Combinatorics deals with problems involving counting... This kind of counting is sometimes used in the modeling of several physical phenomena. Often, in such models, the different combinatorial possibilities are assigned probability values. Assigning probabilities enables the computation of the average values of physical quantities.
Consider the following statements:
P: Combinatorics is always invoked in the modeling of physical phenomena.
Q: Modeling some physical phenomena involves assigning probabilities to combinatorial possibilities in order to compute average values of physical quantities.
Based on the passage above, what can be inferred about statements P and Q?

Question

The passage below is accompanied by four questions. Based on the passage, choose the best answer for each question.
For early postcolonial literature, the world of the novel was often the nation. Postcolonial novels were usually [concerned with] national questions. Sometimes the whole story of the novel was taken as an allegory of the nation, whether India or Tanzania. This was important for supporting anti-colonial nationalism, but could also be limiting - land-focused and inward looking.
My new book "Writing Ocean Worlds" explores another kind of world of the novel: not the village or nation, but the Indian Ocean world. The book describes a set of novels in which the Indian Ocean is at the centre of the story. It focuses on the novelists Amitav Ghosh, Abdulrazak Gurnah, Lindsey Collen and Joseph Conrad [who have] centred the Indian Ocean world in the majority of their novels. . . Their work reveals a world that is outward-looking full of movement, border-crossing and south-south interconnection. They are all very different - from colonially inclined (Conrad) to radically anti-capitalist (Collen), but together draw on and shape a wider sense of Indian Ocean space through themes, images, metaphors and language. This has the effect of remapping the world in the reader's mind, as centred in the interconnected global south. ... The Indian Ocean world is a term used to describe the very long-lasting connections among the coasts of East Africa, the Arab coasts, and South and East Asia.
These connections were made possible by the geography of the Indian Ocean. For much of history, travel by sea was much easier than by land, which meant that port cities very far apart were often more easily connected to each other than to much closer inland cities. Historical and archaeological evidence suggests that what we now call globalisation first appeared in the Indian Ocean. This is the interconnected oceanic world referenced and produced by the novels in my book. For their part Ghosh, Gurnah, Collen and even Conrad reference a different set of histories and geographies than the ones most commonly found in fiction in English. Those [commonly found ones] are mostly centred in Europe or the US, assume a background of Christianity and whiteness, and mention places like Paris and New York. The novels in [my] book highlight instead a largely Islamic space, feature characters of colour and centralise the ports of Malindi, Mombasa, Aden, Java and Bombay. . . . It is a densely imagined, richly sensory image of a southern cosmopolitan culture which provides for an enlarged sense of place in the world.
This remapping is particularly powerful for the representation of Africa. In the fiction, sailors and travellers are not all European. . . African, as well as Indian and Arab characters, are traders, nakhodas (dhow ship captains), runaways, villains, missionaries and activists. This does not mean that Indian Ocean Africa is romanticised. Migration is often a matter of force; travel is portrayed as abandonment rather than adventure, freedoms are kept from women and slavery is rife. What it does mean is that the African part of the Indian Ocean world plays an active role in its long, rich history and therefore in that of the wider world.

Answer 1

A reliable technique for passage-inference questions is to match the strength/quantifier words in each statement against the strength/quantifier words used in the passage itself, since such questions frequently hinge on this distinction rather than on new facts.

Scan the passage for quantifier words: it uses "sometimes" (for how often combinatorics is used in modeling physical phenomena) and "often" (for how often combinatorial possibilities are assigned probability values within such models). Both are partial or qualified quantifiers - they mean "in some cases", not "in every case".

Now scan statement P: it uses the word "always", a universal quantifier. Comparing this to the passage's "sometimes", there is a direct mismatch in strength - the passage supports only a partial claim, but P makes a universal claim. A universal claim is not proven true merely because a partial version of it is true, so P cannot be verified from the passage and must be treated as False.

Now scan statement Q: it uses the word "some", a partial quantifier, which matches the passage's own partial framing ("sometimes"/"often"). The specific mechanism Q describes - assigning probabilities to combinatorial possibilities to compute average values - is stated almost word for word in the passage's final two sentences. Since both the quantifier strength and the factual content match the passage exactly, Q is verifiably True.

This quantifier-matching check gives the same result as the direct content check: P is False, Q is True, which corresponds to option (B).

$\boxed{\text{P False, Q True}}$

Answer 2

A reliable technique for passage-inference questions is to match the strength/quantifier words in each statement against the strength/quantifier words used in the passage itself, since such questions frequently hinge on this distinction rather than on new facts.

Scan the passage for quantifier words: it uses "sometimes" (for how often combinatorics is used in modeling physical phenomena) and "often" (for how often combinatorial possibilities are assigned probability values within such models). Both are partial or qualified quantifiers - they mean "in some cases", not "in every case".

Now scan statement P: it uses the word "always", a universal quantifier. Comparing this to the passage's "sometimes", there is a direct mismatch in strength - the passage supports only a partial claim, but P makes a universal claim. A universal claim is not proven true merely because a partial version of it is true, so P cannot be verified from the passage and must be treated as False.

Now scan statement Q: it uses the word "some", a partial quantifier, which matches the passage's own partial framing ("sometimes"/"often"). The specific mechanism Q describes - assigning probabilities to combinatorial possibilities to compute average values - is stated almost word for word in the passage's final two sentences. Since both the quantifier strength and the factual content match the passage exactly, Q is verifiably True.

This quantifier-matching check gives the same result as the direct content check: P is False, Q is True, which corresponds to option (B).

$\boxed{\text{P False, Q True}}$

Show Hint

The Correct Option is B

Solution and Explanation

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