Critical Reasoning

LSAT question example 3: The Calculus

Another LSAT question! This one is very translatable to the GMAT. As you can see it is one of the first 16 questions and it is one of the major question types on the GMAT. These are characteristics of questions that are good to study (see LSAT to Study GMAT part 2 https://www.beatthegmat.com/lsat-to-stud ... 69915.html).

Source: Official LSAT from June 2000, question 14 of section 2. Question found in "The Next 10 Actual , Official LSAT PrepTests" copyright Law School Admissions Council, 2004, page 84.

"14. Historian: Leibniz, the seventeenth- century philosopher, published his version of calculus before Newton did. But then Newton revealed his private notebooks, which showed he had been using these ideas for at least a decade before Leibniz's publication. Newton also claimed that he had disclosed these ideas to Leibniz in a letter shortly before Leibniz's publication. Yet close examination of the letter shows that Newton's few cryptic remarks did not reveal anything important about calculus. Thus, Leibniz and Newton each independently discovered calculus.

Which one of the following is an assumption required by the historian's argument?

A) Leibniz did not tell anyone about calculus prior to publishing his version of it.

B) No third person independently discovered calculus prior to Newton and Leibniz.

C) Newton believed that Leibniz was able to learn something important about calculus from his letter to him.

D) Neither Newton nor Leibniz knew that the other had developed a version of calculus prior to Leibniz publication.

E) Neither Newton nor Leibniz learned crucial details about calculus from some third source."

Let me give you a tip as you take a shot at this one...

This is another example where you should take the admonition that "conclusion is king," meaning that while the premises are often background information that does not need to be obsessed about, EVERY word on the conclusion could be important.

Official Answer and explanation after a little discussion!

Good Luck!

David@VeritasPrep wrote: "14. Historian: Leibniz, the seventeenth- century philosopher, published his version of calculus before Newton did. But then Newton revealed his private notebooks, which showed he had been using these ideas for at least a decade before Leibniz's publication. Newton also claimed that he had disclosed these ideas to Leibniz in a letter shortly before Leibniz's publication. Yet close examination of the letter shows that Newton's few cryptic remarks did not reveal anything important about calculus. Thus, Leibniz and Newton each independently discovered calculus.

Which one of the following is an assumption required by the historian's argument?

A) Leibniz did not tell anyone about calculus prior to publishing his version of it.

B) No third person independently discovered calculus prior to Newton and Leibniz.

C) Newton believed that Leibniz was able to learn something important about calculus from his letter to him.

D) Neither Newton nor Leibniz knew that the other had developed a version of calculus prior to Leibniz publication.

E) Neither Newton nor Leibniz learned crucial details about calculus from some third source."

IMO E

A: Negate: Leibniz told someone prior to publishing. Still our conclusion stands corrected that Leibniz independently discovered calculus.

B: Negate: Third person independently discovered calculus. But it does not destroy our conclusion that Leibniz and Newton each independently discovered calculus. We can merely add this third person to the list.

C: Clearly irrelevant. It kind of opposes the Premise " Yet close examination of the letter shows that Newton's few cryptic remarks did not reveal anything important about calculus." . Let Newton believe what he thinks but this is not what the author believes.

D: If they (Newton and Leibniz) knew also either of them is working on same thing unless there is SHARING of the relevant thoughts it cannot be hold as a proper assumption.

E: Left after Process of Elimination. If they have copied from a same third resource then there is no way we can say Leibniz and Newton each independently discovered calculus. By negating, the Bold part is violated here.

IMO E

I'll go with E.
Premise - Information about Leibniz and Newton that lead to below conclusion.
Conclusion - Leibniz and Newton each independently discovered calculus.

