Both the middle and upper level contain ISEE quantitative comparison questions in the quantitative reasoning section of the exam.  These questions are typically the hardest for most students because they are not math problems students encounter in school or on other standardized exams. The most important and easiest way for students to have an edge on this section is to be familiar with the directions so they do not have to refer back to them when taking the ISEE.

Here is the exact wording of the directions for the ISEE quantitative comparison section:

Directions: Using all information given in each question, compare the quantity in Column A to the quantity in Column B.  All questions in Part Two have these 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.

Now that students know the directions, here are 3 tips for approaching ISEE quantitative comparison questions.

1.  Estimate

 

The one advantage students have in quantitative comparison questions is that they do not have to find an exact answer.  All they need to do is to compare the answers in both columns to see which is greater. This means that estimation is a great tool to use to quickly arrive at the correct answer.  If both columns involve pure calculations, often times, students can avoid performing the calculations by comparing the numbers in both columns.

Example:

Column AColumn B
3685 x 464876 x 50

4876 is greater than 3685 and 50 is greater than 46.  Therefore, the answer in column B is greater than the answer in column A.  The answer choice here is B.

2.  Picking numbers

 

Picking numbers is one strategy to figuring out if D is a possible answer choice in algebraic problems.  Students should choose numbers to plug into the problem in each column to compare the two columns.  The particular numbers students should choose should include a positive number, negative number, 1 and 0.  Students should make sure they read the question thoroughly. Sometimes there will be information placed in the center and will be applied to the questions in both columns that will restrict the numbers they should pick.

Example:

Column AColumn B
xx²

Since the information in the center mentions that X is greater than 0, negative numbers and 0 itself should not be chosen as numbers to plug in.  1 and 2 are great options to choose.

Plug in 1:  Column A = 1   Column B = 1         Answer: C

Plug in 2:  Column A = 2  Column B = 4        Answer: B

Since there are two possible answers, the answer should be D.

3.  Understanding answer choice D

 

The trickiest thing about quantitative comparison questions is when to choose D.  These questions differ from other math questions on the ISEE because some questions may not have a definite answer.  As a result, the best answer choice would be D, “the relationship cannot be determined from the information given”. Here are some reasons why students may choose D.

a) There is not enough information given to solve the problem.

Example:

John has 3 apples and 5 oranges.  He paid $3.00 for all his fruit.

Column AColumn B
The cost per orangeThe cost per apple

Since the question did not mention how much each apple or orange costs, there is not enough information to determine whether column A or column B is greater.  Therefore, the answer here is D.

b) There is more than 1 possible answer.

Example: 

y ≠ 0

Column AColumn B
-yy

y does not equal 0.

If y = 1:  Column A = -1  Column B = 1         Answer: B

If y = -1:  Column A = 1  Column B = -1        Answer: A

Since there are two possible answers, the answer should be D.

c) D is not a possible answer choice if both columns contain all numbers and no variables.

Example: 

Column AColumn B
¾ + ¼½ + ¾

Since there are only numbers in both column A and B, answer choice D is not an option.

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