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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. 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
Working Together - Add the Rates
Typical rate (speed) relations
Permutation
Arrangements with Constraints
2. Some population that typically increases by a common factor every time period.
Typical rate (speed) relations
Optimization
Population Problems
Simple Factorials
3. 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
Reforming Difficult Problems
Population Problems
Average Rate: RTD Problems
4. 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
Slot Method (for problems where certain choices are restricted)
Standard Deviation (SD)
Proportions
Entirely Unknown Sets
5. Put people or items into groups to maximize or minimize a characteristic in the group.
Equations for Exponential Growth or Decay
Grouping
Population Problems
Concrete values
6. For counting the possible number of ways of putting n distinct objects in order - if there are no restrictions - is n! (n factorial).
Typical time relations
Reforming Difficult Problems
Simple Factorials
Combinatorics
7. 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
Sample Multiple RTD Problems
Slot Method (for problems where certain choices are restricted)
The 1-x Probability Trick
Anagrams
8. Maximize or minimize a quantity by choosing optimal values.
Average Rate: RTD Problems
Multiple RTD Problems
Combination & Permutation Formulas
Optimization
9. 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
Rates & Work Problems
Probability
Multiple Arrangements
Multiple Ratios
10. 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
Slot Method (for problems where certain choices are restricted)
Ratios
Simple Factorials
Arrangements with Constraints
11. 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
Combinatorics & Probability
Simple Factorials
Multiple RTD Problems
Concrete values
12. 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
Prices & Quantities
Anagram Grids
Probability: Multiple Events
Multiple RTD Problems
13. Slower/faster - left... and met/arrived at
Basic Motion - The RTD Chart
Sample Multiple RTD Problems
Combinatorics & Probability
Typical time relations
14. 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
Combinatorics & Probability
Overlapping Sets & Algebraic Representation
Entirely Unknown Sets
Disguised Combinatorics
15. For problems with only two categories or decisions - use a double-set matrix: Rows correspond to the options for one DECISION - columns correspond to the options for the other DECISION. Last row and column contain totals. Bottom right corner has tota
Population Problems
Entirely Unknown Sets
Probability Trees
Overlapping Sets: Double-Set Matrix
16. 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
Multiple Arrangements
Averages: Evenly Spaced Sets
Computation problems
Disguised Combinatorics
17. 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' --
Sample Multiple RTD Problems
The 1-x Probability Trick
Combinatorics & Probability
Average Rate: RTD Problems
18. = 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
Optimization & Grouping
Entirely Unknown Sets
Proportions
19. 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
Multiple RTD Problems
Multiple Ratios
20. 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
Hidden Constraints
Multiple RTD Problems
Weighted Averages
21. 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
Multiple RTD Problems
Combinatorics & Probability
Average Rate: RTD Problems
3-Set Problems: Venn Diagrams
22. 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
Equations for Exponential Growth or Decay
Working Together - Add the Rates
Scheduling
Grouping
23. 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
Combinatorics
The Unknown Multiplier
Optimization & Grouping
Probability Trees
24. 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
Ratios
Probability Trees
The Unknown Multiplier
Population Problems
25. 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.
Multiple Arrangements
Shortcuts for Averages
Ratios
Use Charts to Organize Variables
26. 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
Use Charts to Organize Variables
Overlapping Sets & Percents
Translating Words Correctly
27. 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
Median
Rates & Work Problems
Averages
28. 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
Algebraic Translations
Prices & Quantities
Working Together - Add the Rates
Overlapping Sets & Percents
29. 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
Prices & Quantities
Averages
Grouping
30. Marked by 3 primary components: rate - time & distance or work. Rate x Time = Distance (RT=D) Rate x Time= Work (RT = W)
Main forms of rate problems
Simple ratio problems
Probability: Multiple Events
Rates & Work Problems
31. Scheduling: focus on the extreme possibilities (earliest/latest time slots). Read the problem carefully!
The Unknown Multiplier
Multiple RTD Problems
Proportions
Scheduling & Computation Problems
32. 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.
3-Set Problems: Venn Diagrams
Population Problems
Reforming Difficult Problems
Use a population chart
33. 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
Combinatorics
Basic Motion - The RTD Chart
Probability: Multiple Events
Weighted Averages
34. 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
Equations for Exponential Growth or Decay
Concrete values
Hidden Constraints
Slot Method (for problems where certain choices are restricted)
35. 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
Shortcuts for Averages
Multiple Arrangements
Overlapping Sets & Algebraic Representation
Use Charts to Organize Variables
36. 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
Overlapping Sets & Percents
Grouping
Simple Factorials
37. 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
Multiple Arrangements
Average Rate: RTD Problems
Proportions
Basic Work Problems
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
Main forms of rate problems
Simple Factorials
Hidden Constraints
Slot Method (for problems where certain choices are restricted)
39. Twice/half/n times as fast as - slower/faster - relative rates
Optimization
Probability Trees
Typical rate (speed) relations
Anagram Grids
40. 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
Typical rate (speed) relations
Sample Multiple RTD Problems
3-Set Problems: Venn Diagrams
Use Charts to Organize Variables
41. 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
Reforming Difficult Problems
Equations for Exponential Growth or Decay
Sample Multiple RTD Problems
Working Together - Add the Rates
42. The order a ratio is given in is vital. To avoid reversals - always write units on either the ratio or the variables.
Optimization
Working Together - Add the Rates
Proportions
Probability: Multiple Events
43. 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
Combinatorics & the Domino Effect
Median
Entirely Unknown Sets
Basic Motion - The RTD Chart
44. 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
Prices & Quantities
Median
The 1-x Probability Trick
Grouping
45. 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.
Multiple Arrangements
Slot Method (for problems where certain choices are restricted)
Simple ratio problems
Optimization & Grouping
46. 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
Grouping
Combinatorics
Arrangements with Constraints
Typical rate (speed) relations
47. 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.
Scheduling
Scheduling & Computation Problems
Use a population chart
Combinatorics & the Domino Effect
48. Difficult problems involve rates - times and distances for more than one trip or traveler - expand the RTD chart by adding rows for each trip.
Anagrams
Use a population chart
Multiple RTD Problems
Weighted Averages
49. 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
3-Set Problems: Venn Diagrams
Entirely Unknown Sets
Combinatorics & Probability
Translating Words Correctly
50. 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
Combinatorics & Probability
Permutation
The Unknown Multiplier
Optimization