Column A: $3(8)-5$ / Column B: $20$

The relationship cannot be determined from the information given

$a$ and $b$ are integers such that $a<b<0$. Column A: $a^2$ / Column B: $b^2$

The relationship cannot be determined from the information given

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Quantitative ReasoningFree

Whole numbers, integers, and operations — ISEE Upper practice questions

Whole numbers, integers, and operations on the ISEE Upper Quantitative Reasoning section covers counting numbers, signed integers, and arithmetic with order of operations. Students must evaluate mixed expressions, compare two quantities, reason about negative integers, and recover a pair of positive integers from a given sum and product. The exam often uses quantitative comparison, placing a Column A expression against a Column B number, or asks which of two integers is greater. Common traps include mishandling multiplication next to subtraction, reversing inequalities for negatives, and swapping which factor is larger. Answer choices are usually four options: comparison labels or a short list of integers.

Section: Quantitative Reasoning 37 questions on the paper
123 practice questions in the app

Sample questions

Question 1

Column A	Column B
$3(8)-5$	20

AThe quantity in Column A is greater
BThe quantity in Column B is greater
CThe two quantities are equal
DThe relationship cannot be determined from the information given

Show answer

Answer: B — The quantity in Column B is greater

Column A is 19, so Column B is greater.

Question 2

$a$ and $b$ are integers such that $a<b<0$ .

Column A	Column B
$a^2$	$b^2$

AThe quantity in Column A is greater
BThe quantity in Column B is greater
CThe two quantities are equal
DThe relationship cannot be determined from the information given

Show answer

Answer: A — The quantity in Column A is greater

Since $a<b<0$ , $a$ is more negative than $b$ , so $|a|>|b|$ . Squaring makes both values positive, so $a^2>b^2$ and Quantity A is greater.

Question 3

$p$ and $q$ are positive integers with $p+q=14$ and $pq=45$ . What is the greater of the two integers?

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Answer: C — 9

The integers are the roots of $t^2-14t+45=(t-5)(t-9)$ , so the greater integer is 9.

Practice 123 Whole numbers, integers, and operations questions in the app

Whole numbers, integers, and operations — ISEE Upper practice questions

Sample questions

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Quantitative Reasoning