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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. 1. Basic motion problems 2. Average rate problems 3. Simultaneous motion problems 4. Work problems 5. Population problems
Rates & Work Problems
Main forms of rate problems
Slot Method (for problems where certain choices are restricted)
Anagrams
2. Many word problems with 'how many' are combinatorics. Many combinatorics masquerade as probability problems. Looking for analogies to known problem types will help find a viable solution. Break down complicated counting problems into separate decisio
Shortcuts for Averages
Main forms of rate problems
Disguised Combinatorics
Algebraic Translations
3. 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.
Shortcuts for Averages
Combination & Permutation Formulas
Proportions
Basic Motion - The RTD Chart
4. 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
Anagram Grids
Optimization
Disguised Combinatorics
5. Involve time - rate and work.- work: number of jobs completed or items produced - time: time spent working - rate: ratio of work to time - amount completed in one time unit Often have to calculate the work rate. Always express as jobs per unit of tim
3-Set Problems: Venn Diagrams
Simple ratio problems
Probability Trees
Basic Work Problems
6. 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
Use Charts to Organize Variables
Averages
Arrangements with Constraints
Shortcuts for Averages
7. Difficult problems involve rates - times and distances for more than one trip or traveler - expand the RTD chart by adding rows for each trip.
Scheduling
The 1-x Probability Trick
Multiple RTD Problems
Main forms of rate problems
8. 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
Grouping
3-Set Problems: Venn Diagrams
Concrete values
Averages: Evenly Spaced Sets
9. 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
Overlapping Sets & Algebraic Representation
Multiple Arrangements
Ratios
Arrangements with Constraints
10. Put people or items into groups to maximize or minimize a characteristic in the group.
Grouping
Rates & Work Problems
Typical time relations
Overlapping Sets & Percents
11. 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
Use Charts to Organize Variables
Probability: Multiple Events
Arrangements with Constraints
Multiple RTD Problems
12. 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
Ratios
Standard Deviation (SD)
Concrete values
Probability
13. 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
Entirely Unknown Sets
3-Set Problems: Venn Diagrams
Combinatorics
Average Rate: RTD Problems
14. Twice/half/n times as fast as - slower/faster - relative rates
Overlapping Sets & Percents
Population Problems
Equations for Exponential Growth or Decay
Typical rate (speed) relations
15. 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
The Unknown Multiplier
Population Problems
Use a population chart
Anagrams
16. 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
Concrete values
Weighted Averages
Scheduling
Anagram Grids
17. Maximize or minimize a quantity by choosing optimal values.
The Unknown Multiplier
Combinatorics & the Domino Effect
Optimization
Overlapping Sets & Percents
18. 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
Median
Use a population chart
Main forms of rate problems
Typical rate (speed) relations
19. 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
3-Set Problems: Venn Diagrams
Shortcuts for Averages
Combination & Permutation Formulas
20. 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
Simple Factorials
3-Set Problems: Venn Diagrams
Use Charts to Organize Variables
Combinatorics & Probability
21. Scheduling: focus on the extreme possibilities (earliest/latest time slots). Read the problem carefully!
Algebraic Translations
The 1-x Probability Trick
Equations for Exponential Growth or Decay
Scheduling & Computation Problems
22. 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^(
Equations for Exponential Growth or Decay
The 1-x Probability Trick
Probability Trees
Averages
23. The order a ratio is given in is vital. To avoid reversals - always write units on either the ratio or the variables.
Averages
Proportions
Multiple Arrangements
Combinatorics & Probability
24. 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' --
Multiple Arrangements
Use a population chart
Rates & Work Problems
The 1-x Probability Trick
25. To keep track of branching possibilities and 'winning scenarios': label each branch and input the probabilities - on the second set of branches - input the probabilities AS IF the first pick was made - remember the domino effect! - compute the probab
Average Rate: RTD Problems
Probability Trees
Combinatorics & Probability
Entirely Unknown Sets
26. Some population that typically increases by a common factor every time period.
Population Problems
Combinatorics & the Domino Effect
Multiple RTD Problems
Combinatorics
27. 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
Reforming Difficult Problems
Translating Words Correctly
Entirely Unknown Sets
The Unknown Multiplier
28. If switching elements in a chosen set creates a different set - it is a ______________. There are usually fewer combinations than permutations.
Combinatorics & the Domino Effect
Permutation
Averages
Equations for Exponential Growth or Decay
29. 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
Average Rate: RTD Problems
Weighted Averages
Overlapping Sets & Percents
Averages: Evenly Spaced Sets
30. 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.
Reforming Difficult Problems
Basic Work Problems
Typical time relations
Anagrams
31. 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
Disguised Combinatorics
The 1-x Probability Trick
Typical rate (speed) relations
32. 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
Combinatorics & the Domino Effect
Permutation
Main forms of rate problems
Disguised Combinatorics
33. 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
Basic Work Problems
Combinatorics
Overlapping Sets & Percents
3-Set Problems: Venn Diagrams
34. 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.
Simple ratio problems
Rates & Work Problems
Basic Motion - The RTD Chart
Main forms of rate problems
35. Express a relationship between two or more quantities. - the relationship they express is division. Can be expressed with the word 'to' - using a colon - or by writing a fraction. Can express a part-part relationship or part-whole. Cannot find the qu
The 1-x Probability Trick
Averages: Evenly Spaced Sets
Proportions
Ratios
36. 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
Average Rate: RTD Problems
Simple ratio problems
Overlapping Sets & Percents
Hidden Constraints
37. Indicates how far from the average data points typically fall. A small SD indicates a set is clustered closely around the average while a large SD indicates the set is spread out widely. You will not need to calculate an exact SD. GMAT questions invo
Standard Deviation (SD)
Probability
Sample Multiple RTD Problems
Slot Method (for problems where certain choices are restricted)
38. 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
Hidden Constraints
Probability Trees
Probability: Multiple Events
Typical rate (speed) relations
39. 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
Probability: Multiple Events
Combination & Permutation Formulas
Multiple Arrangements
Prices & Quantities
40. 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
3-Set Problems: Venn Diagrams
Weighted Averages
Concrete values
Typical time relations
41. 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
Typical time relations
Arrangements with Constraints
Concrete values
Averages
42. 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
Grouping
Sample Multiple RTD Problems
Use Charts to Organize Variables
Basic Motion - The RTD Chart
43. 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
Multiple Arrangements
Computation problems
Hidden Constraints
Multiple Ratios
44. 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)!
Combination & Permutation Formulas
Multiple Arrangements
Average Rate: RTD Problems
Optimization & Grouping
45. 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
Scheduling & Computation Problems
Entirely Unknown Sets
3-Set Problems: Venn Diagrams
Grouping
46. 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.
Hidden Constraints
Multiple Ratios
Optimization
Disguised Combinatorics
47. 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
Computation problems
Standard Deviation (SD)
Scheduling
The 1-x Probability Trick
48. 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.
Entirely Unknown Sets
Ratios
Averages: Evenly Spaced Sets
Translating Words Correctly
49. 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
Scheduling
Probability
Optimization & Grouping
Multiple Ratios
50. 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.
Use a population chart
Multiple RTD Problems
Optimization
Permutation