Deductive reasoning questions are the last question type we
cover because they are an entirely different species from the rest
of the GMAT critical reasoning questions.
Note: these questions are
rare on the GMAT. You do not have to memorize the rules; just learn how to
apply them.
Deductive vs. Inductive Reasoning
These questions force you to follow highly specific logical
rules. Most critical reasoning questions use soft and fuzzy inductive
reasoning (with observations, lots of unstated assumptions, etc).
Deductive reasoning is what a computer would do: hard logic following
rules. Deductive reasoning is often used in the legal profession.
You were on your neighbor's property.
It is against trespassing laws to be on a neighbor's property.
You are therefore guilty of trespassing.
Isaac Inductive says: I've noticed that
every time I kick soccer ball up, it comes back down, so I guess this next
time when I kick it up, it will come back down again.
Dennis Deductive says: You are merely
applying Newton's law of gravity. Everything that goes up must come down.
If you kick the ball up, it must come down.
Types of Deductive Reasoning
Which of the following could be answered using pure
deductive reasoning:
1. Did the growth of the population of Connecticut slow last year?
2. Do Connecticut residents appreciate access to the ocean?
3. Are Connecticut legal residents also residents of the United States?
4. Does Connecticut have the highest per capita income of any state in
the United States?
1. It may seem clearcut to look at population data, but what about migrant
workers, etc. who may not be documented? Answering this question actually involves making assumptions, and therefore an inductive guess.
2. This relies on surveying popular opinion, which is fraught with assumptions.
3. In 1789, Connecticut became the first signatory to the U.S.
Constitution and all Connecticut residents became legal residents of the United States.
Thus, this question can be answered using pure deductive reasoning.
4. The income of Connecticut residents is difficult to measure and this
is an observational task, not a deductive one. So this question requires inductive
reasoning.
Rule #1: If A,
then B
If I press the power button, then
the computer will turn off.
Valid Inference: If not B, then not A
If the
computer is on, then I didn't press the power button.
(This logic
rule is called the Contrapositive)
Invalid Inference: If B, then
A
The computer is off; therefore I pressed the power
button.
(Just because the computer cannot be on if I've pressed the power button does not mean if it is off I must have pressed the power button. There could be other reasons for it being off.)
Invalid Inference: If not A, then not
B
If I did not press the power button, then
the computer is not off.
(There are other ways
the computer could have shut off. This is called Denying the
Antecedent.)
Example: Denying the Antecedent
If it rains,
then the grass is wet.
It isn't raining, so the grass must be
dry
(There might have a sprinkler
system.)
Rule #2: If A,
then B, If B, then C
If A, then
B: If I press the power button, the computer will turn
off.
If B, then C: If the computer is off,
then the website will shut down.
Valid Inference: If A, then C
If I press the
power button, then the web site will shut down.
Valid Inference: If not C, then not A
If the website is not shut down, then I did not press the power button.
Invalid Inference: If C, then
A
If website is shut down, then I must have pressed the
power button.
(There may be other reasons for the computer being off (and the website shutting down as a result) and also reasons other than the computer being off for the website shutting down.)
Rule #3: All A
are B
All GMATs are adaptive
tests.
Valid Inference: All nonB's are nonA's.
A test
that is not adaptive is not a
GMAT.
Valid Inference: No nonB is an A.
No test that
is not adaptive is a GMAT.
Invalid Inference: No nonA's are
B's.
No nonGMAT tests are
adaptive.
(Try the GRE.)
Invalid Inference: All B are
A.
All adaptive tests are GMAT tests.
(Try the GRE.)
Rule #4: All A
are B, All B are C.
All A are B: All GMATs are adaptive
All B are C: All adaptive tests are computerized tests.
Valid Inference: All A are C
All GMAT tests are
computerized.
Valid Inference: No nonC is an A
No
noncomputerized test is a GMAT.
Invalid Inference: No nonA is a
C
No nonGMAT test is computerized.
(Try the GRE).
Invalid Inference: All C are A
All computerized tests are GMAT tests.
(Try the GRE).
Rule #5: Some A
are B.
Some MBA programs are parttime
programs.
Valid Inference: Some B are A.
Some parttime
programs are MBA programs.
Invalid Inference: Some A are not
B.
Some MBA programs are not parttime.
Invalid Inference: Some B are not
A.
Some parttime programs are not MBA programs.
Rule #6: Some A
are B and Some B are C
Some A are B: Some MBA programs are parttime programs.
Some B are C: Some parttime programs are poetry degrees.
Valid Inference: Some B are A.
Some parttime
programs are MBA programs.
Valid Inference: Some C are B.
Some poetry
degrees are parttime programs.
Invalid Inference: Some A are
C.
Some MBA programs are poetry degrees.
Invalid Inference: Some C are
A.
Some poetry degrees are MBA programs.