A - Not relevant.
B - Not relevant.
C - This weakens the conclusion. A assumption will place the argument in strong state. This statement is reverse.
D - This strengthens the conclusion but not necessary to have as a premise. This goes against the premises/fact statements - counter premise, and calls into question the validity of the argument. Not a assumption.
E - If this statement is negated - Either Newton or Leibniz learned details from other source, this destroys the argument and calls the conclusion into question. If either got details from other source then both have not discovered calculus independently.

David@VeritasPrep wrote:LSAT question example 3: The Calculus

14. Historian: Leibniz, the seventeenth- century philosopher, published his version of calculus before Newton did. But then Newton revealed his private notebooks, which showed he had been using these ideas for at least a decade before Leibniz's publication. Newton also claimed that he had disclosed these ideas to Leibniz in a letter shortly before Leibniz's publication. Yet close examination of the letter shows that Newton's few cryptic remarks did not reveal anything important about calculus. Thus, Leibniz and Newton each independently discovered calculus.

Which one of the following is an assumption required by the historian's argument?

A) Leibniz did not tell anyone about calculus prior to publishing his version of it.
B) No third person independently discovered calculus prior to Newton and Leibniz.
C) Newton believed that Leibniz was able to learn something important about calculus from his letter to him.
D) Neither Newton nor Leibniz knew that the other had developed a version of calculus prior to Leibniz publication.
E) Neither Newton nor Leibniz learned crucial details about calculus from some third source."

IMO E.
Way of thinking ->
Conclusion - Leibniz and Newton each independently discovered calculus
Premise -
- Leibiniz published before Calculus Newton
- Newton was working on ideas for atleast decade before
- Newton disclosed his ideas in letter
- Remarks in Letter didnt have any important information abt Calculus

Possible Assumptions -
- Letter is the only way Newton might have communicated with Leibniz
- Leibniz didnt get any mild indications about calculus from unimportant contents of letter as well..... (far fetched)

These assumptions came into mind immediately after reading the passage, will check for other assumptions, if any while working with options....

A - If True - If Leibnez told anyone about calculus, and Newton gets to know and then Newton starts working on it.... But then notes show that Newton was working much earlier.
B - If true, then Why didnt 3rd person come into picture or claim abt the same - Out of scope
C - Is against the premise....
D - Similar to B
E - Correct....

I had got down to C and E, and then eliminated C....

OA is E.

Nice work by everyone! You did fine on this one for sure. The words that you guys have in bold - independently and discovered - are the key words here. Excellent. It is clear that you are looking for something that if not true would mean that they did not each independently discover the calculus.

For an explanation, I am going to direct you back to Shovan85's posting. Very good job of negating the answer choices, nice analysis and focus. (By the way, Shovan85, love the tagline about easy and difficult problems!)

The point to emphasize is: The specific conclusion is very important and that is why the new Veritas Essentials course has a section called "Conclusion is King" (my colleague Brian Galvin who will be teaching the online version of the Essentials this weekend came up with this phrase). What "Conclusion is King" means is that you have to focus on the details of the conclusion. WHY? Because the conclusion is the thing that you are strengthening or weakening or in this case, supplying the assumption for...Each word in the conclusion is therefore very important.

Nice work! Any Questions?

The answer should be E.

Great LSAT question by David.

Here's my explanation

Evidence:

Leibniz, the seventeenth- century philosopher, published his version of calculus before Newton did.

Close examination of the letter shows that Newton's few cryptic remarks did not reveal anything important about calculus [counter of counter evidence]

Counter-Evidence:

Newton revealed his private notebooks, which showed he had been using these ideas for at least a decade before Leibniz's publication

Conclusion:

Leibniz and Newton each independently discovered calculus



Now you can see that the HISTORIAN countered the evidence presented by Newton-that of some info about calculus in the letter.After that historian simply leaves us high and dry and concluding that their works were done independently, without negating the other possibilities.

Clearly the historian assumes that there was no other medium by which they should share their knowledge.

A) OUT OF SCOPE-We don't care about others.The argument is about Newton and Leibniz.

