GRE Multiple Choice (Select One): Arithmetic Questions

Arithmetic forms the bedrock of GRE Quantitative Reasoning. Multiple Choice Select One questions in this domain test your fluency with percents, ratios, profit calculations, divisibility rules, and multi-step word problems. The underlying math is rarely advanced, but the GRE makes these questions challenging through layered reasoning, carefully designed wrong answers, and traps that exploit common computational mistakes. This guide walks you through every question pattern you will encounter, provides two fully interactive worked examples, and then lets you practice with six real-format problems complete with step-by-step solution walkthroughs.

What Are Multiple Choice Select One Arithmetic Questions?

On the GRE Quantitative Reasoning section, Multiple Choice Select One (MC1) questions present you with a problem and five answer choices labeled A through E. You select exactly one correct answer. When the content domain is Arithmetic, the question draws on fundamental number concepts: percentages, ratios and proportions, profit and cost calculations, divisibility, prime factorization, rounding, sequences, exponents, and absolute value. These topics may sound elementary, but the GRE tests them through multi-step word problems that require careful tracking of quantities and awareness of deliberately placed distractors.

The correct answer typically requires applying two or more arithmetic operations in sequence. A question might ask you to compute a percentage, then use that result to form a ratio. Or it might require you to calculate total costs from multiple components and then determine profit as a percentage of a specific base. The wrong answer choices are not random numbers. Each distractor corresponds to a specific, predictable mistake: using the wrong base for a percent, flipping a ratio, forgetting a cost component, or rounding to the wrong decimal place. Understanding how distractors are built is as important as knowing how to compute the right answer.

Frequency note: Arithmetic underlies roughly 25 to 30 percent of all GRE Quantitative Reasoning questions. It appears across every question format, but MC1 is the most common delivery vehicle. Expect to see several arithmetic MC1 questions per test section, ranging from Easy to Hard difficulty.

7 Patterns You'll See

Nearly every MC1 Arithmetic question falls into one of seven recognizable patterns. Learning to identify the pattern from the question stem tells you immediately what approach to take and which traps to watch for.

Greatest or Maximum Number Of...

Optimization within a budget constraint. You must find the largest count of items purchasable given a spending limit and item prices. The key insight: always buy the cheapest items first to maximize quantity.

Total Cost or Total Amount

Direct computation of a total from given rates, prices, or piecewise pricing. These questions often involve shipping tiers, tax brackets, or multi-component costs where you must add pieces carefully.

Ratio or Percent Of...

Compute a ratio or percentage from given information. The classic form: if X percent of purchases were online, what is the ratio of online to in-store? Requires converting between percent and ratio notation.

Approximately What Was the Cost...

Estimation-focused questions with widely spaced answer choices. You are expected to round aggressively and compute a ballpark figure. The spacing of the choices guarantees that reasonable estimation lands on exactly one option.

Farthest or Closest to a Value

Number line distance or approximation questions. You compare several values to a reference point and determine which is farthest (or closest) by computing absolute differences.

Multi-Step Word Problem with Unit Conversion

These questions require chaining two or three arithmetic steps, often ending with a format change such as expressing a fraction as a percent or converting units from dollars to cents. Profit-as-percent-of-cost is a classic example.

Least Positive Integer or Number Theory

Questions rooted in prime factorization, divisibility, or factor counting. You may need to find the smallest integer with a specific property, count divisors of a product, or determine remainders using cyclical patterns.

How to Solve MC1 Arithmetic Step by Step

The following five strategies apply across all seven patterns. Internalizing them will prevent the most common errors and speed up your work on test day.

The moment you see a percent in a problem, rewrite it as a decimal or fraction before doing any computation. This single habit eliminates the most frequent arithmetic errors on the GRE. Remember that "40 percent more than X" means $X \times 1.40$ , not $X \times 0.40$ . Write $40\% = 0.40 = \frac{2}{5}$ in your scratch work and proceed from there.

Before computing, glance at the answer choices and estimate the magnitude of the correct answer. If someone buys goods for $80 and marks up by 75%, the selling price should be around $140. Any choice far from this range can be eliminated immediately. This narrows your options and catches computational errors before you commit to a final answer.

