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Test your basic knowledge |
GMAT Word Translations
Start Test
Study First
Subjects
:
gmat
,
reading-and-comprehension
Instructions:
Answer 50 questions in 15 minutes.
If you are not ready to take this test, you can
study here
.
Match each statement with the correct term.
Don't refresh. All questions and answers are randomly picked and ordered every time you load a test.
This is a study tool. The 3 wrong answers for each question are randomly chosen from answers to other questions. So, you might find at times the answers obvious, but you will see it re-enforces your understanding as you take the test each time.
1. Pay close attention to the wording of the problem to see if you need to use algebra to represent the unknowns.From the relationships in the table - set up an equation to solve for unknowns. With that information - fill in the rest of the double-set m
Hidden Constraints
Algebraic Translations
Entirely Unknown Sets
Overlapping Sets & Algebraic Representation
2. To combine ratios with common elements - multiply all of the ratios by the same number (a common multiple). Make the term you are working with the least common multiple of the current values.
Disguised Combinatorics
Multiple Ratios
Anagram Grids
Hidden Constraints
3. 1. Basic motion problems 2. Average rate problems 3. Simultaneous motion problems 4. Work problems 5. Population problems
Main forms of rate problems
Overlapping Sets & Algebraic Representation
Simple ratio problems
Translating Words Correctly
4. Multiply the probabilities of events in a sequence - taking earlier events into account. When you have a symmetrical problem with multiple equivalent cases - calculate the probability of one case (often using the domino effect rule above). Then multi
Simple Factorials
Equations for Exponential Growth or Decay
Optimization & Grouping
Combinatorics & the Domino Effect
5. = sum/# of terms If you know the average - use this formula: (average) x (# of terms) = (sum) - All that matters is the sum of the terms - not the individual terms. To keep track of two average formulas - set up an RTD-style table.
Averages
Main forms of rate problems
Scheduling
Arrangements with Constraints
6. 1. Assign variables - make up letters to represent unknown quantities to set up equations - choose meaningful letters - avoid subscripts - try to minimize the number of variables 2. Write equations - translate verbal relationships into math symbols.
Scheduling
Use Charts to Organize Variables
Grouping
Algebraic Translations
7. Combination: selection of items from a larger pool where the order doesn't matter. Number of r items chosen from a pool of n items: n!/(n-r)!*r! Permutation: selection of items from a larger pool where the order matters. n!/(n-r)!
Simple Factorials
Median
Multiple RTD Problems
Combination & Permutation Formulas
8. Counting the number of possibilities/ways you can arrange things.Fundamental Counting Principle: if you must make a number of separate decisions - then MULTIPLY the numbers of ways to make each individual decision to find the number of ways to make a
Rates & Work Problems
Combinatorics
Overlapping Sets: Double-Set Matrix
Disguised Combinatorics
9. If a probability problem seems to require extensive calculation - try to reformulate it in a way that either takes advantage of symmetry in the problem or groups several individual cases together at once.
The 1-x Probability Trick
Basic Motion - The RTD Chart
Reforming Difficult Problems
Optimization & Grouping
10. If you have to construct and manipulate completely abstract sets - use alphabetical order to make the sets a little more concrete. If the problem is complex - create a column chart. Each column is a number in the set. Put the columns in order with t
Entirely Unknown Sets
Translating Words Correctly
Main forms of rate problems
Overlapping Sets: Double-Set Matrix
11. For problems involving percents or fractions - use smart numbers and a double-set matrix to solve. For problems with percents - pick a total of 100. For problems with fractions - pick a common denominator for the total. You can only assign a number t
Probability: Multiple Events
Overlapping Sets & Percents
The Unknown Multiplier
Simple Factorials
12. Slower/faster - left... and met/arrived at
Typical rate (speed) relations
Typical time relations
Hidden Constraints
Optimization
13. Don't just add and divide! If something moves the same distance twice but at different rates - then the average rate will NEVER be the average of the two given rates. The average rate will be closer to the slower of the two rates. Find the total comb
Use a population chart
Simple ratio problems
Average Rate: RTD Problems
The Unknown Multiplier
14. Planning a timeline to coordinate events to a set of restrictions. Focus on the extreme scenarios: 1. Be aware of both explicit and hidden constraints.2. Choose the highest or lowest values of the variables. 3. Be very careful about rounding.
