4 Basic Questions Types
a) must be true, b) not necessarily true, c) could be true, d) cannot be true
Except, unless, until, and without - Method 1
Whatever word immediately follows one of these words will be your necessary condition. Then, whatever other clause if present in the conditional statement will, when negated, become your sufficient condition.
i.e. "Not B unless A" becomes "If B then A" for the conditional statement.
Only works for sentences in the "negative variable - annoying word - positive variable" format
Except, unless, until, and without - Method 2
Replace the annoying words with "if not," therefore taking these words to represent the negation of the sufficient condition. Then take the contrapositive so you are not dealing with a conditional statement with two negative statements.
i.e. "Not B unless A" becomes "Not B if not A" Rearranged in the traditional sufficient-necessary format we get, "if not A, not B." The contrapositive leaves you with "If B then A."
Speed in "acceptability" questions
Take each rule and apply it individually to all five answer choices. Eliminate answer choices that violate the rule.
When only two variables can occupy a slot. I.e. "Either H or J must be inspected on the third day."
Split Dual Options
When a variable can occupy only two slots. I.e. "H is inspected on the third or the fifth day"
an event or circumstance whose occurence indicates that a necessary condition must also occur. Vocab indicators: "if, when"
An event or circumstance whose occurrence is required in order for the sufficient condition to occur. Vocab indicators: "then, only, only if, unless, until, except, without"
If a sufficient condition occurs, you automatically know that the necessary condition also occurs. If a necessary condition occurs then it is possible that the sufficient condition will occur, but not certain.
Denies the necessary condition thereby making it impossible for the sufficient condition to occur
Feature exactly the same number of variables as available slots. For example, eight people for eight slots.
feature a fewer number of variables than available slots. i.e. 7 passengers assigned to 9 seats on a plane
feature a greater number of variables than available slots. i.e. 8 piano lessons taught over 5 days. These are often the most difficult of linear games.
allocates one set of variables into another set of variables. Occurs in every game type except for mapping games
The Word "Except" in a question stem
a) must be true except turns into not necessarily true, b) not necessarily true except turns into must be true, c) could be true except turns into cannot be true, and d) cannot be true except turns into could be true.
a) must be false = cannot be true, b) not necessarily false = could be true, c) could be false = not necessarily true, and d) cannot be false = must be true
Apply one rule to all answer choices one at a time. Take the one that is visually the easiest to apply first
Fill a slot Questions
First check and see if any variables violate a rule when placed in the slot. Then check all not laws for that slot and see if any answers can be eliminated on that basis
you must control the variables in order to produce the optimal situation to either maximize or minimize the situation. This is always a "must be true" question.
when two groups are placed in a fixed number of spaces, there will be an overlap between the groups if the sum of the two groups is greater than the total number of spaces. i.e. if there are 3 chairs, 2 of which a boy sits in and 2 of which are green it follows that a boy has to sit in at least one of the green chairs.
FYI for Advanced Linear
When a game has a majority of global questions, it often indicates that the game contains deep and challenging inferences.
analyze the variables in terms of what can and cannot be together. Emphasis on ordering is not present
Defined - Grouping Game
The exact number of variables to be selected is fixed in the rules. For example, "Exactly six people will be selected to attend a dinner party."
Undefined - Grouping Game
The number of variables to be selected is not fixed, and is only limited by the total number of variables. For example, "A music store carries exactly ten types of CDs. The store is having a sale on some of these types of CDs."
Partially Defined - Grouping Game
There is a minimum and/or maximum number of variables to be selected, but the exact number of variables selected in the game cannot be determined. For example, "A committee of at least three members is formed from among ten candidates." These games often appear with numberical distributions.
Moving - Defined Grouping Game
The exact number of variables to be selected are indicated, but there are still subgroups within the set that are undefined, or "moving." For example, "Each of 6 people will play exactly one of two sports." The moving designation is often associated with numerical distribution.
Fixed - Defined Grouping Game
The selection group is set and there is no movement within the group or any existing sub-group. For example, "A committee must reduce 5 of 8 expenditures."
Attacking Grouping Games Steps
1) Look for linkage, 2) look for restrictions, 3) hurdle the uncertainty, and 4) recycle inferences
Hurdle the Uncertainty
Even though you cannot determine the exact variables being selected, you can "leap" that uncertainty to determine the other variables that must be selected. For example, "Three variables - A, B, & C - are available for two spaces. A&B cannot be selected together." Hurdling the uncertainty would be recognizing that this means C must fill one of the two spaces. Appear in virtually every grouping game.
New inferences sometimes appear as a result of combining a previously discovered inference with the original rules.
Grouping/Linear Combo Games
Always consider the grouping elements before the linearity elements. Typically in these combo games an overloaded set of variables must be narrowed down, then the remaining variables placed in a diagram with a linear element. For example, "7 of 9 plays must be presented over 7 months."
Variations of linear games. The interactions of the broad rules often produce deep-seated patterns within the game but very little setup info. For this reason most pattern games will have few global questions, and a lot of local questions. Look for local questions with the greatest amount of info for insight.
Pure Sequencing Games
Involve the ordering of the variables. Can be differentiated from linear games because linear games contain rules that fix the position (i.e. P is third), while sequencing games contain rules that leave the variables relative and not precisely fixed. This uncertainty is the focus of the questions. Keep in mind that unless otherwise ruled out variables can be equal. If equality is present it will probably be tested on at some point. Key is avoid making unwarranted assumptions.
Circular Linearity Games
Consist of a fixed number of variables assigned to spaces distributed around a circle. Draw spokes rather than a table. In games with an even # of variables opposite rules are most important followed by block rules. In games with an odd # of variables block rules are most important. Always remember person in the "first" seat and person in the "last" seat are sitting next to each other.
The only non-numerical game type. Often contain grouping elements. Three types: a) spatial relations, b) directional, and c) supplied diagram
Spatial Relations - Mapping Games
The rules do not fix physical relationships among the variables. You can ascertain the relationship among variables, but not their exact position. Whether a variable is north or south of another is generally meaningless. Best diagrammed with arrows or lines
Directional - Mapping Games
These games involve a fixed point and all other variables are placed north, east, south and west of that point. The best approach is to have a fixed point and draw the 4 quadrants around it.
Supplied Diagram - Mapping Games
A diagram is supplied to represent the relationship of the variables - use it!
Drawing Diagrams - Mapping Games
Always consider: a) what is the direction of connection between variables, b) do the lines have to be straight (critical when they cannot intersect), and c) can the lines intersect. If the lines are straight and there are no intersections the game will have limited solutions.
Numerical Distribution Recognize
Look for a greater number of variables being distributed over a fewer number of variables, or look for rules that include numbers or phrases such as, "at least," "exactly," and "at most." The more complex the distribution, the more likely you will be tested on your ability to identify the distribution. Always consider the numerical distribution first, then the grouping elements, and finally the linear elements.