GRE Arithmetic Guide for Nepali Students

GRE Arithmetic Guide for Nepali Students explains the tested number properties, operations, fractions, decimals, exponents, roots, ratios, rates, percent, estimation and practical review methods. Use this guide to turn familiar school mathematics into accurate GRE decisions, not just longer calculations.

Information checked on 24 July 2026 against the current ETS Quantitative Reasoning overview, Math Review, official strategies and POWERPREP information. Confirm test details with ETS before test day.

Key facts at a glance

Understand the official arithmetic scope

ETS lists arithmetic as one of four GRE Quantitative content areas. It includes properties and types of integers, divisibility, factorisation, prime numbers, remainders, odd and even integers, arithmetic operations, exponents, roots, estimation, percent, ratio, rate, absolute value, the number line, decimal representation and number sequences.

The broader Quantitative measure uses high-school mathematics and statistics, generally no higher than a second algebra course. It does not require trigonometry, calculus or other higher mathematics. Arithmetic questions still demand careful reasoning because familiar concepts appear inside comparisons, word problems and data displays.

Start with integer language

Know the distinction among positive integers, negative integers, zero and non-integers. Zero is neither positive nor negative. A prime number is an integer greater than 1 with exactly two positive divisors, 1 and itself; therefore 1 is not prime.

Translate verbal conditions precisely. “Consecutive integers” differ by 1, consecutive even or odd integers differ by 2, and a multiple of a number can include zero unless the question adds a restriction. Write a small example to test your interpretation before applying a rule.

Use divisibility and factorisation efficiently

Prime factorisation reveals divisibility, common factors, common multiples and the number of divisor combinations. Break a positive integer into prime powers and use those powers rather than listing large sets of multiples.

For a greatest common factor, take the shared prime factors with the smaller exponents. For a least common multiple, take every required prime factor with the larger exponent. Verify the result against the words “greatest” and “least”; reversing these operations is a common avoidable error.

Reason with odd and even numbers

Parity rules can answer a question without full calculation. Even plus even and odd plus odd are even; even plus odd is odd. A product is odd only when every integer factor is odd. If any integer factor is even, the product is even.

Apply parity only when the values are integers. A variable described merely as a real number cannot automatically be labelled odd or even. Record restrictions before using a memorised rule.

Master remainder structure

When an integer n is divided by a positive integer d, write n = dq + r, where q is an integer and the remainder r satisfies 0 ≤ r < d. This structure prevents impossible remainders and clarifies repeated-pattern questions.

For powers or long sequences, look for a cycle of remainders instead of computing the entire value. Test enough early cases to establish the cycle, then map the requested exponent or position to that pattern.

Control signs and order of operations

Treat subtraction as addition of an opposite when signs become confusing. Apply grouping symbols first, then exponents, multiplication and division from left to right, followed by addition and subtraction from left to right.

A negative sign outside a square is not the same as a negative base inside parentheses. For example, -x² means the negative of x², while (-x)² is nonnegative. Rewrite ambiguous-looking expressions before calculating.

Work accurately with fractions

For addition or subtraction, create a common denominator. For multiplication, cancel common factors before multiplying. For division, multiply by the reciprocal of the divisor, while remembering that division by zero is undefined.

Compare positive fractions by using a common denominator, cross-products or distance from a benchmark such as one-half or 1. Check signs separately when negatives are involved, because multiplying an inequality comparison by a negative reverses direction.

Connect fractions, decimals and percent

Move among equivalent forms according to the task. A fraction may expose cancellation, a decimal may help estimate, and a percent may make a relative change clearer. Build fluency with common equivalents while retaining exact values when rounding could change an answer.

Percent means per hundred. Distinguish “x percent of y,” “x is what percent of y,” and “percent change from old to new.” For percent change, divide the change by the original value, not the new value.

Avoid the percent-change reversal trap

An increase followed by the same percentage decrease does not generally return to the starting value because the second percentage uses a different base. Model successive changes with multipliers: increase by p percent means multiply by 1 + p/100, while a decrease means multiply by 1 – p/100.

