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

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

What this topic is

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.

Sample questions

Pick an answer to see whether it is right — nothing is saved, and nothing needs an account.

Question 1Easier

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

The quantity in Column A is greater✗ Not this oneThe quantity in Column B is greater✓ CorrectThe two quantities are equal✗ Not this oneThe relationship cannot be determined from the information given✗ Not this one

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Answer: B — The quantity in Column B is greater

Column A is 19, so Column B is greater.

Question 2Easier

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

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

The quantity in Column A is greater✓ CorrectThe quantity in Column B is greater✗ Not this oneThe two quantities are equal✗ Not this oneThe relationship cannot be determined from the information given✗ Not this one

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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 3Easier

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

5✗ Not this one7✗ Not this one9✓ Correct14✗ Not this one

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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.

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

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

What this topic is

Sample questions

More ISEE Upper topics

Quantitative Reasoning