A 6 min read

In this article, we’ll look at the solution to this GMAT Official guide critical reasoning question. We have analyzed the 5 answer choices and arrived at the correct choice through 4 steps:

1. Understanding the Argument
2. Vizualization of Argument
3. Prethinking
4. Answer Choice Analysis

General Information on the GMAT OG CR question

Question: Newton developed mathematical concepts…

Newton developed mathematical concepts and techniques that are fundamental to modern calculus. Leibniz developed closely analogous concepts and techniques. It has traditionally been thought that these discoveries were independent. Researchers have, however, recently discovered notes of Leibniz’s that discuss one of Newton’s books on mathematics. Several scholars have argued that since the book includes a presentation of Newton’s calculus concepts and techniques, and since the notes were written before Leibniz’ own development of calculus concepts and techniques, it is virtually certain that the traditional view is false. A more cautious conclusion than this is called for, however. Leibniz’ notes are limited to early sections of Newton’s book, sections that precede the ones in which Newton’s calculus concepts and techniques are presented.

In the historian’s reasoning, the two portions in boldface play which of the following roles?

[Refer to GMAT Official Guide for options].

Solution: Newton developed mathematical concepts…

For Boldface questions, we need to understand not only the logic of the argument but also the roles of every statement and the relationships between the statements. Let us solve this question!

Understanding the argument

The argument presents an argument made by the historian. The question stem also asks us for the role of the two boldfaces in the historian’s argument.

So, as far as this argument goes, the historian is the author.

Historian: Newton developed mathematical concepts and techniques that are fundamental to modern calculus.

• This is a fact that seems to be setting the context for the argument.
• Fact: Newton developed mathematical concepts and techniques that are fundamental to modern calculus.

Leibniz developed closely analogous concepts and techniques.

• Another fact.
• Fact: Leibniz (another scientist/mathematician like Newton, actually!) developed concepts and techniques that were very similar to Newton’s concepts and techniques for calculus.

It has traditionally been thought that these discoveries were independent.

• Traditional Belief/Opinion: Newton and Leibniz discovered these similar concepts and techniques independently, i.e., one did not copy/get inspired by the other.
• Here, “these discoveries were independent is a belief or opinion, not a fact.
• This is simply a third-party opinion at this point. We do not know at this point if the historian (author) shares the same belief.
• However, the overall statement is a fact. It is a fact that there is this traditional belief about the discoveries being independent.

Researchers have, however, recently discovered notes of Leibniz’s that discuss one of Newton’s books on mathematics.

• This line introduces a recent discovery.
• It is a fact. It is a fact that researchers have discovered these notes of Leibniz’s.
• It is also a fact that these notes discuss one of Newton’s books on mathematics.

Several scholars have argued that since the book includes a presentation of Newton’s calculus concepts and techniques,

• Fact: The book written by Newton includes a presentation of his calculus concepts and techniques. This is a fact.
• “since the book includes…”. The word “since” indicates that whatever is given next is the reasoning behind what the scholars are arguing for.
• This line introduces some people called scholars and introduces us to one of the reasons used by the scholar to make some point (we are yet to see what this point is).

and since the notes were written before Leibniz’ own development of calculus concepts and techniques,

• This statement builds on the previous statement.
• “and since” – indicates reasoning number two for what the scholars want to argue for. Reason number one was what we saw in the last statement, the fact that Newton’s book includes a presentation of his calculus concepts and techniques.
• Reasoning number 2: This is also a fact. These notes of Leibniz were written before Leibniz’ own development of calculus concepts and techniques.
• Think and Infer: Can we predict what the scholar’s argument would be even before reading the next statement? Yes.
  • Leibniz’s notes discuss one of Newton’s books on mathematics.
  • This book by Newton discusses his calculus concepts and techniques.
  • Liebniz’s notes, which obviously came later (because it discusses Newton’s book), were written before Leibniz himself developed calculus concepts and techniques.
  • Implication/Prediction: the scholars will argue that Leibniz’s work was derived from Newton (inspired/copied) i.e., the traditional view (both evolved independently) is incorrect.
• BF1:
  • Factual statement.
  • Reasoning #2 behind the scholar’s argument.

it is virtually certain that the traditional view is false.

• This is the conclusion being made by the scholar based on the reasoning highlighted above.
• This is a claim/conclusion made by the scholars (not a fact). This view challenges the traditional view that Newton and Leibniz developed calculus independently.
• So, as per the scholar, the two mathematicians/scientists did not independently develop calculus. Leibniz’s work was derived from Newton’s work.

A more cautious conclusion than this is called for, however.

• This is a claim/conclusion being made by the historian (author).
• This is the first claim made by the author. Before confirming if this is the main conclusion, we need to read the rest of the argument.
• Author/Historian’s claim: A more cautious conclusion than saying that the traditional view is false is needed. In other words, the historian(author) is claiming that the scholar’s conclusion is not cautious/careful enough. It is a criticism of the scholar’s conclusion.
• The word “however” is also a clue that this view is not in the same direction as the scholar’s view.

Leibniz’ notes are limited to early sections of Newton’s book, sections that precede the ones in which Newton’s calculus concepts and techniques are presented.

