A Recent Survey Showed That 50 Percent of People Polled Believe that Elected Officials Should Resign GMAT Problem Solving

Question: A recent survey showed that 50 percent of people polled believe that elected officials should resign if indicted for a crime, whereas 35 percent believe that elected officials should resign only if they are convicted of a crime. Therefore, more people believe that elected officials should resign if indicted than believe that they should resign if convicted.

The reasoning above is flawed because it

(A) draws a conclusion about the population in general based only on a sample of that population

(B) confuses a sufficient condition with a required condition

(C) is based on an ambiguity of one of its terms

(D) draws a conclusion about a specific belief based on responses to queries about two different specific beliefs

(E) contains premises that cannot all be true

A Recent Survey Showed That 50 Percent of People Polled Believe that Elected Officials Should Resign GMAT Problem Solving - is a topic of the GMAT Quantitative reasoning section of GMAT. This question has been taken from the book “GMAT Official Guide Quantitative Review”. To solve GMAT Problem Solving questions a student must have knowledge about a good amount of qualitative skills. The GMAT Quant topic in the problem-solving part requires calculative mathematical problems that should be solved with proper mathematical understanding.

This question has only one approach.

Solution and Explanation:

Approach Solution: 

The stimulus states:

"A recent survey showed that 50 percent of people polled believe that elected officials should resign if indicted for a crime, whereas 35 percent believe that elected officials should resign only if they are convicted of a crime. Therefore, more people believe that elected officials should resign if indicted than believe that they should resign if convicted."

Words like "if" and "only if" helps us to secure necessary and enough conditions within conditional reasoning.

Here, in this problem statement, the first sentence states "A recent survey showed that 50 percent of people polled believe that elected officials should resign if indicted for a crime" (the "if" sets off a sufficient condition).

If we rearrange this statement, we can see that "if indicted for a crime (I), then that elected official should resign (R)"

When we put the question in the form of diagram, the statements above should look similar to this:

I--->R

The second problem sentence states "35 percent believe that elected officials should resign (R) only if they are convicted of a crime (C)."

The phrase "only if" sets off a necessary condition. The diagram of this statement should look as follows:

R--->C

The concluding argument says "Therefore, more people believe that elected officials should resign if indicted than believe that they should resign if convicted."

This condition is flawed. The statement would be diagrammed as follows:

More people believe that I--->R than believe C--->R; or more simply I--->R, C--->R

The sufficient and necessary (required) conditions have been confused. A proper meaningful conclusion based on these statements would be:

"Therefore, more people believe that elected officials should resign if indicted than believe that they should resign only if convicted."

The correct diagram of these statements would look like this:

I--->R, R--->C

In short, the conclusion confuses a sufficient condition with a necessary (required) condition, as reflected in answer choice B.

Correct Answer: B

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