Question

a, b, c, d, and x are all non-zero integers. Is the product \( ax \cdot (bx)^2 \cdot (cx)^3 \cdot (dx)^4 \) negative? Statement (I): \( a < c < x < 0 \)
Statement (II): \( b < d < x < 0 \)

• A. Statement (I) alone is sufficient.
• B. Statement (II) alone is sufficient.
• C. Both statements (I) and (II) are sufficient.
• D. Neither statement is sufficient.

Hint:

When evaluating the sign of a product with exponents, always simplify the expression first. Even powers of non-zero variables are always positive, allowing you to ignore them when determining the sign of the whole product.

Answer 1

The Correct Option is A

Step 1: Understanding the Question:
The objective is to select the grammatically accurate sentence that uses the correlative conjunction pair "neither...nor".


Step 2: Detailed Explanation:
Per English grammar rules for subject-verb agreement, when "neither...nor" links two subjects, the verb must match the subject nearest to it.
Here, the subjects are "the manager" (singular) and "the employees" (plural).
Because "the employees" is adjacent to the verb, a plural verb ("were") is required.
Furthermore, "neither...nor" is the correct conjunction pair, which rules out any options using "neither...or".
Consequently, "Neither the manager nor the employees were aware of the meeting." is the grammatically sound sentence.


Step 3: Final Answer:
The correct choice is (B).