• This statement is a fact.
• This statement provides the historian’s reasoning to support his/her conclusion above.
• We can now confirm that the last statement was the main conclusion.
• Author/Historian Reasoning for Conclusion:
  • Leibniz’ notes only contain sections of Newton’s book that are before Newton introduces calculus concepts.
  • Implication: Leibniz has not really referred to sections of Newton’s book that talk about calculus. So, we cannot be sure if Leibniz had knowledge of Newton’s calculus concepts. It is possible that Leibniz had no idea about the calculus aspects and arrived at calculus concepts independently.
• BF2:
  • Factual statement
  • Support for Main Conclusion

Visualization of Argument

Let us understand the various claims and how they are supported in the argument.

1. Traditional belief: Newton and Leibniz came up with calculus independently.
   • No support presented
2. Scholar’s conclusion: The above belief is false (against traditional view). (Leibniz’ work is derived from Newton). Based on these points –
   • Leibniz’s notes discuss one of Newton’s books on mathematics.
   • This book by Newton discusses his calculus concepts and techniques.
   • Liebniz’s notes which obviously came later (because it discusses Newton’s book), were written before Leibniz himself developed calculus concepts and techniques.
3. Author’s Conclusion (Main Conclusion): A more cautious conclusion than above is called for (we cannot just say the traditional view is false)- against scholar’s conclusion. Supported by –
   • Leibniz’ notes only contain sections of Newton’s book that are before Newton introduces calculus concepts.

Prethinking

Now let us prethink the roles and relationships of each BF – with each other and with the main conclusion.

Aspect	Type	Relationship with the main conclusion	Relationship with the other BF
BF1	Fact/Reasoning	Not directly related. BF1 supports a conclusion challenged by the Main Conclusion (MC). But it does not challenge the MC.	Not directly related
BF2	Fact/Reasoning	Supports the Main Conclusion	Not directly related

Option Choice Analysis

Choice A: The first provides evidence in support of the overall position that the historian defends; the second is evidence that has been used to support an opposing position.

Incorrect:

BF1 -> BF1 provides evidence in support of the scholar’s position, which the historian attacks (not defends). Hence, BF1 is incorrect.

BF2 -> BF2 provides evidence in support of the main conclusion. “Opposing position of the position the historian defends” cannot be the main conclusion because the main conclusion is obviously the position that historian defends. The only opposing position is the scholar’s argument, which has nothing to do with BF2. Hence, BF2 is also incorrect.

Choice B: The first provides evidence in support of the overall position that the historian defends; the second is that position.

Incorrect:

BF1 -> BF1 provides evidence in support of the scholar’s position, which the historian attacks (not defends). Hence, BF1 is incorrect.

BF2 -> BF2 is a fact, not a position/claim. Hence, BF2 is also incorrect.

Choice C: The first provides evidence in support of an intermediate conclusion that is drawn to provide support for the overall position that the historian defends; the second provides evidence against that intermediate conclusion.

Incorrect:

BF1 -> The only issue is “provide support for.” In reality, the first provides evidence in support of an intermediate conclusion (scholar’s view) that goes against the traditional belief (which the historian defends) and is challenged by the main conclusion. The intermediate conclusion here (the scholar’s conclusion) does not provide support for the overall position taken by the historian at any level. Hence, BF1 is incorrect.

BF2 -> The second provides evidence to support the main conclusion. In the argument, BF2 is not used as evidence against the scholar’s conclusion, only as support for the main conclusion. Hence, BF2 is also incorrect.

Choice D: The first is evidence that has been used to support a conclusion that the historian criticizes; the second is evidence offered in support of the historian’s own position.

Correct:

BF1 -> The first is factual evidence, used as reasoning to support the scholar’s conclusion, which the historian indeed criticizes/challenges. Refer to our prethinking. BF1 is correct.

BF2 -> The second is factual evidence offered in support of the main conclusion, which is indeed the historian’s own position. Hence, BF2 is also correct.

Option D is the correct answer.

Choice E: The first is evidence that has been used to support a conclusion that the historian criticizes; the second is further information that substantiates that evidence.

Incorrect:

BF1 -> The first is factual evidence used as reasoning to support the scholar’s conclusion, which the historian indeed criticizes/challenges. Refer to our prethinking. BF1 is correct.

BF2 -> The second BF does not further substantiate/support the evidence presented in BF1. In fact, it weakens the point made by using that evidence. Hence, BF2 is incorrect.

Core Learnings from this question:

1. Even in Boldface question, we should understand the core logic of the argument. This makes the identification of roles and relationships of each Boldface easier.
2. Focusing on keywords (However, since, etc.) is useful to understand the logical flow of the argument.
3. We need to be extremely careful with option choice analysis in Boldface questions.

Planning to take the GMAT? We can give you access to quality online content to prepare. We are the most reviewed GMAT prep company on the GMAT club with more than 2200+ reviews and have delivered 10x 700+ scores than the average GMATClub partner. Why don’t you take a free trial and judge it for yourself? Write to us at acethegmat@e-gmat.com in case of any queries.