GRE Multiple Choice (Select One or More): Arithmetic Questions

On the GRE Quantitative Reasoning section, "Select One or More" questions present you with square checkboxes and a variable number of choices. Unlike standard multiple choice, there is no single correct answer — you must identify every correct choice and only those choices. There is no partial credit. When combined with arithmetic content — integers, divisibility, prime factorization, percentages, ratios, and number properties — these questions reward systematic checking over intuition. Below you will learn the four stem patterns that appear, work through two interactive examples step by step, and then practice with six questions drawn from a verified question bank.

What Are Select One or More Arithmetic Questions?

These are GRE Quantitative Reasoning questions that combine the Select One or More format (square checkboxes, variable number of correct answers, no partial credit) with arithmetic content — integers, divisibility, prime factorization, percentages, ratios, number properties, and number line reasoning. You must select every correct answer and only correct answers. If a question has three correct choices and you select two, or if you select all three plus one wrong choice, you receive zero credit.

The arithmetic itself is rarely complex. The difficulty comes from the format: you cannot rely on the process of elimination that works for single-answer questions. Instead, you must independently verify or eliminate each choice against the constraints in the question stem. This makes systematic work — not gut instinct — the winning approach.

Format reminder: On screen, Select One or More questions display square checkboxes (not circles). The directions line reads "Select one or more answer choices." The number of correct answers ranges from one to all of the choices offered. Never assume a fixed count.

Four Stem Patterns You Will See

Nearly every MCM arithmetic question falls into one of four patterns. Recognizing the pattern tells you how to structure your checking process.

Divisibility and Factor Testing

Given constraints on a number (such as 'n must divide 60, 84, and 72'), determine which values from a list satisfy all constraints. Each choice must be independently tested. The key tool is GCD or prime factorization.

Percentage Threshold Problems

Given data (often from a chart or table), determine which categories exceed a computed threshold. Convert the threshold to a percentage or convert percentages to absolute numbers, whichever makes comparison easier, then check each choice.

Number Property Verification

Given relationships between numbers (such as '

a^2 + b^2

is odd'), determine which algebraic statements must be true. Test each statement using parity rules or plug in concrete values that satisfy the given condition.

Constraint Satisfaction

Given multiple arithmetic constraints (such as a price markup followed by a discount within a range), determine which parameter values satisfy all conditions. Set up the formula once, then substitute each choice.

How to Solve MCM Arithmetic Step by Step

These five strategies apply across all four patterns. Because "select all that apply" questions offer no partial credit, a disciplined process is essential.

Read the question stem and extract the mathematical condition. For example, "the number of students must evenly divide 60, 84, and 72" becomes "find common factors of 60, 84, and 72." Do this before glancing at any answer choice so you are not anchored by the options.

When a problem involves multiples, factors, or LCM/GCD, break every relevant number into its prime factorization. This makes it mechanical to determine what divides what. For example, $60 = 2^2 \cdot 3 \cdot 5$ , $84 = 2^2 \cdot 3 \cdot 7$ , $72 = 2^3 \cdot 3^2$ , so $\text{GCD} = 2^2 \cdot 3 = 12$ , and the valid choices are the factors of 12.

After finding one or two correct answers, it is tempting to submit. Resist this urge. The GRE is designed so that overlooking one correct answer earns zero credit. Work through every choice mechanically, marking each as "satisfies" or "fails." Only submit after you have verified all of them.

For percentage threshold problems ("which sectors represent more than 40,000?"), convert the absolute threshold to a percentage or vice versa — whichever matches the form of the given data. If the data is in percentages and the threshold is in absolute numbers, divide the threshold by the total to get a percentage cutoff.

If the stem says "must be true," the statement must hold for every possible value satisfying the conditions. A single counterexample disproves it. If the stem says "could be true," you only need one example that works. Be precise about which type of question you are answering.

Pro tip: For "must be true" questions about number properties, test with the simplest specific numbers that satisfy the given condition. If a statement fails for even one valid input, it is not a correct choice. If it passes your test cases, try to see why it must always hold.

Worked Example: GCD and Divisibility

This example demonstrates the systematic approach to a common MCM arithmetic pattern: finding which values from a list satisfy a divisibility constraint. Work through each step below.

Interactive Walkthrough0/6 steps

Common Factors via GCD

A group of students equally divided 60 bottles of water, 84 packs of gum, and 72 energy bars. Each student received the same whole number of each item, with nothing left over in any case.

Which of the following could be the number of students in the group? Select all that apply.

Step 1: Identify the constraint

The number of students must be a common factor of which numbers?

Step 2: Prime factorize each number

Step 3: Compute the GCD

Step 4: List all factors of the GCD

Step 5: Check each choice

Step 6: Determine the correct set

Worked Example: Percentage Markup and Reversal

This example tackles a constraint satisfaction pattern: a price is raised by p percent and then lowered by p percent. You must determine which values of p produce a final price within a specified range. This is a classic "select all that apply" setup because each choice must be tested independently.

Interactive Walkthrough0/5 steps

Successive Percentage Changes

A store raises the price of an item by p percent and then lowers the new price by p percent. You are told the final price is at least 75% but less than 99% of the original price.

Which of the following could be the value of p? Select all that apply.

