Critical Reasoning

"If you don't study well for the following test, you are sure to fail", said the professor to his students. "Only those of you who study for at least 10 hours have a chance of passing."

Which of the following can best be inferred, based on the professor's statements ?

(A) Anyone who studies for more than ten hours has more of a chance of passing the test than those who study for fewer than ten hours.

(B) No number of hours will suffice to ensure a passing grade.

(C) If someone does not want to fail the test, he or she had better study for at least ten hours.

(D) Those who don't study for at least 10 hours will surely fail the course.

(E) The professor's course is one of the harder courses of that year.

On inference questions the bar for a correct answer is very high. It must absolutely, 100% be true, no exceptions allowed. Moving through the answer choices here:

A - This is not necessarily true, because not "anyone" may have more of a chance of passing this way. What if student John was bound to fail no matter how many hours he studied. Then if he studies more than 10 hours, he still does not have a higher chance of passing the test than does a student who studies fewer hours (and is therefore bound to fail), because he is also bound to fail.

B - This is not necessarily true. We don't know if this is true or not. Over 10 hours of studying may guarantee you a passing grade, or over 100, or maybe none, we don't know.

C - This is a correct inference and therefore the correct answer. Because you are bound to fail the test if you study for fewer than 10 hours, then if you want to pass you must study for at least 10 hours.

D - Scope shift. The argument is about the test, not the course.

E - Other courses are completely out of scope and irrelevant, we don't know this.

Hi experts,

I solved this CR in in some way and my answer is B.
From Q stem we have: 1. If Do not study well ---> Then Fail.
2. If Study more than 10 hrs ---> Then Chance of Passing. (10 hrs is Necessary but not Sufficient).
Now take answer choices:
(A) Anyone who studies for more than ten hours has more of a chance of passing the test than those who study for fewer than ten hours. This is not true for all since 10 hrs DO NOT suffice to pass, a guy can fail after studying 20 hrs too, and he stands no way more chances of passing to one who fails studying, say, 5 hrs.

(B) No number of hours will suffice to ensure a passing grade. True. We do not have a SUFFICIENT condition of passing (in terms of hrs)

(C) If someone does not want to fail the test, he or she had better study for at least ten hours. Maybe true and may not be. This asks about how to minimize the chance to FAIL which can be done by study well. No. of hrs is related to passing, as per the professor.

(D) Those who don't study for at least 10 hours will surely fail the course. Not 100% true. If they STUDY WELL they will not FAIL.

(E) The professor's course is one of the harder courses of that year.Irrelevant.

Pls tell me where am I wrong??

~Binit.

binit wrote:Hi experts,

I solved this CR in in some way and my answer is B.
From Q stem we have: 1. If Do not study well ---> Then Fail.
2. If Study more than 10 hrs ---> Then Chance of Passing. (10 hrs is Necessary but not Sufficient).
Now take answer choices:
(A) Anyone who studies for more than ten hours has more of a chance of passing the test than those who study for fewer than ten hours. This is not true for all since 10 hrs DO NOT suffice to pass, a guy can fail after studying 20 hrs too, and he stands no way more chances of passing to one who fails studying, say, 5 hrs.

(B) No number of hours will suffice to ensure a passing grade. True. We do not have a SUFFICIENT condition of passing (in terms of hrs)

(C) If someone does not want to fail the test, he or she had better study for at least ten hours. Maybe true and may not be. This asks about how to minimize the chance to FAIL which can be done by study well. No. of hrs is related to passing, as per the professor.

(D) Those who don't study for at least 10 hours will surely fail the course. Not 100% true. If they STUDY WELL they will not FAIL.

(E) The professor's course is one of the harder courses of that year.Irrelevant.

Pls tell me where am I wrong??

~Binit.

Hey Binit, the mistake that you are making with answer choice B is that you are going beyond the argument. Answer choice B may be true or it may be false, the argument doesn't address it. We know that if you study for fewer than 10 hours you will fail the test. That is all that we know in terms of hours. Therefore, maybe if you study over 10 you maybe will pass, or maybe if you study over 10 you definitely will pass, or maybe if you study between 10 and 20 hours you maybe will pass but if you study over 20 hours you definitely will pass...we don't know, these are all possibilities. All of this is outside of the scope of the argument, and therefore we cannot make any inferences regarding it. You are assuming that because no mention is made of a number of studying hours that will make passing a guarantee, that it doesn't exist. We can't infer that.

Answer choice C nicely rewords the premise, making it a great correct answer to an inference question. The premise states that you must study for at least 10 hours to have a chance at passing, meaning that if you study for fewer than 10 hours you are doomed to fail. Answer choice C says the same thing because if you do not want to be doomed to fail the test, then you had better study for at least 10 hours.

Does all of that make sense? Be careful with scope on inference questions, because tricky wrong answers (like B here) are often wrong because they go beyond the scope of the argument and are thus not necessarily true.

Side note, answer choice D is wrong because of the scope shift between test and course, not because of the reasoning that you gave. If they study for fewer hours they are guaranteed to fail the test, and if answer choice D had used the word "test" it would be a correct inference.

Thanks a ton Brandon. Your post was an eye opener for me. I was definitely not hitting the bulls-eye of the problem. I tried it by drawing Venn-diagram (May not be a proper one, pls excuse) and the whole thing became clear to me. You were right, I was taking choice B too far. Pls have a look:


10+ - students who studied 10+ hrs
P - passed; out side P implies failed.
NW - not studied well.
C is easily following from here.

~Binit.

Hi Binit,

I have seen your posts earlier for such questions and they have all used this venn diagram approach. Can you please shed some light or share references to explore this approach?

bubbliiiiiiii wrote:Hi Binit,

I have seen your posts earlier for such questions and they have all used this venn diagram approach. Can you please shed some light or share references to explore this approach?

Aaaaaaaah, what to say? Somehow this suits me and the peculiar thing is that I really don't remember a time when I learned how to apply Venn diagrams in CR problems. Maybe I have an affinity for diagrams (and repulsion for texts: RC )
On a more serious note, Venn is good (if u like it, and draw it fast) for Conditional CR problems but can waste ur precious time as well in Causality problems (as per my opinion)
Pls explore and share ur thought.

~Binit.