When the problem asks "what is the greatest number of..." or "how many items did he sell," try the answer choices themselves. Start with the largest (or smallest) plausible value and check whether it satisfies all the constraints. If it does, you have your answer without setting up an equation. If it fails, move to the next choice. This approach is often faster than algebraic setup for word problems.

When working with ratios, reduce to lowest terms as your first step. A ratio of 55:45 should become 11:9 before you compare with answer choices. This prevents errors from working with unnecessarily large numbers and makes the correct choice easier to spot. Always check whether the GCD of the two parts is greater than 1.

In rate problems, cost problems, and mixture problems, write out the units at every step: dollars per pen, grams of solution A per total grams, items sold times price per item. Tracking units prevents you from accidentally combining incompatible quantities — for example, adding a cost (in dollars) to a count (in items). If the units do not cancel correctly in your final expression, you have made an error somewhere upstream.

Pro tip: If a word problem has many numbers and conditions, write out the relationship as a formula before plugging in values. For example, write Profit = Revenue - Total Cost, where Total Cost = Item Cost + Fixed Costs. Then substitute the specific numbers. This symbolic-first approach prevents you from losing track of which number goes where.

Worked Example: Commission Calculation

Work through each step below. You must answer each mini-challenge correctly to unlock the next step.

Interactive Walkthrough0/5 steps

Computing Total Earnings with Commission

A salesperson earns a base salary of $400 per week plus a 6% commission on all sales above $5,000. In one week, the salesperson's total sales were $12,500.

What was the salesperson's total earnings for that week?

Step 1: Find the commission-eligible amount

Commission applies only to sales above $5,000. How much of $12,500 is above the threshold?

Step 2: Calculate the commission

Step 3: Add the base salary

Step 4: Identify the threshold trap

Step 5: Verify the answer

Worked Example: Average Speed Round Trip

This example teaches why you cannot simply average speeds — a trap the GRE sets frequently. Work through each step to understand the total-distance / total-time framework.

Interactive Walkthrough0/5 steps

Average Speed Round Trip Problem

A cyclist rides 30 miles uphill at a speed of 10 miles per hour and then returns the same 30 miles downhill at a speed of 30 miles per hour.

What is the cyclist's average speed, in miles per hour, for the entire 60-mile round trip?

Step 1: Calculate the uphill time

Time = Distance / Speed. How long does the uphill leg take?

Step 2: Calculate the downhill time

Step 3: Find total distance and total time

Step 4: Understand the averaging-speeds trap

Step 5: Verify

Practice Questions

Apply what you have learned. Each question below is a standalone MC1 arithmetic problem. After you submit your answer, click through the step-by-step solution walkthrough to compare your approach against the optimal method.

Question 1 — Successive Percentage Changes

A store increases the price of a television by 25%, then raises it again by 20%, and finally offers a sale discount of 30% on the resulting price. If the original price of the television was $200, what is the final sale price?

Question 2 — Markup, Discount, and Profit Percent

A merchant purchases goods at $80 per unit and marks the price up by 75%. To attract customers, the merchant then offers a 20% discount on the marked price. What is the merchant's profit as a percentage of the cost price?

Question 3 — Working Backward Through Percent Changes

The population of a town increased by 20% in the first year, decreased by 10% in the second year, and then increased by 15% in the third year. If the population at the end of the third year was 49,680, what was the population at the beginning of the first year?

Question 4 — Weighted Average with Raises

A company has three departments. Department X has 20 employees with an average salary of $4,000 per month, Department Y has 30 employees with an average salary of $5,000 per month, and Department Z has 50 employees with an average salary of $7,000 per month. If Department X receives a 25% raise, Department Y receives a 10% raise, and Department Z receives no raise, what is the new average monthly salary across the entire company?

Question 5 — Sequential Fraction Distribution

A sum of $2,400 is to be distributed as follows: first, Person P receives

\frac{1}{4}

of the total. From the remainder, Person Q receives

\frac{2}{5}

. From what is left after P and Q have been paid, Person R receives

\frac{3}{4}

, and the rest goes to a charity fund. How much money does the charity fund receive?

Question 6 — Consecutive Integers

The sum of 21 consecutive integers is 630. What is the product of the smallest and the largest of these integers?

