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MGMAT Flashcards

1
Q

What is the Algebraic Translation strategy

A
  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.
    - book 4, pg. 14
  3. Solve the equations.
  4. Answer the right question.
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2
Q

4 Tips for Translating Words Correctly

A

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.

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3
Q

When should you use charts to organize variables

A

Make a chart when several quantities and multiple relationships.
Ex: age problems - people in rows, times in columns

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4
Q

How to use charts to organize variables

A
  1. Assign variables.
    - try to use 1 variable for simplicity.
  2. Write equations.
    - use leftover information/relationships to write equations.
  3. Solve the equations.
  4. Answer the right questions.
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5
Q

In a typical Price_quality problem, what are the 2 relatiionships

A

1) the quantities sum to a total AND 2) the monetary values sum to a total.

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6
Q

How to go about solving Prices & Quantities problems

A

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.
    - for every X number of variables assigned, write X-1 equations.
    - columns in a table = price, qty, total value
    - rows = types of items, total
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7
Q

When a variable indicates how many objects there are, it must be WHAT kind of number

A

MUST be a WHOLE number

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8
Q

You can solve a data sufficiency question with little information if

A

whole numbers are involved.

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9
Q

You can use a table to generate, organize, and eliminate information when there are WHAT numbers.

A

WHOLE numbers.

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10
Q

POSITIVE CONSTRAINTS =

A

POSSIBLE ALGEBRA

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11
Q

Rates & Work Problems are marked by what 3 primary components

A

rate, time & distance or work.

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12
Q

Rate x Time =

A

Distance (RT=D)

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13
Q

Rate x Time=

A

Work (RT = W)

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14
Q

Five main forms of rate problems:

A
  1. Basic motion problems
  2. Average rate problems
  3. Simultaneous motion problems
  4. Work problems
  5. Population problems
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15
Q

Basic motion problems involve

A

rate, time and distance.

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16
Q

D = R T

A 
Rate = ratio of distance and time
Time = a unit of time
Distance = a unit of distance
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17
Q

Difficult problems involve rates, times and distances for

A

more than one trip or traveler.

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18
Q

Solve multiple RTD problems by…

A
  • expanding the RTD chart by adding rows for each trip.
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19
Q

Typical rate (speed) relations:

A
  • twice/half/n times as fast as
  • slower/faster
  • relative rates
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20
Q

Typical time relations:

A
  • slower/faster

- left… and met/arrived a

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21
Q

Sample Multiple RTD Problems

A

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 chase. SUBT SAME SUBT
  4. the round trip VARIES ADD ADD
  5. following footsteps VAR VAR SAME
  6. second-guessing (same person) VAR VAR SAME

When using variables, use them for R or T to make math easier.

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22
Q

If something moves the same distance twice but at different rates, then the average rate will ALWAYS-SOMETIMES-OR NEVER be the average of the two given rates.

A

NEVER

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23
Q

On Average RTD Problems,

A

Find the total combined time and the total combined distance. Find the average rate from these totals.

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24
Q

Basic Work Problems

A

Involve time, rate and work.

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25
Q

In basic work problems, Work stands for

A

work: number of jobs completed or items produced

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26
Q

In basic work problems, TIME stands for

A
  • time: time spent working
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27
Q

In basic work problems, RATE stands for

A
  • rate: ratio of work to time, amount completed in one time unit
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28
Q

Always express as jobs per unit of time, not as

A

time per job.

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29
Q

how to Determine the combined rate of all the workers working together

A

sum the individual working rates.

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30
Q

What do If one agent is undoing the work of another,

A

subtract their working rates

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31
Q

If a work problem involves time relations, then the calculations are just like

A

distance problems.

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32
Q

What happens in Population problems

A

Some population that typically increases by a common factor every time period.

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33
Q

What to do with a population problem

A

Use a population chart:
Make a table with a few rows with NOW in the middle row. Work forwards and backwards from NOW using the problem’s information.

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34
Q

what number should you pick for the starting point in a populaton problem

A

Maybe pick a smart number for the starting point - choose a number that makes the math simple.

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35
Q

A ratio expresses WHAT

A

Express a relationship between two or more quantities.

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36
Q

A relationship a RATIO expresses

A

division

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37
Q

RATIOs Can be expressed with the word “to”, using a WHAT, or by writing a WHAT

A

using a colon, or by writing a fraction.

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38
Q

Ratios can express a ___-_____ relationship or ___-____

A

part-part relationship or part-whole.

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39
Q

Can you find the quantity of each item from a ratio

A

Cannot find the quantity of each item from a ratio, but if 2 quantities have a constant ratio they are in direct proportion to each other.

