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