On a more microscopic level,you may find that Newton too MAY be among others.Let's assume that Newton was told about calculus prior to its publishing.It still doesn't prove that Newton discovered it.

eg: Let's say I have discovered something great.You are my best friend.I tell you about the thing that I have discovered and that I am gonna publish it.But does that mean you too discovered what I discovered? CLEARLY NO!

B) IRRELEVANT

The argument is about Newton and Leibniz and not about some third person.The conclusion DOES NOT SAY "Newton and Leibniz were the ONLY one's who discovered calculus independently"

C) CONTRADICTORY

An answer choice CAN NEVER CONTRADICT THE EVIDENCE of the argument.It has already been stated in Evidence that nothing important about Calculus was found.

You may say that the evidence talks about "IMPORTANT and not anything related to CALCULUS",but the answer choice too says the words " SOMETHING IMPORTANT".

D) INCORRECT-OPPOSITE

This may be difficult to discern.

Negate the statement " Both Newton and Leibniz knew that the other had developed a version of calculus prior to Leibniz publication"

Because the conclusion is about "Leibniz and Newton independently discovering independently a version of calculus",a statement "negation of answer choice" should prove that this does not happen,but instead,the negation makes it even more likely that each developed a version of calculus independently because each of them knew that the other had developed his own version of calculus.

E) This answer choice fits my paraphrase :"Clearly the historian assumes that there was no other medium by which they should share their knowledge.".This answer choice negates one of the many other ,possible, reasons.

You can even negate the answer and see:

" Newton and Leibniz learned (dunno why American English uses learned.I was used to learnt (British English).lol) crucial details about calculus from a third source"

If,they learned from a third source about calculus,can you conclude they discovered calculus independently?

I don't think so.


Therefore,I choose E.

David@VeritasPrep wrote: For an explanation, I am going to direct you back to Shovan85's posting. Very good job of negating the answer choices, nice analysis and focus. (By the way, Shovan85, love the tagline about easy and difficult problems!)

Thanks a lot David!!!

E looks correct to me

Bringing this thread up again because I hit on this problem now

I am still not convinced with E. I strongly feel D should be the answer

E states that neither newton or Leibniz learned crucial details about calculus from some third source

When i was solving this problem i eliminated E because it seemed out of scope to me. Here is my thought process
Discovering calculus does'nt necessarily mean discovering everything that leads to discovery of calculus
For instance Math may be crucial to discovery cf calculus. Newton or Leibniz may have learned math from someone else but still may have discovered calculus independtly

Further if we negate E
it means either Newton or Leibniz learnt some crucial details about calculus from a third source
This inturn hnts that some third source already discovered calculus(is'nt this same as B ??). newton or Leibniz learned details about calculus from this third souce

I may be sounding silly with the math explanation for calculus but unfortunatelyy this is what stuck my mind and i did not even consider E as a contender

You are over-thinking this question and making it more difficult than it is.

First, lets deal with choice B, you said

Further if we negate E
it means either Newton or Leibniz learnt some crucial details about calculus from a third source
This inturn hnts that some third source already discovered calculus(is'nt this same as B ??). newton or Leibniz learned details about calculus from this third souce

The difference between Choice E and B is that if you negate choice B this does not indicate that this "third person" had any contact with either Newton of Leibniz. It could be that someone discovered calculus, wrote it down and buried the box in the ground and it was only found this year. Some unknown papers buried in the ground would not have given any assistance to Newton or Leibniz.

If you take away choice E, it simply says "Either Newton or Leibniz (or both) learned crucial details of calculus from some third source."

Do you see the key word there? If you learn crucial details from someone else then you did not independently discover did you?

People say Columbus discovered North America, yet we know that the Vikings, possible the Chinese, and certainly the Native Americans were here first. If Columbus did not know that these groups had been hear then you could still say he "discovered it" independently. If he was following a map from one of the earlier groups then he learned "crucial details" from another source and therefore did not discover it independently.