(Why are C and
D invalid? Although A and C have B in common, there does not need to be any overlap between MBA programs and poetry degrees.)
Rule #7: Some A
are B and All B are C.
Some A are B: Some MBA programs are accounting programs.
All B are C: All accounting programs are mathintensive programs.
Valid Inference: Some B are A.
Some accounting programs are MBA
programs.
Valid Inference: Some A are C.
Some MBA programs are mathintensive programs.
Valid Inference: Some C are A.
Some mathintensive programs are
MBA programs.
Invalid Inference: All C are A.
All mathintensive programs are
MBA programs.
Invalid Inference: All C are B.
All MBA programs are mathintensive programs.
Rule #8: Either
A or B, but not both
Either a dog or a
cat.
Valid Inference: If A, then not B.
If a dog, then
not a cat.
Valid Inference: If B, then not A.
If a cat, then
not a dog.
Valid Inference: If not B, then A.
If a not a
cat, then a dog.
Valid Inference: If not A, then B.
If a not a
dog, then a cat.
There are two main types of Deductive Reasoning (Must Be True) Questions:
1. Make a deduction: extend the premises to make a direct
logical conclusion?
If the statements above are true, which of the following must also be true?
Which of the following may be correctly inferred?
Which of the following inferences (inference means the same
thing as "must be true" on the test) is best supported by the statement
made above?
(Conclusions differ from inferences in that
conclusions are the result of premises and inferences must be true if
the premises are true.)
2. What's the missing premise? (Here you find out what
premise would be necessary to make the argument logically valid.)
The passage's conclusion is only true if which of the following
statements is also true?
Which of the following, if introduced into the argument as a
premise, makes the argument logically correct?


Most critical reasoning questions are about what may or may not be true based on assumptions.
For example: Which of the following is the best, the most, or the least likely to satisfy the question?
Deductive questions will never use those indicators. They are
written in terms of certainty: must be true, required, necessary, etc... 


How to tackle Deductive Reasoning (Must Be True
Questions):
1. Read the passage and look for the argument. Note that Must Be True questions may not be an argument. They may
just be a series of facts. Nevertheless, try to find the argument.
2. Must Be True questions always should be
tackled using POE (process of elimination). Go through every answer choice
systematically and check if it is ALWAYS true. If you can find a situation
where it is not true, eliminate it. Gradually eliminate answer choices
until you have one left.
Example
Every store on Main Street in Summitville has an awning. All of these awnings are either green or red.
If the statements
above are true, which one of the following must also be true?
I.
Some awnings in Summitville are green.
II. If a store in Summitville
does not have an awning, then it is not on Main Street .
III. If a
store in Summitville has a red awning, then it is on Main Street .
(A)
I only
(B)
II only
(C) I and II only
(D)
I and III only
(E) I, II, and III
Explanation: The correct answer is B. Note
that this question is not an argument per se because it requires
deductive reasoning.
Statement I may not be true. The question
states that all of the awnings on Main Street are either green or red,
but this does not preclude the possibility that all of the awnings on
Main Street are red.
Statement III may not be true either. The
question states that every store on Main Street has either a red awning
or a green awning, but this does not preclude the possibility that a
store on some other street has a red awning.
Statement II must be
true. If every store on Main Street has an awning, then a store without
an awning cannot be on Main Street . The correct answer is B.
Example
The mathematical constant "e" ( the
base of the natural logarithm) is transcendental and therefore
irrational. In 1882, the mathematician Johann Heinrich Lambert
proved that the number pi is irrational. Pi must therefore be transcendental.
Which of the following statements, if true,
most weakens the conclusion drawn above about the number pi?
(A) The exact value of transcendental numbers cannot be
given.
(B) The number √2 is irrational but not transcendental.
(C) The mathematician Fernard von Lindermann used the
fact that e is transcendental to prove that pi is transcendental.
(D) The number √3 is transcendental but not irrational.
(E) It is extremely difficult to prove that a number is
transcendental.
Explanation: The correct answer is B. This question asks you to weaken the
conclusion, which states that pi must be transcendental. The key
phrase here is “must be.” We know "e" to be transcendental and therefore
irrational, but all we’re told about pi is that it is irrational, so the
conclusion that pi must therefore be transcendental is
unfounded. Pi might be transcendental (and in fact is), but the
information in the passage can’t logically lead us to that
conclusion. A statement weakening the conclusion will show that pi is not necessarily transcendental. Choices (A), (C) and (E) are
irrelevant. Choice (B) states that a number can be irrational and not
transcendental. This shows that pi is not necessarily
transcendental. Choice (D) gives us the reverse of what we want
since it tells us that a number can be transcendental and not
irrational. We already know that pi is irrational, so this doesn’t
weaken the conclusion. Choice (B) does, and is the best
answer.
