ISEE Quantitative Reasoning:Question Types and Common Errors

Question counts and question types by level

This section explains which level a student takes and which question types the student will see. The ISEE (Independent School Entrance Exam) is administered by ERB (Educational Records Bureau). The level is determined by the grade the student is applying to enter, not by the grade the student currently attends.

Level	Applying to grade	Quantitative Reasoning questions	Time	Word problems	Quantitative comparisons
Lower Level	Grades 5–6	38	35 minutes	Yes	No
Middle Level	Grades 7–8	37	35 minutes	Yes	Yes
Upper Level	Grades 9–12	37	35 minutes	Yes	Yes

Source: official ERB ISEE materials.

At all three levels, the average time available is less than 1 minute per question. The official guides list the following areas of assessment:

• Estimating numerical values
• Using logic to determine what a question is asking
• Comparing quantities
• Analyzing and interpreting data and graphs
• Inferring the probability of events
• Understanding measurement concepts and their applications

The questions are written to the standards of the National Council of Teachers of Mathematics (NCTM) and cover the strands of number and operations, algebra, geometry, measurement, data analysis and probability, and problem solving. The score report does not break down the Quantitative Reasoning score by strand.

The Primary 2, 3 and 4 levels consist only of reading, mathematics and related sections and have no separate Quantitative Reasoning section. This page therefore does not apply to students applying to grades 2 through 4.

How Quantitative Reasoning differs from Mathematics Achievement

This section explains what each of the two ISEE mathematics sections assesses. The Lower, Middle and Upper Levels each have two scored mathematics sections: Quantitative Reasoning and Mathematics Achievement. The two cover similar content but test it in different ways.

In its official preparation guides, ERB explains that Quantitative Reasoning does not test how much mathematics a student has learned but how the student thinks mathematically. Most questions require little calculation or none at all. Mathematics Achievement, by contrast, is written to curriculum standards, and its questions usually require one or more steps of calculation to reach the answer.

Item	Quantitative Reasoning	Mathematics Achievement
Official purpose	Assesses mathematical reasoning; most questions require little or no calculation	Assesses mastery of curriculum content; questions require one or more steps of calculation
Lower Level questions and time	38 questions · 35 minutes	30 questions · 30 minutes
Middle / Upper Level questions and time	37 questions · 35 minutes	47 questions · 40 minutes
Question types	Word problems; Middle and Upper add quantitative comparisons	Standard four-option questions
Calculator	Not permitted	Not permitted

Source: official ERB ISEE materials.

In other words, Quantitative Reasoning tests the ability to compare, estimate and judge without carrying out a full calculation. When a question can be answered by estimating, by noticing its structure or by eliminating choices, the student should not calculate it digit by digit. The official guides give the same advice for word problems: first ask whether the question can be answered with an estimate instead of an exact calculation.

Recognizing and answering word problems

Word problems appear at all three levels. Each consists of a written description and four answer choices. The official guides explain that these word problems differ from the traditional questions in Mathematics Achievement: some require no calculation, and others require only simple calculation.

Word problems usually test reading and modeling: finding the conditions that actually matter in a passage of text, deciding how many steps are needed and choosing the fastest route. The official guides also point out two patterns that students can use:

1. The four answer choices are arranged in order from least to greatest or from greatest to least. A student can first estimate an approximate range and then see which choice falls within it.
2. Wrong answer choices often correspond to common misunderstandings. A result that matches one of the choices is not necessarily correct; the student should still check which quantity the question actually asks for.

Recognizing and answering quantitative comparisons

Quantitative comparison questions appear only at the Middle and Upper Levels. Each question presents two quantities, Column A and Column B, sometimes with an additional condition, and the student determines the relationship between the two quantities. Every comparison question uses the same four answer choices:

Choice	Meaning
(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

Source: official ERB ISEE materials.

The official method has three steps:

1. Before writing anything, decide whether the information is sufficient to make a comparison; if it is not, choose D.
2. When a calculation is needed, estimate first where possible, and write the estimate next to the corresponding column.
3. Some questions include a condition outside the two columns; read all of the information before answering.

The key to this question type is that the student must establish that the relationship is certain, not merely find one example. If both columns are fixed values, the answer cannot be D. If the question contains a variable, the student must check whether different values change the relationship.

Common errors

This section lists the three causes of lost points that EDUBUS sees most often in teaching. Each corresponds to a habit that can be trained.

Treating a reasoning question as a calculation question

Many students with strong school math grades run short of time on Quantitative Reasoning. A common cause is calculating every question in full: working out both products when comparing two products, or finding a common denominator for every fraction before comparing. This approach usually produces the correct answer, but it takes time away from later questions and increases the chance of a calculation error. The remedy is to look at the structure first, for example whether the two expressions share a common part and which term is the only difference, and then decide whether any calculation is needed.

Not using substitution in comparison questions

Comparison questions that contain a variable cause the most errors. Students often substitute a single number, such as 2, and draw a conclusion from it. The correct approach is to substitute several kinds of numbers with different properties and check whether the relationship always holds. A standard order of checking is:

1. 1
2. A whole number greater than 1
3. A fraction between 0 and 1
4. When the conditions allow, 0 and negative numbers

If two substitutions produce different relationships, the answer is D.

Confusing units and ratios

A common trap in word problems is inconsistent units, for example one quantity in yards and another in inches, or one in minutes and another in hours. A student who multiplies or divides the two numbers directly often arrives at a result that matches one of the wrong answer choices. Ratio questions carry a similar risk: a student treats a part-to-part ratio as a part-to-whole ratio. Students should label every number with its unit in their scratch work and convert to a common unit before calculating.