Step 1: Derive the formula

After raising by p% then lowering by p%, the final price ratio is:

Step 2: Set up the inequality

Step 3: Check p = 15

Step 4: Check p = 55

Step 5: Identify all valid choices

Practice Questions

Apply what you have learned. Each question below is a "select all that apply" problem. After you submit your answer, click through the solution walkthrough one step at a time. Remember: on the real GRE, you must select every correct choice to earn credit.

Question 1 — GCD Constraint (Select All That Apply)

If n is a positive integer less than 40 such that GCD(n, 18) = 6, which of the following could be the value of n? Indicate all such values.

Question 2 — Number Properties (Select All That Apply)

a

and

b

are integers such that

a^2 + b^2

is odd, which of the following statements must be true? Indicate all such statements.

Question 3 — Units Digit Cycle (Select All That Apply)

Let

S = 7^1 + 7^2 + 7^3 + \cdots + 7^{40}

. Which of the following could be the units digit of

S

? Indicate all such values.

Question 4 — Counting Diagonals / Combinatorics (Select All That Apply)

A convex polygon has n sides. If the number of diagonals is between 25 and 50, inclusive, which of the following could be the value of n? Indicate all such values.

Question 5 — Perfect Square Reasoning (Select All That Apply)

n

is a positive integer such that

n^3

is a perfect square, which of the following statements must be true? Indicate all such statements.

Question 6 — Consecutive Integers (Select All That Apply)

The product of three consecutive positive integers is divisible by 80. Which of the following could be the smallest of the three integers? Indicate all such values.

Three Common Traps

Trap 1 — Confusing factors of $n$ with factors of $n^2$ . If a problem states that

n^2

must be a multiple of some value, the constraints on

n

are different. Exponents in

n

must be at least half the exponents required in

n^2

(rounded up to the next integer). For example, if

n^2

must be divisible by

2^3

, then

n

must be divisible by

2^2

(since you need

2e \geq 3

, so

e \geq 2

Trap 2 — Forgetting one of multiple constraints. In problems with multiple divisibility requirements, a value might divide two of three quantities but not the third. You must check every constraint for every choice. A systematic table (choice vs. constraint) prevents this error.

Trap 3 — Assuming a fixed number of correct answers. Select One or More questions can have any number of correct answers. Some questions have a single correct choice; others have five out of six. Never assume "two or three" is typical. The only way to get credit is to check all choices and select exactly those that pass.

Recognizing MCM Arithmetic at a Glance

Not every multiple-choice question with checkboxes involves arithmetic. Use this table to quickly identify MCM arithmetic questions and distinguish them from other MCM types.

Clue in the Question Stem	Likely Pattern	First Move
"Which of the following are divisors/multiples of..."	Divisibility / Factor Testing	Prime-factorize all relevant numbers and find GCD or LCM
"Which sectors represent more than X?"	Percentage Threshold	Convert the absolute threshold to a percentage (or vice versa)
"Which of the following must be true about..."	Number Property Verification	Determine parity or other constraints, then test each statement
"Which could be the units digit of..."	Units Digit Cycle	Compute the first four powers to find the repeating cycle
"Which values of p satisfy..." with a formula	Constraint Satisfaction	Derive the formula, solve for the valid range, then check each choice
"Which of the following could be the value of n?" with GCD/LCM	Divisibility / Factor Testing	Compute the GCD or LCM, then check factors or multiples

The visual cue is the square checkbox and the direction "Select one or more answer choices." Once you see that, immediately shift your mindset from "eliminate to find the one" to "test each choice independently."

Study Checklist

MCM Arithmetic Mastery Checklist0/8 complete

Frequently Asked Questions

How many answers should I select on GRE Select One or More questions?

There is no fixed number. You must select every correct answer and only correct answers. A question could have one correct choice or all choices could be correct. The GRE does not tell you how many to pick. You must evaluate each choice independently against the given constraints. In the practice set above, Question 3 has a single correct answer while the GCD question from the guide has five correct answers out of six choices.

Is there partial credit on GRE Select One or More questions?

No. You receive full credit only if you select exactly the set of correct answers. If you miss even one correct choice, or include even one incorrect choice, you receive zero credit for that question. This is why systematic checking of every choice is so important — skipping one correct answer is just as costly as including one wrong answer.

What arithmetic topics appear most often in Select One or More questions?

The most common arithmetic topics are divisibility and factor testing (GCD, LCM, prime factorization), number properties such as even/odd parity and perfect squares, units digit cycle patterns for powers, and percentage or ratio threshold problems. These topics naturally produce multiple valid answers, which is why they pair so well with the "select all that apply" format.

How do I avoid missing a correct answer on these questions?

The best strategy is systematic elimination. First, determine the mathematical constraint from the question stem. Then test every single choice against that constraint, one at a time. Do not stop after finding one or two correct answers — always check all remaining choices. Drawing a quick table (choice versus constraint) on your scratch paper is an effective way to ensure completeness.

What is the difference between Select One and Select One or More on the GRE?

Select One questions have radio buttons (circles) and exactly one correct answer. Select One or More questions have checkboxes (squares) and can have any number of correct answers, from one up to all choices offered. The visual cue is the shape of the selection indicator: circles mean exactly one answer, squares mean possibly many. The directions line for Select One or More always reads "Select one or more answer choices."