To keep the analogy going and deal with this point you made

When i was solving this problem i eliminated E because it seemed out of scope to me. Here is my thought process
Discovering calculus does'nt necessarily mean discovering everything that leads to discovery of calculus
For instance Math may be crucial to discovery cf calculus. Newton or Leibniz may have learned math from someone else but still may have discovered calculus independtly

I would say that sailing is crucial to being able to discover North America. So is having a ship. Someone taught Columbus about sailing and I have never heard it said that he built ships, so someone built the ships. Someone taught him navigation as well. Someone financed the operation. So he got lots of help of all kinds but that does not mean that he did not "discover" North America "independently."

Again you have to focus on the main point here, "what is being discovered?" No one alleges that Columbus invented sailing. And no one is saying that Newton and Leibniz invented this giant thing called "math." The conclusion is that "Leibniz and Newton each independently discovered calculus."

I am still not convinced with E. I strongly feel D should be the answer

Choice D is certainly temping because the prompt has you thinking about how the influenced each other. But if you negate D you see that it does not matter if they each knew that the other had discovered it. Newton could have learned that Leibniz discovered something called calculus but when Newton goes on to discover it himself it is still "independently" unless he actually gets some help. Columbus may have heard that there was some land somewhere that the Vikings had visited. His discovery is still independent. If he gets a map from the Vikings it is not.

Now I am going to give a little "tough love." I want to help you and all who read this...

I am glad that you brought this up

I am still not convinced with E.

This is an official LSAT question, and the answer choice has been given to you by a registered expert here on Beat the GMAT. I do not understand why you need to be "convinced." Unless you doubt the LSAT test writers (or the GMAT test writers which is more to the point) then you can trust the official answer to an official question. Unofficial questions are a different story. Maybe someone writes a bad question and the answer is not really what it should be. If it is an unofficial question you might say something like "are we sure that choice E is right?" But with an official question the correct answer is the correct answer.

If this question were recently posted you might think that the poster indicated the wrong answer as being correct. It happens frequently on Beat the GMAT. But I have given the source and page number and the question was discussed already by several people. So it is not likely that I wrote the answer down wrong.

So here we have an official question with a verified correct answer as explained by a certified expert. So why do you feel that it is necessary to be "convinced?"

In fact, what you did when you saw that E was the correct answer was to got through your mind looking for ways in which E could be wrong.

You say that E is out of scope and just like B - and I appreciate all of that and I am really glad that you asked the question so that I could help you, but I want to talk about your mind set.


****Read carefully now -- this is important***

What do you do when you see that the official answer to a Quant problem is 27 and you thought it was 42? Be honest. You know what you do, you say "27, huh, I must have made a mistake. How did I end up with 42, let me see what I did wrong here so that I do not do it again."

Right?

You do NOT you say, "I bet it is 42 and I am going to think of reasons why it is 42 and not 27." That would seem ludicrous right?

I mean a Quant problem only has one correct answer and if you get a different answer you made a mistake and need to figure out why you missed it right?

Okay well here is something that it takes students a long time to learn - A verbal question only has one correct answer as well. And if you got a different answer you need to say "what did I do wrong and how can I not make this mistake in the future.

I have had tutoring students who wanted to argue the answers on verbal questions, particularly CR and RC, but SC sometimes as well. I finally had to say to one student, "Do you want to get a GMAT score and go to business school? Because if you do you need to focus on why you did not get the correct answer and how you can get it next time."


Like I said, some tough love. I am glad to answer your questions and I am not saying "how dare you challenge me?" In fact, when I write original questions of my own I welcome it when students debate the merits of the question. I then edit it to make it better. What I am saying is that your mind set should be "Why did I get this wrong?" "What can I do better next time?" Rather than "I am not convinced with this official answer to this official question."

It may seem like a slight difference, but it is the difference between a 600 and a 700.