Word translations
62 flashcards covering Word translations for the GMAT Quantitative section.
Word translations in the GMAT Quantitative section refer to the process of converting everyday language descriptions into mathematical equations or expressions. For example, phrases like "twice as many" might translate to "2x" in an equation, helping you model real-world scenarios such as costs, rates, or mixtures. This skill is essential because many problems disguise math concepts in words, requiring you to break down and accurately represent the information numerically.
On the GMAT, word translations appear in problem-solving and data sufficiency questions, often testing algebra, percentages, or ratios. Common traps include misinterpreting keywords—such as confusing "at least" with "exactly"—which can lead to incorrect setups. Focus on identifying key phrases, practicing logical translation, and checking for constraints to avoid errors. A solid grasp here boosts your accuracy on timed questions.
Always underline key words in the problem before translating.
Terms (62)
- 01
Equals in word problems
In word problems, the word 'is' or 'equals' typically indicates an equality, meaning the quantities on both sides are the same, which translates to an equation like x = 5.
- 02
Sum keywords
Words like 'sum,' 'total,' or 'added to' indicate addition, so they translate to plus signs in equations, such as turning 'the sum of a and b' into a + b.
- 03
Difference keywords
Terms such as 'difference,' 'less than,' or 'subtracted from' signify subtraction, translating to minus signs, like '5 less than x' becoming x - 5.
- 04
Product keywords
Phrases like 'product,' 'times,' or 'multiplied by' mean multiplication, so 'the product of x and y' becomes x y in an equation.
- 05
Quotient keywords
Words such as 'quotient,' 'divided by,' or 'per' indicate division, turning 'the quotient of a and b' into a / b.
- 06
Ratio in word problems
A ratio describes a comparison of two quantities, often written as a fraction or with a colon, like 'the ratio of a to b' translating to a:b or a/b.
- 07
Percentage as a fraction
Percentages in word problems are fractions out of 100, so '20% of x' translates to (20/100) x or 0.20x.
- 08
Increase and decrease
An increase means adding a percentage or amount, while a decrease means subtracting it, such as '10% increase in x' becoming x + 0.10x.
- 09
Average formula
The average of a set of numbers is the sum divided by the count, so 'the average of three numbers' translates to (number1 + number2 + number3) / 3.
- 10
Age problems setup
In age problems, current ages are variables, and future or past ages involve addition or subtraction of years, like 'in 5 years, Alice will be twice Bob's age' becoming A + 5 = 2(B + 5).
- 11
Work rate translation
Work rates describe how much of a task is completed per unit time, so 'A can paint a house in 4 hours' translates to A's rate as 1/4 houses per hour.
- 12
Pipes filling tanks
For pipes problems, rates of filling or emptying are combined, such as two pipes filling a tank at 1/2 and 1/3 per hour, translating to a combined rate of 1/2 + 1/3 per hour.
- 13
Distance formula
Distance in word problems is speed multiplied by time, so 'a car travels at 60 mph for 2 hours' translates to distance = 60 2 miles.
- 14
Speed, time, and distance
These are related by the formula distance = speed × time, so phrases like 'how long to travel 100 miles at 50 mph' translate to time = distance / speed.
- 15
Mixture problems
Mixture problems involve combining solutions with different concentrations, translating to equations like total amount = amount1 + amount2 and total concentration = (amount1 concentration1 + amount2 concentration2) / total amount.
- 16
Alligation method
Alligation simplifies mixture problems by finding the ratio of ingredients based on their concentrations, such as mixing a 10% solution with a 20% solution to get 15%.
- 17
Simple interest formula
Simple interest is calculated as principal × rate × time, so 'interest on $100 at 5% for 2 years' translates to interest = 100 × 0.05 × 2.
- 18
Compound interest
Compound interest involves repeated multiplication, like 'principal grows at 5% annually for 2 years' translating to principal × (1 + 0.05)^2.
- 19
Profit and loss
Profit is selling price minus cost price, and loss is cost price minus selling price, so 'sold for $150 after buying for $100' translates to profit = 150 - 100.
- 20
Discount and markup
Discount reduces the original price by a percentage, while markup increases cost price, such as '20% discount on $50' translating to new price = 50 - (0.20 × 50).
- 21
Sets and Venn diagrams
Sets in word problems represent groups with unions and intersections, like 'number in A or B' translating to |A ∪ B| = |A| + |B| - |A ∩ B|.
- 22
Probability events
Probability from words is favorable outcomes divided by total outcomes, so 'chance of drawing a red card from a deck' translates to number of red cards / total cards.
- 23
Permutations from words
Permutations arrange items in order, translating phrases like 'arranging 3 out of 5 items' to 5P3 = 5! / (5-3)!.
- 24
Combinations from words
Combinations select items without order, so 'choosing 2 from 4' becomes 4C2 = 4! / (2! × (4-2)!).
- 25
Area from descriptions
Geometric areas are calculated from word descriptions, like 'rectangle with length 5 and width 3' translating to area = 5 × 3 square units.
- 26
Volume from words
Volume of solids like cubes or cylinders is derived from dimensions, such as 'cube with side 4' becoming volume = 4^3 cubic units.
