Critical Reasoning

29. If there are any inspired musical performances in the concert, the audience will be treated to a good show. But there will not be a good show unless there are sophisticated listeners in the audience, and to be a sophisticated listener one must understand one's musical roots. If all of the statements above are true, which one of the following must also be true?

a) If there are no sophisticated listeners in the audience, then there will be no inspired musical performances in the concert.
b) No people who understand their musical roots will be in the audience if the audience will not be treated to a good show.
c) If there will be people in the audience who understand their musical roots, then at least one musical performance in the concert will be inspired.
d) The audience will be treated to a good show unless there are people in the audience who do not understand their musical roots.
e) If there are sophisticated listeners in the audience, then there will be inspired musical
performances in the concert.

A

The correct conditional statements for the passage above are:
(where I = Inspired Musical Performance, GS = Good Show, S = Sophisticated Listener, R = Understanding one's musical roots)

1. I -> GS
2. GS -> S
3. S -> R

The question I have is around the interpretation of causal relationships from the given statements, particularly with the 1st case.

The first sentence would imply that if there is an inspired musical performance, then the audience would be treated to a good show ( I -> GS).

However, could this not be interpreted as a Good Show containing an inspired musical performance ( GS -> I)? In other words, the precondition of an Inspired Musical Performance must be true for a Good Show to occur.

I have known A -> B, to be defined as "if A is true then B must be true". Then in this case, could we not say that if there is a Good Show, then it must be true that an Inspired Musical Performance must have taken place? Am I missing something here?

The latter logic seems to apply to the other two sentences:

2. GS -> S - A good show must mean that sophisticated listeners exist in the audience.
3. S -> R - A sophisticated listener must understand one's musical roots.

Why then can't we say that a Good Show, must mean that there was an inspired performance? This would yield GS -> I, similar to 2 and 3.

It folloows the reasoning If x then Y .. If not X not Y... Please feel free to comment... I have observed it in few questions.

I guess my main query is how to determine A -> B or B -> A based on the language in the paragraph.

If A is described as an action rather than a state of being, and it causes another action/reaction B, then this is a cause and effect version of A -> B. In the first sentence, the inspired musical performance causes a good show - the action/reaction, yielding I -> GS.

In the other two sentences, the paragraph describes the conditions that must be met for something to be true. i.e. a Good Show must have sophisticated listeners (GS -> S) and a Sophisticated listener must understand one's roots (S -> R). This to me seems to be more of a possessive relationship, rather than a 'cause and effect', in that in A -> B
A is a state of 'being' rather than an 'action' for which B must be true (a pre-condition, so to speak).

Is this a fair approach to these questions? Comments appreciated...

In GMAT, seek out what the author is trying to say, rather than what you think should be said.

I guess my main query is how to determine A -> B or B -> A based on the language in the paragraph.

Use the language the author has used as a clue. Understand what he has said.

Has he said "If inspired musical performance, then good show" or has he said "If good show, then inspired musical performance"?

(What you are doing, is a logical error called "converse". https://www.jimloy.com/logic/converse.htm might be able to shed more light about the logic of it. )

Also, if the author has used "If THEN", then I prefer to use conditionality, rather than cause-effect relationships. In this case, if you consider all the statements as conditional it becomes quite easy, rather than use a mix of conditionality as well as causality.

Hmm... why is D wrong in this question?

vikramveer wrote:It folloows the reasoning If x then Y .. If not X not Y... Please feel free to comment... I have observed it in few questions.

Not really.

If X then Y.

so the contrapositive is if No Y then No X.

if it rains today , I will bring umbrella to office.

So the contrapositive will be : If I dont bring Umbrella to office then it doesn't rain today.
Apply this logic for A and u will see how it turns out to be.

If there are any inspired musical performances in the concert, the audience will be treated to a good show. But there will not be a good show unless there are sophisticated listeners in the audience, and to be a sophisticated listener one must understand one’s musical roots. If all of the statements above are true, which one of the following must also be true?

In symbols,

IMP ---> GS ---> SLA ---> UMR


d) The audience will be treated to a good show unless there are people in the audience who do not understand their musical roots.

In conditional terms, it is
NOT GS --> NOT UMR

This is basically a wrong negation error, and hence it is wrong.

This question requires a pure logical concept (and I guess, not common in GMAT).
Hereis the concept:
To affirm the conclusion:
A --> B
If-then only tells us 2 things:
1) If A is true, then B is true as well
2) If B is false, then A is false as well (contrapositive)

In this case,
IMP --> GS
~SL --> ~GS
MR --> SL

where IMP stands for Inspired Music Performance; GS: Good show; SL: Sophisticated listeners; MR: Music Roots.

We can write the formula above as:
IMP--> GS
GS --> SL
then, IMP --> SL
or ~SL --> ~IMP

the other option:
IMP --> GS
GS --> SL
~SL--> ~MR
then ~GS --> ~MR

Lets analyze the answer choices.
A. ~SL --> ~IMP (correct)
B. ~MR --> ~GS (incorrect, it should be ~GS --> ~MR)
C. MR --> IMP (incorrect)
D. ~MR --> GS (incorrect)
E. SL --> IMP (incorrect, the reverse is correct)

Thus, the answer is A.

There are three conditional relationships from the stimulus.

1. IMP --> GS
2. GS --> SL
3. SL --> UMR

You can use the transitive property and combine these statements to yield many different possible inferences

1 + 2 = IMP --> SL
2 + 3 = GS --> UMR
1 + 2 + 3 = IMP --> UMR

or you could have the contrapositive of any of these statements.

(A) ~SL --> ~IMP is the correct answer and is the contrapositive of the inference from the first two statements.
(B) ~GS --> ~UMR is the negation of the inference of the second and third statements.
(C) UMR --> IMP is the reversal of the inference of all three statements.
(D) ~GS --> ~UMR is the negation of the inference of the second and third statement.
(E) SL --> IMP is the reversal of the first statement.

For statements involving "unless"

_______ , unless ________.

What comes after unless is the necessary condition. Everything else gets negated and thrown into the sufficient condition.