Solutions

1. (A)
2. (A)

   When you divide by a negative number, you must reverse the direction of the inequality symbol.

3. (C)

   If G² < G, then G must be positive (because G² will never be negative), and G must be less than 1, because otherwise, G² > G. Thus, 0 < G < 1. You can eliminate choices (D) and (E) because they violate the condition that G be positive. Then test choice (A): 1 is not less than 1, so you can eliminate (A). Choice (B) is greater than 1, so only choice (C) satisfies the inequality.

4. (C)

   If |A| > 19, then A > 19 OR A < −19. The only answer choice that does not satisfy either of these inequalities is choice (C), 18.

5. (A)

   If A is positive, B³ must be negative. Therefore, B must be negative. If A is positive and B is negative, the product AB must be negative.

6. (D)

   To evaluate the absolute value, set up two equations and isolate x:

   + (2x − 5) ≤ 7 2x − 5 ≤ 7 2x ≤ 12 x ≤ 6

   and

   −(2x − 5) ≤ 7 −2x + 5 ≤ 7 −2x ≤ 2 x ≥ −1

   Combine the information from the two equations:

   	|2x − 5| ≤ 7
   Quantity A		Quantity B
   −1 ≤ x ≤ 6		3

   There are possible values of x greater than and less than 3. The relationship cannot be determined.

7. (D)

   To find the minimum and maximum values of xy, test the boundaries of x and y:

   x	y	xy
   Min 1	Min −2	(1) × (−2) = −2
   Min 1	Max 1	(1) × (1) = 1
   Max 5	Min −2	(5) × (−2) = −10
   Max 5	Max 1	(5) × (1) = 5

   Combine the information from the chart to show the range of xy:

   	1 ≤ x ≤ 5 and 1 ≥ y ≥ −2
   Quantity A		Quantity B
   −10 ≤ xy ≤ 5		−10

   Quantity A can be either greater than or equal to −10. The relationship cannot be determined.

8. (C)

   Plug in 4 for x in Quantity A.

   	x = 4
   Quantity A		Quantity B
   |2 − x| = |2 − (4)| = |−2| = 2		2

   The two quantities are equal.