For reverse-percent questions, define the unknown original and write an equation. If a price after a 20 percent discount is known, the final price represents 80 percent of the original, not an amount from which you simply add 20 percent.

Use ratios and proportions with labels

A ratio compares quantities in a stated order. Keep labels attached, especially when units or groups differ. If the ratio of A to B is 3:5, write A = 3k and B = 5k when both values scale by a common factor.

Use a proportion only when the relationship is genuinely proportional. A fixed fee plus a per-unit charge is linear but not directly proportional because the total does not become zero when the number of units is zero.

Translate rates and units

A rate compares quantities with different units, such as kilometres per hour or rupees per kilogram. Write the units as part of the fraction and cancel them deliberately. This exposes inverted rates and conversion errors.

For average speed, divide total distance by total time. Do not automatically average two speeds, especially when the times or distances differ. Build a small distance-time table before selecting a shortcut.

Apply exponents correctly

When multiplying powers with the same nonzero base, add exponents; when dividing, subtract exponents; when raising a power to a power, multiply exponents. A zero exponent gives 1 for a nonzero base, and a negative exponent indicates a reciprocal.

Exponent rules require matching structures. You cannot distribute an exponent over a sum in the same way as over a product. Test a tempting rule with small numbers before trusting it.

Interpret roots and absolute value

The principal square root symbol represents the nonnegative square root. An equation such as x² = 9 has two solutions, but √9 is 3. Keep that distinction clear when solving and when simplifying expressions.

Absolute value measures distance from zero and is never negative. Translate |x| = a as two possibilities when a is positive. Translate |x – c| as the distance between x and c, which helps with equations and inequalities.

Estimate before using the calculator

The GRE provides a basic on-screen calculator for Quantitative Reasoning, but ETS says it supplements rather than replaces mathematical knowledge. Estimate the sign, magnitude and plausible range first, then use the calculator only when it improves efficiency.

Round strategically rather than randomly. If answer choices are far apart, a rough estimate may decide the problem. If choices are close, preserve accuracy and use an exact method.

Handle Quantitative Comparison arithmetic

For a Quantitative Comparison question, compare Quantity A and Quantity B under every stated condition. The four outcomes are A greater, B greater, equal or impossible to determine. One example can disprove a fixed relationship, but one example cannot prove a relationship for all allowed values.

Simplify both quantities, inspect restrictions and test boundary or sign cases. If variables are unrestricted, try positive, negative, zero and fractional values when permitted.

Use an arithmetic error log

Classify each miss: concept gap, translation error, sign mistake, denominator error, wrong percent base, unit mismatch, premature calculator use or incomplete case analysis. Record the shortest reliable correction.

Re-solve the question after a delay without viewing the answer. A correct second attempt matters only if you can explain the rule and identify why the original method failed.

Practise with official resources

Use the ETS Quantitative Reasoning overview to verify the current scope and question formats. The official GRE Math Review includes definitions, properties, examples and exercises across arithmetic, algebra, geometry and data analysis.

Begin with topic drills, then mix arithmetic with other Quantitative content and response formats. Use POWERPREP for current timing, navigation and review behaviour. Review correct guesses as seriously as incorrect answers.

Follow a seven-step problem routine

Read the question and response requirement; list given information and restrictions; define the target; estimate a range; choose a method; calculate with units; then test sign, scale and conditions. This routine is short enough for timed work and strong enough to prevent many careless errors.

Do not assume every question needs long computation. Factor, cancel, compare, estimate or test answer choices when those approaches are more direct.

Connect preparation with application planning

For graduate study planning, documents and destination guidance, visit MKS Education. For organised GRE learning and practice support, explore MKS Prep. Verify each university’s current GRE policy and score expectations directly.

Treat the GRE as one part of the application. Set a score goal from programme evidence, complete timed official practice and keep enough time for score reporting and document preparation.

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