- 27
Inequality keywords
Words like 'greater than' or 'at least' translate to inequality symbols, such as 'x is at least 5' becoming x ≥ 5.
- 28
Absolute value phrases
Absolute value represents distance from zero, so 'the absolute value of x is 3' translates to |x| = 3, meaning x = 3 or x = -3.
- 29
Quadratic equations from words
Word problems leading to quadratics involve scenarios like areas or projectiles, translating to equations like x^2 - 5x + 6 = 0.
- 30
Systems of equations
Multiple variables from words form a system, such as 'twice A plus B is 10, and A minus B is 2' translating to 2A + B = 10 and A - B = 2.
- 31
Functions defined verbally
A function from words assigns outputs to inputs, like 'f(x) is x squared plus 1' translating to f(x) = x^2 + 1.
- 32
Arithmetic sequences
An arithmetic sequence has a constant difference, so 'sequence starting at 2 with common difference 3' translates to 2, 5, 8, etc.
- 33
Geometric sequences
A geometric sequence has a constant ratio, like 'sequence starting at 3 with ratio 2' becoming 3, 6, 12, etc.
- 34
Exponential growth
Exponential growth multiplies by a factor, such as 'population doubles every year' translating to P = P0 × 2^t.
- 35
Units and conversion
Word problems require converting units, like 'convert 10 kilometers to miles' using the factor 1 km = 0.621 miles.
- 36
Time and work problems
These involve rates over time, such as 'A and B together complete a job in 6 hours' translating to (A's rate + B's rate) × 6 = 1 job.
- 37
Boats and streams
Boat speeds in still water minus or plus current speed, like 'boat speed 10 mph, current 2 mph' translating to downstream speed = 10 + 2.
- 38
Trains and platforms
Train problems add lengths and speeds, such as 'train A overtakes train B' translating to relative speed equations.
- 39
Shadow problems
These use similar triangles for heights and shadows, like 'object height h, shadow length s, angle theta' translating to tan(theta) = h/s.
- 40
Clock angles
Clock problems calculate angles between hands, such as 'angle at 3:00' translating to 90 degrees between hour and minute hands.
- 41
Coin problems
These set up equations for total value, like '5 dimes and 3 quarters total $1.25' becoming 0.105 + 0.253 = 1.25.
- 42
Digit problems
Digit sums or products form equations, such as 'a two-digit number where tens digit is x and units is y' translating to 10x + y.
- 43
Number properties from words
Properties like even, odd, or prime are translated, such as 'an even number greater than 4' becoming 2k where k > 2.
- 44
Even and odd translations
Even numbers are divisible by 2, odd are not, so 'sum of two evens' translates to even result.
- 45
Prime numbers in context
A prime is a number greater than 1 with no divisors other than 1 and itself, like 'find primes less than 10' translating to 2, 3, 5, 7.
- 46
Divisibility rules
Rules like a number is divisible by 3 if the sum of digits is, translating phrases like 'divisible by 9' to sum of digits divisible by 9.
- 47
Remainders in words
Remainders from division are expressed as modulo, such as 'when 10 is divided by 3, remainder is 1' translating to 10 mod 3 = 1.
- 48
Modular arithmetic basics
Modular arithmetic deals with remainders, like 'x congruent to 2 mod 5' meaning x leaves a remainder of 2 when divided by 5.
- 49
Series sums
The sum of a series is the total of its terms, such as 'sum of first n natural numbers' translating to n(n+1)/2.
- 50
Coordinate geometry from words
Points and lines from descriptions, like 'point at (2,3)' translating to plotting on a graph.
- 51
Slope from words
Slope is rise over run, so 'line rising 3 units for every 4 units right' translates to slope = 3/4.
- 52
Equations of lines
Lines from points or slopes, such as 'line through (1,2) with slope 3' becoming y - 2 = 3(x - 1).
- 53
Circles from words
A circle's equation from center and radius, like 'circle with center (0,0) and radius 5' translating to x^2 + y^2 = 25.
- 54
Triangles: Pythagoras
In right triangles, a^2 + b^2 = c^2, so 'legs 3 and 4' translates to hypotenuse sqrt(9 + 16) = 5.
- 55
Area and perimeter
For shapes, area is the enclosed space and perimeter the boundary, like 'square with side 4' translating to area = 16, perimeter = 16.
- 56
Data sufficiency setup
In data sufficiency, statements provide information to solve equations from words, determining if they're sufficient individually or together.
- 57
Value questions
These ask for a specific value, translating word problems into equations to find exact numbers.
- 58
Yes/No questions
These require determining if a statement is true, translating words into inequalities or conditions to verify.
- 59
Common traps in translations
Traps include misinterpreting keywords, like confusing 'and' with 'or' in sets, leading to incorrect equations.
- 60
Strategy for word problems
Define variables for unknowns, translate words to equations, and solve step by step to ensure accuracy.
- 61
Variables in context
Variables represent unknowns in word problems, such as letting x be the number of items to find a relationship.
- 62
Constants in equations
Constants are fixed values in word problems, like 'a fixed cost of $10' that doesn't change with variables.