(A) Don’t be misled by the word daily into finding the actual daily rent of the man in column A, by dividing his monthly rent by the number of days in a month. You may waste a lot of time deciding whether to divide by 31, 30, or 30.25 to obtain a messy figure you don’t need. Since you know there are 12 months in a year, multiply 975 by 12 to obtain $11,700 as the annual rent in (A), which is greater than quantity (B), $11,650. A man who pays more rent per year will also pay more rent per day.

(D) Quantity (B) “seems greater” by exactly 1x + 1y, because (3x + 4y) – (2x + 3y) = 1x + 1y. Though (B) appears greater, x and y may be negative numbers, so (D) is correct. For example, if x = y = 1, then (A) = 5 < (B) = 7, but if x = y = –1, then (A) = –5 > (B) = –7.

(C) When lines intersect, the vertical angles, those directly across from each other, are equal. This means that we can label the three angles within the triangle 2x°, 3x°, and 4x°. By the triangle sum theorem, 2x° + 3x° + 4x° = 180°. Then 9x = 180, and x = 20. So 5x = 100, (C).

(A) Expand (m + 5)(m – 5) as m ²– 5m + 5m – 25 = m ²– 25. If this equals 0, then m ²= 25.

Similarly, (k + 4)(k – 4) = k ² – 4k + 4k – 16 = k ² – 16 = 0. Add 16 to both sides, and k ²= 16, (A) is greater.

(A) In a triangle, the larger sides are across from the larger angles, and the smaller sides are across from the smaller angles. Since the side length x + .001 > x, the angle opposite x + .001 is greater than the angle opposite x. So y > z, (A).

(D) By substitution, m = 3(5p) = 15p. This means that m is 15 times p. It looks as if m, Quantity (A), is greater, but if the variables are negative, p is greater, so (D) is correct.

(B) Solve 4ⁿ = 256 by multiplying fours on your calculator until you reach 256 as a product. Note that 4 × 4 × 4 × 4 = 16 × 16 = 256, meaning that the exponent n equals 4. Then (A) is 3⁴ = 3 × 3 × 3 × 3 = 9 × 9 = 81. Quantity (B) is greater, because (3/2) × 4 ³ = (3/2) × 64 = 96, and 96 > 81.