Quantitative Comparision
The quantitative comparison questions test the ability to reason quickly and accurately about the relative sizes of two quantities or to perceive that not enough information is provided to make such a comparison.
To solve a quantitative comparison problem, you must compare the quantities that are given in two columns, Column A and Column B, and decide whether one quantity is greater than the other, whether the two quantities are equal, or whether the relationship cannot be determined from the information given. Information about the two quantities is given in the columns themselves or may be centered above the columns.
Here are some examples with the correct answers indicated according to the following answer choices.
(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 from the information given.
| Column A | Column B | Correct Answer | |
|---|---|---|---|
| Example 1: | 23 | 32 | B |
| Example 2: | The smallest prime number greater than 20 | 23 | C |
m is an integer. | |||
| Example 3: | 3m + 7 | 7 | D (since m can be positive, negative, or zero) |
Some questions only require some manipulation to determine which of the quantities is greater; other questions require more reasoning or thinking of special cases in which the relative sizes of the quantities are reversed. The following strategies may help in answering quantitative comparison questions.
- Do not waste time performing needless computations in order to eventually compare two specific numbers. Simplify or transform one or both of the given quantities only as much as is necessary to determine which quantity is greater or whether the two quantities are equal. If you determine that one quantity is greater than the other, do not take time to find the exact sizes of the quantities. Answer and go on to the next question.
- Consider all kinds of appropriate real numbers before you make a decision. As soon as you establish that the quantity in one column is greater in one case while the quantity in the other column is greater in another case, choose "The relationship cannot be determined from the information given" and move on to the next question.
- Geometric figures may not be drawn to scale. Comparisons should be based on the given information together with your knowledge of mathematics rather than on the exact appearance of the figure. You can sometimes find a clue by sketching another figure that conforms to the information given. (Scratch paper will be provided.) Try to visualize the parts of the figure that are fixed by the information given and the parts that are changeable. If the figure can be changed in such a way that the relative sizes of the quantities in the columns are reversed while still conforming to the information given, then the answer is "The relationship cannot be determined from the information given."
Here are some more examples:
| Column A | Column B | Correct Answer | |
|---|---|---|---|
| Example 4: | PN | NR | D (since equal measures cannot be assumed, even though PN and NR appear to be equal) |
| Example 5: | x | y | B (since N is between P and R) |
| Example 6: | w + z | 180 | C (since PR is a straight line) |
A machine was in operation for t minutes. | |||
| Example 7: | The number of seconds that the machine was in operation | 60t | C |
| A farmer has two plots of land that are equal in area. The first plot is divided into 16 parcels with m acres in each parcel, and the second plot is divided into 20 parcels with n acres in each parcel. | |||
| Example 8: | m | n | A |
| Example 9: | 9.8 | sqrt(100) | B |
Note: In Example 9, denotes 10, the positive square root of 100. (For any positive number x, denotes the positive number whose square is x.) Since 10 is greater than 9.8, the best answer is (B). It is important not to confuse this question with a comparison of 9.8 and x where x2 = 100. The latter comparison would yield (D) as the correct answer because x2 = 100 implies that either x = 10 or x = –10, and there would be no way to determine which value x would actually have.
Directions: Each of the sample questions consists of two quantities, one in Column A and one in Column B. There may be additional information, centered above the two columns, that concerns one or both of the quantities. A symbol that appears in both columns represents the same thing in Column A as it does in Column B.
You are to compare the quantity in Column A with the quantity in Column B and decide whether:
(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 from the information given.
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