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Test your basic knowledge 
GMAT Word Translations
Start Test
Study First
Subjects
:
gmat
,
readingandcomprehension
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 reenforces your understanding as you take the test each time.
1. 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!/(nr)!*r! Permutation: selection of items from a larger pool where the order matters. n!/(nr)!
Combination & Permutation Formulas
Optimization & Grouping
Probability Trees
Combinatorics & the Domino Effect
2. 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
Basic Work Problems
Disguised Combinatorics
Prices & Quantities
Average Rate: RTD Problems
3. Can be solved with a proportion. 1. Set up a labeled proportion. 2. Crossmultiply to solve. Cancel factors out before multiplying to save time. Can cancel either vertically within a fraction or horizontally across the equals sign.
Combinatorics & the Domino Effect
Overlapping Sets & Percents
Ratios
Simple ratio problems
4. 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
Overlapping Sets & Algebraic Representation
Averages: Evenly Spaced Sets
Use a population chart
Weighted Averages
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' 
Optimization & Grouping
The 1x Probability Trick
Average Rate: RTD Problems
Weighted Averages
6. 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
The 1x Probability Trick
Reforming Difficult Problems
Median
Probability: Multiple Events
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.
Multiple RTD Problems
Optimization
Grouping
Median
8. 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 doubleset m
Sample Multiple RTD Problems
Disguised Combinatorics
Overlapping Sets & Algebraic Representation
The 1x Probability Trick
9. 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
Reforming Difficult Problems
Basic Motion  The RTD Chart
Computation problems
Disguised Combinatorics
10. 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
Combinatorics
Ratios
Proportions
Probability Trees
11. 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.
Algebraic Translations
Average Rate: RTD Problems
Basic Motion  The RTD Chart
Combinatorics
12. 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
Averages: Evenly Spaced Sets
Shortcuts for Averages
Concrete values
13. 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.
Weighted Averages
Slot Method (for problems where certain choices are restricted)
Reforming Difficult Problems
Population Problems
14. 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
Probability
Slot Method (for problems where certain choices are restricted)
Combinatorics & Probability
Typical time relations
15. The order a ratio is given in is vital. To avoid reversals  always write units on either the ratio or the variables.
Overlapping Sets: DoubleSet Matrix
Ratios
Proportions
Combinatorics & Probability
16. If switching elements in a chosen set creates a different set  it is a ______________. There are usually fewer combinations than permutations.
Combination & Permutation Formulas
Scheduling
Permutation
Ratios
17. 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
Equations for Exponential Growth or Decay
Multiple Ratios
Standard Deviation (SD)
Ratios
18. 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
Averages: Evenly Spaced Sets
Arrangements with Constraints
Multiple Ratios
19. 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.
Typical time relations
Combinatorics & the Domino Effect
Anagram Grids
Multiple Arrangements
20. 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 Arrangements
Average Rate: RTD Problems
Grouping
Use Charts to Organize Variables
21. 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.
Computation problems
Average Rate: RTD Problems
3Set Problems: Venn Diagrams
Shortcuts for Averages
22. 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
Equations for Exponential Growth or Decay
Combinatorics & the Domino Effect
Computation problems
23. Maximize or minimize a quantity by choosing optimal values.
Grouping
Optimization
Equations for Exponential Growth or Decay
Standard Deviation (SD)
24. 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
Hidden Constraints
Rates & Work Problems
Permutation
Main forms of rate problems
25. 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^(
Basic Work Problems
Combinatorics & Probability
Equations for Exponential Growth or Decay
Entirely Unknown Sets
26. 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
3Set Problems: Venn Diagrams
Combinatorics & the Domino Effect
Simple Factorials
Combination & Permutation Formulas
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
Multiple RTD Problems
Optimization
Overlapping Sets & Algebraic Representation
28. 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 partpart relationship or partwhole. Cannot find the qu
Scheduling
Probability
Entirely Unknown Sets
Ratios
29. 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
Shortcuts for Averages
Typical time relations
Use Charts to Organize Variables
Grouping
30. 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
Multiple RTD Problems
Permutation
Concrete values
Slot Method (for problems where certain choices are restricted)
31. 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
Population Problems
Slot Method (for problems where certain choices are restricted)
Concrete values
Overlapping Sets & Algebraic Representation
32. 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
The Unknown Multiplier
Probability: Multiple Events
Combinatorics & the Domino Effect
33. 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.
Entirely Unknown Sets
Sample Multiple RTD Problems
Shortcuts for Averages
Multiple Ratios
34. = 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 RTDstyle table.
Sample Multiple RTD Problems
Probability
Probability: Multiple Events
Averages
35. 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
Probability: Multiple Events
Prices & Quantities
Entirely Unknown Sets
Shortcuts for Averages
36. 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
Probability Trees
Anagram Grids
Probability: Multiple Events
Simple ratio problems
37. 1. Basic motion problems 2. Average rate problems 3. Simultaneous motion problems 4. Work problems 5. Population problems
Population Problems
Probability Trees
Ratios
Main forms of rate problems
38. For counting the possible number of ways of putting n distinct objects in order  if there are no restrictions  is n! (n factorial).
The Unknown Multiplier
Standard Deviation (SD)
Simple Factorials
Combinatorics & the Domino Effect
39. 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
Combinatorics & Probability
Probability Trees
Anagrams
40. Slower/faster  left... and met/arrived at
Combinatorics
Typical time relations
The 1x Probability Trick
Permutation
41. 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.
Shortcuts for Averages
Proportions
Basic Motion  The RTD Chart
Scheduling
42. Twice/half/n times as fast as  slower/faster  relative rates
Computation problems
Typical rate (speed) relations
Overlapping Sets & Algebraic Representation
Combination & Permutation Formulas
43. 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
The Unknown Multiplier
Arrangements with Constraints
Use a population chart
Basic Work Problems
44. 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
Grouping
Computation problems
Anagram Grids
Anagrams
45. 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
Anagrams
Concrete values
Weighted Averages
Ratios
46. Scheduling: focus on the extreme possibilities (earliest/latest time slots). Read the problem carefully!
The 1x Probability Trick
Scheduling & Computation Problems
Average Rate: RTD Problems
Disguised Combinatorics
47. 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
Use a population chart
Prices & Quantities
Sample Multiple RTD Problems
Averages
48. 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
The 1x Probability Trick
The Unknown Multiplier
Standard Deviation (SD)
Weighted Averages
49. For problems with only two categories or decisions  use a doubleset 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
Algebraic Translations
Sample Multiple RTD Problems
Averages
Overlapping Sets: DoubleSet Matrix
50. Marked by 3 primary components: rate  time & distance or work. Rate x Time = Distance (RT=D) Rate x Time= Work (RT = W)
Simple Factorials
Translating Words Correctly
Probability
Rates & Work Problems