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

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

What this topic is

Questions on Whole numbers, integers, and operations test sign rules, order of operations and the behavior of negative numbers.

Many appear as quantitative comparisons, where Column A is weighed against Column B and the four choices say that A is greater, B is greater, the two are equal, or the relationship cannot be determined. That last choice matters when variables are involved: if two integers are both negative, their product is positive but their sum is negative, so careful reasoning about signs settles the comparison.

Another frequent slip is solving a sum-and-product clue correctly, then reporting the wrong one of the two numbers. Arithmetic stays light; reasoning carries the weight.

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 $p q = 45$ . 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 $t^{2} - 14 t + 45 = (t - 5) (t - 9)$ , 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