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40
Q

Simple ratio problems can be solved with

A

a proportion.

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41
Q

How to solve a simple ratio problem with a proportion

A

a proportion.

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42
Q

Cancel Tips

A

Cancel factors out before multiplying to save time. Can cancel either vertically within a fraction or horizontally across the equals sign.

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43
Q

Unknown Multiplier Technique

A

Represent ratios with some unknown number/variable to reduce the number of variables and make the algebra easier.

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44
Q

How often can you use the Unknown Multiplier Technique

A

You can only use it once per problem. You should use it when neither quantity in the ratio is already equal to a number or variable.

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45
Q

How to combibe ratios with common elements

A

multiply all of the ratios by the same number (a common multiple).

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46
Q

In Multipls Ratios, what should you make the term you are working with

A

the least common multiple of the current values.

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47
Q

in COMBINATORICS, what are you countng

A

Counting the number of possibilities/ways you can arrange things.

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48
Q

Fundamental Counting Principle:

A

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 all the decisions.

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49
Q

When use the Slot Method

A

for problems where certain choices are restricted

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50
Q

How to use the Slot Method

A
  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 combinations.
51
Q

SImple Factorial Formula

A

For counting the possible number of ways of putting n distinct objects in order, if there are no restrictions, is n! (n factorial).

52
Q

What are anagrams

A

A rearrangement of the letters in a word or phrase.

53
Q

How to solve ANAGRAMS

A

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 the total number of letters, divided by the factorial(s) corresponding to each set of repeated letters.

54
Q

What USE to solve combinations with repetition.

A

Use anagram grids

55
Q

How to set uip an anagram grid

A

Set up an anagram grid to put unique items or people on the top row. Only the bottom row should have repeats.

56
Q

How to count ANAGRAM possible groups in a grid

A

divide the total factorial by two factorials: one for the chosen group and one for those not chosen

57
Q

If a GMAT problem requires you to choose two or more sets of items from separate pools(aka multiple arrangements) what to do

A

count the arrangements separately. Then multiply the numbers of possibilities for each step.

58
Q

If a problem has unusual constraints, what should you try

A

try counting arrangements without constraints first. Then subtract the forbidden arrangements.

59
Q

What is a probability

A

Quantity that expresses the chance, or likelihood, of an event.

60
Q

How to find a probability

A

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.
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.

61
Q

Why use a counting tree

A

to find the likelihood of an outcome.

62
Q

If X and Y are independent events, AND means

A

multiply the probabilities You will wind up with a smaller number, which indicates a lower probability of success.

63
Q

If X and Y are mutually exclusive

A

OR means add the probabilities. You will wind up with a larger number, which indicates a larger probability of success.

64
Q

If an OR problem has events that CAN occur together, use WHAT formula to find the probability:

A

P(A or B) = P(A) + P(B) - P(A and B)

65
Q

If on a problem, “success” contains multiple possibilities – especially if the wording contains phrases such as “at least” and “at most” – then consider

A

finding the probability that success doesn’t happen. If you can find this “failure” probability more easily (x), then the probability you really want to find will be 1-x.

66
Q

Use probability trees to:

A

keep track of branching possibilities and “winning scenarios”:

67
Q

How to set up probability trees

A
  • 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 probability of winning scenarios by multiplying down the branches and adding across the results.
68
Q

If you don’t know the average, solve with this formula:

A

Average = sum/# of terms

69
Q

If you know the average, use this formula:

A

(average) x (# of terms) = (sum)

70
Q

The average of consecutive integers

A

the middle term

71
Q

The average ofany set with terms that are evenly spaced

A

the middle term

72
Q

If the set has two middle terms, take the average of

A

the two middle numbers.

73
Q

To find the average (middle term) of a large set,

A

add the first and last term and divide the sum by 2.

74
Q

A weighted average will be closer to the number with the

A

the bigger weight.

75
Q

If the weights don’t add to one

A

sum the weights and use that to divide in order to have a total weight of one.

76
Q

Weighted average

A

= weight/sum of weights(data point) + weight/sum of weights(data point)…

77
Q

Weighted average

A

= weight(data point) + weight(data point)…/sum of weights

78
Q

You don’t need concrete values to find the weights. Having WHAT will allow you to find the weighted average.

A

Having the ratios of the weights

Write the ratio as a fraction; use the numerator and denominator as weights.

79
Q

If you are finding a weighted average of rates whose units are fractions, then the weights correspond to what

A

the units appearing in the denominator of the rate (hrs in mph).

80
Q

For sets with an odd number of values, the median is the

A

middle value when in order.