Disguised Combinatorics
The 1-x Probability Trick
Scheduling & Computation Problems
Scheduling
15. Be able to write word problems with two different types of equations: - relate the quantities or numbers of different goods - relate the total values of the goods. 1. Assign variables - try to use as few variables as possible. 2. Write equations - fo
Concrete values
Typical rate (speed) relations
Prices & Quantities
Weighted Averages
16. Will be closer to the number with the bigger weight. If the weights don't add to one - sum the weights and use that to divide in order to have a total weight of one. Weighted average = weight/sum of weights(data point) + weight/sum of weights(data po
Reforming Difficult Problems
Weighted Averages
Multiple Ratios
Computation problems
17. If X and Y are independent events - AND means multiply the probabilities. You will wind up with a smaller number - which indicates a lower probability of success. If X and Y are mutually exclusive - OR means add the probabilities. You will wind up wi
Probability: Multiple Events
Multiple RTD Problems
Permutation
Typical time relations
18. Determine the combined rate of all the workers working together: sum the individual working rates. If one agent is undoing the work of another - subtract their working rates. If a work problem involves time relations - then the calculations are just
Working Together - Add the Rates
Overlapping Sets: Double-Set Matrix
Slot Method (for problems where certain choices are restricted)
Simple ratio problems
19. For sets with an odd number of values - the median is the middle value when in order. For sets with an even number of values - the median is the average of the two middle values. You maybe able to determine a specific value for the median even if unk
Probability
Median
Concrete values
Anagrams
20. Avoid writing relationships backwards. Quickly check your translations with easy numbers. Write an unknown percent as a variable divided by 100. Translate bulk discounts and similar relationships carefully.
Proportions
Arrangements with Constraints
Translating Words Correctly
Permutation
21. Optimization: inversion between finding the min/max and the values givens typical. Be careful to round up or down appropriately. Grouping: determine the limiting factor on the number of complete groups. Think about the most or least evenly distribute
Optimization & Grouping
Overlapping Sets: Double-Set Matrix
Use Charts to Organize Variables
Probability
22. The numbers in the same row of an RTD table will always multiply across. The specifics of the problem determine which columns will add up into a total row. R x T = D 1. The kiss (or crash) ADD SAME ADD 2. the quarrel (away from) ADD SAME ADD 3. The c
Sample Multiple RTD Problems
Rates & Work Problems
Overlapping Sets & Percents
Average Rate: RTD Problems
23. Difficult problems involve rates - times and distances for more than one trip or traveler - expand the RTD chart by adding rows for each trip.
Prices & Quantities
Typical rate (speed) relations
Overlapping Sets & Algebraic Representation
Multiple RTD Problems
24. Can be solved with a proportion. 1. Set up a labeled proportion. 2. Cross-multiply to solve. Cancel factors out before multiplying to save time. Can cancel either vertically within a fraction or horizontally across the equals sign.
Grouping
Simple ratio problems
Multiple RTD Problems
Algebraic Translations
25. Make a chart when several quantities and multiple relationships. Ex: age problems - people in rows - times in columnsn 1. Assign variables - try to use 1 variable for simplicity. 2. Write equations - use leftover information/relationships to write eq
Grouping
3-Set Problems: Venn Diagrams
Ratios
Use Charts to Organize Variables
26. Use anagram grids to solve combinations with repetition. Set up an anagram grid to put unique items or people on the top row. Only the bottom row should have repeats. To count possible groups - divide the total factorial by two factorials: one for th
Probability Trees
Shortcuts for Averages
Anagram Grids
Sample Multiple RTD Problems
27. Some population that typically increases by a common factor every time period.
Entirely Unknown Sets
Sample Multiple RTD Problems
Weighted Averages
Population Problems
28. The order a ratio is given in is vital. To avoid reversals - always write units on either the ratio or the variables.
Anagram Grids
Proportions
The Unknown Multiplier
Equations for Exponential Growth or Decay
29. Make a table with a few rows with NOW in the middle row. Work forwards and backwards from NOW using the problem's information. Maybe pick a smart number for the starting point - choose a number that makes the math simple.
Combinatorics
Hidden Constraints
Use a population chart
Computation problems
30. A rearrangement of the letters in a word or phrase. Count the anagrams of a simple word with n letters by using n! When there are repeated items in a set - reduce the number of arrangements. The number of arrangements of a word is the factorial of th
Slot Method (for problems where certain choices are restricted)
Basic Work Problems
Averages: Evenly Spaced Sets
Anagrams
31. The average of consecutive integers is the middle term - same for any set with terms that are evenly spaced. The average is the middle term. If the set has two middle terms - take the average of the two middle numbers. To find the average (middle ter
