The least complicated option is to plug in values for m and n that adhere to the rules you’re
given, making m negative and n positive. Testing each answer choice using those values
allows you to eliminate any that don’t work out to be true. Even if you have several answer
choices remaining after crossing out the ones that don’t work with those numbers, picking a
second set of numbers—still playing by the rules!—and testing each of your remaining
answer choices with your new values should help you narrow it down to one. Alternatively,
consider your answer choices. For (A), a positive number divided by a negative number will
produce a negative number, not something greater than 1. Cross this answer out. For (B),
remember that absolute value makes the inside result positive, and this will happen to both n
and m. Then |n| is squared, which will still be positive. A positive number, |n^2 |, may or may
not be bigger than another positive number, |m|, so cross this answer out. In (C), subtract 2
from both sides, and then multiply both sides by 7, so the expression becomes simply n > m,
which you know to be true. Keep this answer. In (D), squaring both m and n make both values
positive, without any sense of how large or small these newly positive numbers are. Thus,
even after adding 1, there’s still no way to say for sure which side is larger or smaller. As for
(E), n−2 and m−2, which are and and , are both positive numbers, but again you’re
given no sense of which is larger or smaller. The only answer that must be true is (C).
56 . J
There are several ways to think about this question. There’s not a lot of information to go on,
so it becomes really important to pay very careful attention to what you do know and, since
you’re being asked to compare two things, any relationships you can discern. Noticing that
the 55° angle and the 125° angle were supplementary might lead you to match up the a-sides