Common Traps

Trap 1 — Percent "of" versus percent "more than." 40% of $102 is $40.80, but 40% more than $102 is $142.80. These are fundamentally different operations, yet the GRE routinely includes both values as answer choices. Before computing, read the phrasing carefully: "of" means multiply by the percent; "more than" means multiply by (1 + percent). Getting this distinction right eliminates one of the two most popular wrong answers on any percent problem.

Trap 2 — Successive percent changes are not additive. A 25% increase followed by a 20% increase is not a 45% increase. The correct approach is to multiply the factors:

1.25 \times 1.20 = 1.50

, which represents a 50% increase. Adding the percentages (to get 45%) gives the wrong answer, and the GRE will always include that wrong answer among the choices. Similarly, a 75% markup followed by a 20% discount is not a 55% net markup — it is

1.75 \times 0.80 = 1.40

, a 40% net gain.

Trap 3 — Profit as percent of cost versus percent of selling price. When a question asks "profit was what percent of cost," the denominator is the cost, not the selling price. If cost is $500 and selling price is $625, profit is $125 and profit as percent of cost is

125/500 = 25\%

. Dividing by the selling price instead gives

125/625 = 20\%

, which is a different (and wrong) answer. The GRE always includes the wrong-denominator result as a distractor.

Recognition / When to Apply

Not every question with numbers is an arithmetic question. Use the table below to quickly identify which questions fall into the arithmetic domain and which technique to apply.

Question Stem Signal	Pattern	First Move
"greatest number of items..."	Optimization	Divide budget by cheapest price
"what is the total cost..."	Total computation	List all cost components, then sum
"what is the ratio of X to Y"	Ratio / percent	Find both quantities, simplify
"approximately what was..."	Estimation	Round aggressively, compute ballpark
"which is farthest from..."	Number line distance	Compute absolute differences
"profit as a percent of cost"	Multi-step word problem	Set up Profit = Revenue - Cost first
"least positive integer..."	Number theory	Write prime factorization
"rounded to the nearest tenth"	Rounding	Identify the digit at the target place, look right

The key is to read the question stem before looking at the answer choices. The phrasing tells you which pattern you are dealing with, which in turn dictates your approach. Once you have identified the pattern, the computation itself is typically straightforward — the difficulty lies in selecting the right method and avoiding the predictable traps.

Study Checklist

MC1 Arithmetic Mastery Checklist0/8 complete

Frequently Asked Questions

How many arithmetic questions appear on the GRE Quantitative section?

Arithmetic underlies roughly 25 to 30 percent of all GRE Quantitative Reasoning questions. You can expect to see arithmetic concepts tested across multiple question formats including Multiple Choice Select One, Quantitative Comparison, and Numeric Entry. Proficiency in percents, ratios, and number properties is essential for a competitive score.

What is the difference between "percent of" and "percent more than"?

"Percent of" means you multiply the base by the percentage directly. For example, 40 percent of 200 is 80. "Percent more than" means you add the percentage to the original: 40 percent more than 200 is 200 plus 80, which equals 280. The GRE regularly includes both values as answer choices to catch test-takers who confuse the two operations.

Should I memorize formulas for GRE arithmetic?

You should know a handful of core relationships rather than memorize dozens of formulas. The essential ones are: profit equals revenue minus cost, percent change equals (new minus old) divided by old times 100, and successive percent changes are computed by multiplying factors rather than adding percentages. Everything else on the GRE arithmetic domain follows from these building blocks.

How do I handle successive percentage changes on the GRE?

Convert each percentage change into a multiplication factor. A 25 percent increase becomes 1.25, a 10 percent decrease becomes 0.90, and a 30 percent discount becomes 0.70. Then multiply all factors together and apply the result to the original value. Never add or subtract the percentages directly, as this leads to wrong answers that the GRE deliberately includes among the choices.

What is the best way to maximize item count in a budget problem?

To maximize the number of items you can buy within a fixed budget, always purchase the cheapest items first. Divide the total budget by the lowest unit price and take the integer part. Do not average the prices of different item types, and do not try mixed combinations unless the question specifically requires a minimum of each type. The greedy approach — all cheap items — always yields the maximum count.