ACCUPLACER Question of the Day

Rationale:

The original sentence contains a run-on, incorrectly joining multiple independent clauses. The correct revision, "Before this innovation, books were laboriously copied by hand. They were expensive and rare, so literacy rates remained low across Europe," effectively corrects this by separating the initial clauses into distinct sentences and appropriately joining the last two with a comma and the coordinating conjunction "so," showing cause and effect.

The option stating "Before this innovation, books were laboriously copied by hand, they were expensive and rare, literacy rates remained low across Europe" incorrectly uses commas to connect independent clauses, creating a comma splice. The choice that begins "Before this innovation, books were laboriously copied by hand; consequently they were expensive and rare..." also contains a comma splice after "rare" and misuses the semicolon before "consequently" without a subsequent comma. Finally, the revision "Before this innovation, books being laboriously copied by hand, expensive and rare, with literacy rates remaining low across Europe" transforms the sentence into an ungrammatical fragment, failing to convey complete thoughts or logical connections.

Rationale:
The word "gauge" in this context means to assess or evaluate. The narrator is attempting to understand or determine the nature of their roommate's expression, specifically looking for "any hint of apprehension or judgment." Therefore, "assess" is the most appropriate meaning, as it captures the act of evaluating or forming an estimate of something.

"Measure" is a common definition of "gauge," but it typically refers to quantifying physical dimensions or amounts, which is not applicable to an emotional expression. "Create" implies bringing something into existence, which is not what the narrator is doing with the expression. "Conceal" means to hide, which is the opposite of trying to observe and understand.

Rationale:
To evaluate $f(g(-1))$, we must first determine the value of the inner function, $g(-1)$. This value then serves as the input for the outer function, $f(x)$. This process demonstrates a cause-and-effect relationship where the output of $g(x)$ acts as the "cause" (input) for $f(x)$ to produce its "effect" (output).

First, calculate $g(-1)$:

• $g(x) = 2x + 1$
• $g(-1) = 2(-1) + 1 = -2 + 1 = -1$

Next, use this result as the input for $f(x)$:

• $f(x) = 3x^2 - x$
• $f(g(-1)) = f(-1) = 3(-1)^2 - (-1) = 3(1) + 1 = 3 + 1 = 4$

Thus, $f(g(-1)) = 4$. Distractor 9 results from reversing the order of composition ($g(f(-1))$). Distractor 30 is obtained by an error in evaluating $g(-1)$ (e.g., calculating $g(-1) = -3$). Distractor 2 is obtained by an algebraic error in evaluating $f(-1)$ (e.g., $3(-1)^2 - (-1)$ is incorrectly computed as $3-1=2$).

Rationale:
The passage introduces the human microbiome and then elaborates on its critical and diverse roles in health, from digestion to immune function and mood. It concludes by emphasizing the importance of 'understanding and nurturing a diverse and balanced microbiome.' Therefore, the author's primary purpose is to inform readers about the microbiome's comprehensive importance and implicitly advocate for its careful management, making the correct option an accurate summary of both purpose and main idea.

Distractor 1 is too narrow; while medications are mentioned as a factor, warning against them is not the primary, overarching purpose of the entire passage, which focuses on the broader importance of the microbiome. Distractor 2 misinterprets the passage's tone and scope; the passage mentions diet but does not 'critique' trends or argue for specific dietary changes in an argumentative manner. Distractor 3 is entirely outside the scope of the passage, which offers no historical overview of microbiological understanding.

Rationale:

The correct revision, "is far more complex than scientists once believed. Each of its numerous components has distinct functions that contribute to the overall health of the cell," successfully corrects all subject-verb agreement errors. The singular subject "structure" requires the singular verb "is," and the singular subject "Each" requires the singular verb "has." Additionally, the plural subject "functions" requires the plural verb "contribute."

The option beginning "are far more complex than scientists once believed" fails to correct the first and third errors, leaving "are" instead of "is" for "structure" and "contributes" instead of "contribute" for "functions." Another incorrect option, which uses "Each of its numerous components have distinct functions that contributes," incorrectly retains "have" for the singular subject "Each" and "contributes" for the plural subject "functions." The final incorrect choice, "is far more complex than scientists once believed. Each of its numerous components has distinct functions that contributes to the overall health of the cell," corrects the first two errors but still incorrectly uses the singular verb "contributes" with the plural subject "functions."