59 . D Disjoint regions are non-overlapping regions. 7 vertical lines and 7 horizontal lines
overlapping each other create a grid with a 6 × 6 section of enclosed rectangles, which each
have a finite, nonzero area. There are also 2- or 3-sided areas around the outside that are
open on 1 or 2 sides, which would have an infinite area. So the number of disjoint regions is
6 × 6 = 36. Choice (E) incorrectly counts 7 × 7 disjoint regions, and (C) incorrectly counts 5
× 5 disjoint regions.
60 . G Because any number raised to an even power will always be positive, in order for x^3 y^4 z^6 < 0
to be true, x^3 must be less than 0, which means that x must be less than 0. Since y and z can be
either positive or negative, start by plugging in negative numbers for all three. Plug x = −2, y
= −3, and z = −4, into the answer choices. Choice (F) is incorrect because (−2)(−3) = 6.
Choice (H) is incorrect because (−3)(−4) = 12. Next try changing the y value to positive, so
that x = −2, y = 3, and z = −4. Choice (J) is incorrect because (−2)(3)(−4) = 24. Then change
the z value to positive also, so that x = −2, y = 3, and z = 4. Choice (K) is incorrect because
(−2)^2 (3)^2 (4)^3 = (4)(9)(64) = 2,304. Only (G) is less than 0 with any combination of values.