Original sample questions

The following four sample questions were written by the EDUBUS teaching team. As on the test, the question stems and answer choices are in English.

Sample 1 (Quantitative Reasoning · word problem · logical reasoning)

The sum of three consecutive whole numbers is 48. What is the greatest of the three numbers?

(A) 15 (B) 16 (C) 17 (D) 18

Explanation

The answer is C. The sum of three consecutive whole numbers is 3 times the middle number, so the middle number is 48 ÷ 3 = 16 and the greatest number is 17. The question does not require an equation; it tests an understanding of the structure of consecutive whole numbers.

Distractor analysis: (A) 15 is the least of the three numbers; the student did not notice which number the question asks for. (B) 16 is the middle number; the student stopped after finding the quotient and missed the final step. (D) 18 treats 16 as the least number and adds 2, confusing the middle number with the least number.

Levels: Lower, Middle, Upper.

Sample 2 (Quantitative Reasoning · word problem · measurement and units)

A ribbon is 3 yards long. Lena cuts the whole ribbon into pieces that are each 9 inches long. How many pieces does she get?

(A) 3 (B) 4 (C) 12 (D) 36

Explanation

The answer is C. 1 yard equals 3 feet and 1 foot equals 12 inches, so 1 yard equals 36 inches, which can be cut into exactly 4 pieces of 9 inches. A ribbon of 3 yards therefore yields 4 × 3 = 12 pieces. Working out how many pieces 1 yard produces first avoids handling larger numbers.

Distractor analysis: (A) 3 comes from calculating 9 ÷ 3 directly and ignoring the units entirely. (B) 4 treats 3 yards as 3 feet (36 inches) and then divides by 9. (D) 36 is the number of inches in 1 yard; the student completed the unit conversion but did not go on to divide. The question tests unit conversion and the habit of converting to a common unit before calculating.

Levels: Lower, Middle, Upper.

Sample 3 (Quantitative Reasoning · quantitative comparison · number and operations)

Column A: 37 × 48

Column B: 38 × 47

(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.

Explanation

The answer is B. Neither product needs to be calculated. Split each column into a common part plus a remainder: Column A is 37 × 47 plus 37, and Column B is 37 × 47 plus 47. The common parts are equal, and the extra 47 in Column B is greater than the extra 37 in Column A, so Column B is greater, by 10.

Distractor analysis: (A) comes from the intuition that Column A contains the larger factor, 48, so its product must be greater. (C) comes from the misconception that two columns using the same four digits should produce equal results. (D) cannot be correct, because both columns are fixed values and their relationship can be determined. The question tests the ability to observe the structure of an expression and avoid a full calculation.

Levels: Middle, Upper. The Lower Level Quantitative Reasoning section has no comparison questions.

Sample 4 (Quantitative Reasoning · quantitative comparison · algebra and substitution)

x is a positive number.

Column A: 1/x

Column B: x

(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.

Explanation

The answer is D. Check three kinds of positive numbers by substitution. When x = 1, both columns equal 1, so the quantities are equal. When x = 2, Column A is 1/2 and Column B is 2, so Column B is greater. When x = 1/2, Column A is 2 and Column B is 1/2, so Column A is greater. The same condition produces different relationships, so the relationship cannot be determined.

Distractor analysis: (A) corresponds to substituting only fractions between 0 and 1. (B) corresponds to substituting only whole numbers greater than 1, such as 2 or 3, which is the most common error. (C) corresponds to substituting only 1. The question tests the properties of reciprocals and the habit of substituting several kinds of values to check whether a relationship holds.

Levels: Middle, Upper. The Lower Level Quantitative Reasoning section has no comparison questions.

Practice methods

This section sets out practice methods that can be built directly into a weekly plan. Every exercise should be completed without a calculator.

Exercise	Method
Estimate before calculating	Before working any question, write down an estimated range, then see which choice falls within it. In the early stages of practice, students can be asked to write the estimate next to the question number.
Substitution checklist	For comparison questions with a variable, check in the order 1, a whole number greater than 1, a fraction between 0 and 1, 0, and a negative number, skipping any number the conditions exclude.
Unit labeling	In word problems, label every number with its unit and convert before calculating.
Timed full sections	Regularly complete a full Quantitative Reasoning section under official timing (38 questions in 35 minutes at the Lower Level; 37 questions in 35 minutes at the Middle and Upper Levels) to build pacing.
Error categories	Record each error in one of four categories: content not known, calculation slip, inefficient method, or misreading. The inefficient method category usually shows most clearly how Quantitative Reasoning differs from Mathematics Achievement.
Mathematical English	Students whose first language is not English should deliberately learn words that appear often in question stems, such as consecutive, at least, remainder and product; misreading a single word can cost the entire question.

The EDUBUS assessment: improvement in Quantitative Reasoning comes mainly from habits, not from new content. For students whose content knowledge is already on track, focused practice in estimation, substitution and unit checking is usually more effective than working through large numbers of calculation problems.

Quantitative Reasoning in EDUBUS classes

EDUBUS offers fall classes at the Lower, Middle and Upper Levels in three modules: Verbal Reasoning, Reading Comprehension, and Quantitative Reasoning with Math. Students may enroll in a single module or in all three. The Quantitative Reasoning with Math module combines Quantitative Reasoning and Mathematics Achievement: within each content unit, Mathematics Achievement questions first check whether the content has been mastered, and Quantitative Reasoning questions then train estimation, comparison and substitution, so that preparation for the two sections reinforces each other.

Students who need a more flexible schedule can choose a private tutoring package. The ISEE online learning system built by EDUBUS provides practice by module, realistic practice tests and error analysis, and is suited to homework practice alongside classes. Course schedules and prices are listed on the ISEE courses and assessment page.