BTGmoderatorDC wrote:Which of the following are/is prime?

I. 143
II. 147
III. 149

(A) II only
(B) III only
(C) I & II
(D) I & III
(E) I, II, & III

Source: Magoosh

\[?\,\,\,:\,\,\,{\text{prime(s)}}\]
It´s useful to know that 1-4+3 = 0 guarantees that 143 is divisible by 11 (*), hence I. is refuted and we are left with alternative choices (A), (B) only.
(*) Check this: https://www.math.hmc.edu/funfacts/ffiles/10013.5.shtml

The number 147 may be written as 140+7 (**) therefore from the fact that 140 and 7 are both divisible by 7, we are sure their sum (147) is also divisible by 7.
Hence II. is refuted and we are left with alternative choice (B) as the only "survivor". We are done!

(**) This is the "breaking numbers" technique, presented and extensively used in our method since the very beginning!


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

Regards,
Fabio.

P.S.: people like to believe that our course, probably the most mathematical-oriented of the whole PLANET(!), would not take the alternative choices into account.
VERY far from true. The winning triad is the backbone of our method and "alternative choices evaluation" is its third leg!