Averages: Evenly Spaced Sets
Reforming Difficult Problems
Proportions
Optimization
32. Maximize or minimize a quantity by choosing optimal values.
Computation problems
Optimization
Rates & Work Problems
Simple Factorials
33. Venn diagrams should ONLY be used for problems that involve 3 sets with only 2 choices per set. Work from the inside out when filling in. When filling in each outer level - remember to subtract out the members in the inner levels. To determine the to
Arrangements with Constraints
3-Set Problems: Venn Diagrams
Proportions
Typical rate (speed) relations
34. Marked by 3 primary components: rate - time & distance or work. Rate x Time = Distance (RT=D) Rate x Time= Work (RT = W)
Rates & Work Problems
Sample Multiple RTD Problems
Hidden Constraints
Equations for Exponential Growth or Decay
35. I - or interval - amount of time given for the quantity to grow or decay S - or starting value - size of the population at time zero t - or time - is the variable (make sure all time units are the same) x - growth or decay factor - Population = S*x^(
Typical rate (speed) relations
Equations for Exponential Growth or Decay
Main forms of rate problems
Anagram Grids
36. In certain types of OR problems - the probability of the desired event NOT happening may be easier to find. If on a problem - 'success' contains multiple possibilities -- especially if the wording contains phrases such as 'at least' and 'at most' --
The 1-x Probability Trick
Entirely Unknown Sets
Averages
Slot Method (for problems where certain choices are restricted)
37. If a problem has unusual constraints - try counting arrangements without constraints first. Then subtract the forbidden arrangements. Glue Method: for problems in which items or people must be next to each other - pretend that the items 'stuck togeth
Average Rate: RTD Problems
Arrangements with Constraints
Probability: Multiple Events
Ratios
38. 1. Draw empty slots corresponding to each of the choices you have to make. 2. Fill in each slot with the number of options for that slot. Choose the most restricted opt ins first. 3. Multiply the numbers in the slots to find the total number of combi
Slot Method (for problems where certain choices are restricted)
Working Together - Add the Rates
Use a population chart
Basic Motion - The RTD Chart
39. Quantity that expresses the chance - or likelihood - of an event. To find a probability - you need to know the total number of possibilities and the number of successful scenarios. All outcomes must be equally likely. Use a counting tree to find the
Multiple RTD Problems
Ratios
Probability
Anagrams
40. For complicated ratio problems - the unknown multiplier technique is useful. Represent ratios with some unknown number/variable to reduce the number of variables and make the algebra easier. You can only use it once per problem. You should use it whe
The Unknown Multiplier
Disguised Combinatorics
Simple ratio problems
Use a population chart
41. For counting the possible number of ways of putting n distinct objects in order - if there are no restrictions - is n! (n factorial).
Simple Factorials
Probability: Multiple Events
Overlapping Sets: Double-Set Matrix
Scheduling
42. In some probability problems - both the 'desired' possibilities and the total possibilities require counting. Use combinatorial methods to calculate the numbers of possibilities. After finding the numbers - set up the probability as a fraction - 'win
Combinatorics & Probability
Algebraic Translations
Median
Use a population chart
43. Basic motion problems involve rate - time and distance. Rate = ratio of distance and time Time = a unit of time Distance = a unit of distance - Use an RTD chart to solve. Fill in 2 of the variables then use the RT=D formula to solve.
Grouping
Basic Motion - The RTD Chart
Probability
Simple Factorials
44. Changes to Mean: Change in mean = New term - Old mean / New number of terms -- Using residuals: Residual = Data point - Mean - Keep track of signs of residuals. The residuals sum to zero in any set. All residuals cancel out.
Slot Method (for problems where certain choices are restricted)
Equations for Exponential Growth or Decay
Use a population chart
Shortcuts for Averages
45. If a GMAT problem requires you to choose two or more sets of items from separate pools - count the arrangements separately. Then multiply the numbers of possibilities for each step.
Multiple Arrangements
Scheduling
Simple ratio problems
3-Set Problems: Venn Diagrams
46. If switching elements in a chosen set creates a different set - it is a ______________. There are usually fewer combinations than permutations.
Permutation
Scheduling & Computation Problems
Averages: Evenly Spaced Sets
Shortcuts for Averages
47. You don't need ____________ to find the weights. Having the ratios of the weights will allow you to find the weighted average. Write the ratio as a fraction; use the numerator and denominator as weights. If you are finding a weighted average of rates
Combination & Permutation Formulas
Probability: Multiple Events
Concrete values
Multiple Ratios
48. Check the problem to see if the are any implied constraints to variables like whole numbers. You can solve a data sufficiency question with little information if whole numbers are involved. You can use a table to generate - organize - and eliminate i
Combinatorics & Probability
Use Charts to Organize Variables
3-Set Problems: Venn Diagrams
Hidden Constraints
49. Twice/half/n times as fast as - slower/faster - relative rates
Multiple Arrangements
Typical rate (speed) relations
Overlapping Sets & Percents
Combination & Permutation Formulas
50. Contains no variables; simply plug and chug. 1. Take careful inventory of qtys - numbers and units. 2. Use math techniques and tricks to solve; assign variables. 3. Draw diagrams - tables and charts to organize the information. 4. Read the problem ca
Overlapping Sets & Percents
Basic Work Problems
Computation problems
Multiple Arrangements