Strategies for Quantitative Comparisions

• consider values that are fractional (between 0 and 1), zeros, negative, or non-integer,
• factor out, then cancel, any common expressions or quantities in both columns A and B
• these questions should be simpler than the multiple choice, look closely, is the answer apparent without any working out?
• write on the diagrams in the test booklet to clarify any lengths, values, angles etc.
• choose the answer that seems most likely, rather than solving the question,
• simplify as much as possible
• there are only four choices so do not ever guess the answer is Choice E!

Question:
5 < xy < 20 and x and y are integers

Column A	Column B
xy	x + y

(A) the quantity in Column A is greater
(B) the quantity in Column B is greater
(C) the two quantities are equal
(D) the relationship cannot be determined

Answer: D

Explanation: Since x and y are integers, xy must be an integer, and the problem states that xy is between 5 and 20. If for example, xy=6, then the values of x and y could be 6 and 1, 2 and 3, -6 and -1, or -2 and -3. For these values, x + y is greater than 6 and in some cases x + y is less than 6. Since the relationship between xy and x + y varies, depending on which values of x and y are taken, the relationship between the quantity in Column A and the quantity in Column B cannot be determined.

Question:
x is a positive integer Column B

Column A
The number of distinct prime factors of x	The number of distinct prime factors of x cubed

(A) the quantity in Column A is greater
(B) the quantity in Column B is greater
(C) the two quantities are equal
(D) the relationship cannot be determined

Answer: C

Explanation: Plug in the first three numbers (never more than three) from a class of numbers eg. x=1, 2, and 3. If x=1, then x has no prime factors, likewise for x cubed. Next, if x=2, then x has one prime factor, 2, and x cubed equals 8 also has one prime factor, 2. Finally, if x=3, then x has one prime factor, 3, and x cubed equals 27 also has one prime factor, 3. In all three cases, the columns are equal.

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