choices evaluation from bottom to the top, with all respect to our colleague's different beliefs.
In short: we see no "scientific" (statistical, information available) arguments for the claim ("the correct answer is typically closer to the bottom than to the top").
(We read the link provided above and, with due respect, we believe the "statistical sample" mentioned there is not significant.)

While a sample size of 28 might not be a large enough to make prove/validate my recommendations, I can tell you that, from my experience, the correct answer to these kinds of questions is typically closer to E than to A.
That said, if it were the case that, with this question type, the correct answer is equally likely to be A, B, C, D or E, then it would make no difference whether one checked the answer choices from A to E or from E to A.
However, if it is, indeed, the case that D and E are more likely to be the answer, then it makes sense to try E and D first.

Cheers,
Brent

Dear Brent,
I am here to contribute to this community and to have the opportunity to make my preparation known to international students, after more than 18 years teaching in Brazil.
I will tell the advice I give to my own students on this matter, just for our readers to have a "second opinion":
I BELIEVE the examiner chooses one of the FIRST alternative choices when each "choice-test" is time-consuming, because he/she does not want the student to spend a lot of time in the "testing process".
(As you mentioned in your article-related, it is more common/"natural" to test from A to E, therefore the examiner knows how long a student "would take" on average "per testing", if he/she goes this "natural way".)
When each "choice-testing" is quick (like here, it takes less than 5 seconds each), then I BELIEVE the examiner does not care in which alternative choice the right answer was put on.
That´s only my opinion.
Still my opinion: we are dealing with beliefs, not with facts.
I will not take this discussion further, and I respect your opinion and your experience.
Regards,
fskilnik.