81
Q

For sets with an even number of values, the median is

A

the average of the two middle values.

82
Q

how to 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 unknowns are present.

Solve double-barreled average problems

A

by writing expressions for both the median and the arithmetic mean.

83
Q

Standard Deviaton

A

Indicates how far from the average (mean) the data points typically fall

84
Q

For problems with only two categories or decisions, use

A

use a double-set matrix:

85
Q

What do ROWS and Columns correspond to in a Double Matrix set

A

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 total of everything in the problem.

Fill in the chart using the information given then use totals to fill in the rest.

86
Q

For problems involving percents or fractions, use

A

For problems involving percents or fractions, use smart numbers and a double-set matrix to solve.

87
Q

For problems with percents,

A

pick a total of 100.

88
Q

For problems with fractions,

A

pick a common denominator for the total.

89
Q

You can only assign a number to the total if it is

A

If it is undetermined and if the problem contains only percents or fractions.

90
Q

Pay close attention to the wording of the problem to see

A

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 matrix.

91
Q

Venn diagrams should ONLY be used for

A

problems that involve 3 sets with only 2 choices per set.

92
Q

How to set up Vinn Diagrams

A

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 total, add up all the sections.

93
Q

Minor problem type - optimizaton

A

maximize or minimize a quantity by choosing optimal values.

94
Q

Minor problem type - Grouping

A

Grouping: put people or items into groups to maximize or minimize a characteristic in the group.

95
Q

Minor problem type -Scheduling:

A

Scheduling: planning a timeline to coordinate events to a set of restrictions.

96
Q

When focusing on extreme scenarios

A
  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.
97
Q

Optimization & Grouping

A

Optimization: inversion between finding the min/max and the values givens typical (bk. 4, pg. 135-136). 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 distributed arrangements to create extreme cases.

98
Q

How to solve Scheduling problems

A

Scheduling: focus on the extreme possibilities (earliest/latest time slots). Read the problem carefully!

99
Q

How to solve

A

Computation problems: 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 carefully.
100
Q

On data sufficiency computation problems, there is no need to do what

A

no need to actually perform computations

101
Q

You don’t need concrete values to find the weights. Having WHAT will allow you to find the weighted average.

A

Having the ratios of the weights

Write the ratio as a fraction; use the numerator and denominator as weights.

102
Q

If you are finding a weighted average of rates whose units are fractions, then the weights correspond to what

A

the units appearing in the denominator of the rate (hrs in mph).

103
Q

For sets with an odd number of values, the median is the

A

middle value when in order.

104
Q

For sets with an even number of values, the median is

A

the average of the two middle values.

105
Q

how to 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 unknowns are present.

Solve double-barreled average problems

A

by writing expressions for both the median and the arithmetic mean.

106
Q

Standard Deviaton

A

Indicates how far from the average (mean) the data points typically fall

107
Q

For problems with only two categories or decisions, use

A

use a double-set matrix:

108
Q

What do ROWS and Columns correspond to in a Double Matrix set

A

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 total of everything in the problem.

Fill in the chart using the information given then use totals to fill in the rest.

109
Q

For problems involving percents or fractions, use

A

For problems involving percents or fractions, use smart numbers and a double-set matrix to solve.

110
Q

For problems with percents,

A

pick a total of 100.

111
Q

For problems with fractions,

A

pick a common denominator for the total.

112
Q

You can only assign a number to the total if it is

A

If it is undetermined and if the problem contains only percents or fractions.

113
Q

Pay close attention to the wording of the problem to see

A

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 matrix.

114
Q

Venn diagrams should ONLY be used for

A

problems that involve 3 sets with only 2 choices per set.

115
Q

How to set up Vinn Diagrams

A

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 total, add up all the sections.

116
Q

Minor problem type - optimizaton

A

maximize or minimize a quantity by choosing optimal values.

117
Q

Minor problem type - Grouping

A

Grouping: put people or items into groups to maximize or minimize a characteristic in the group.

118
Q

Minor problem type -Scheduling:

A

Scheduling: planning a timeline to coordinate events to a set of restrictions.

119
Q

When focusing on extreme scenarios

A
  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.
120
Q

Optimization & Grouping

A

Optimization: inversion between finding the min/max and the values givens typical (bk. 4, pg. 135-136). 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 distributed arrangements to create extreme cases.

121
Q

How to solve Scheduling problems

A

Scheduling: focus on the extreme possibilities (earliest/latest time slots). Read the problem carefully!

122
Q

How to solve

A

Computation problems: 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 carefully.
123
Q

On data sufficiency computation problems, there is no need to do what

A

no need to actually perform computations

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