Question

In the figure above, if 0 represents the center of a circular clock and the point of the clock hand is on the circumference of the circle, does the shaded sector of the clock represent more than 10 minutes?
(1)The clock hand has a length of 10.
(2)The area of the sector is greater than 1671.

• A. Data in statement I alone is sufficient.
• B. Data in statement II alone is sufficient.
• C. Data in both statements together is sufficient.
• D. Data in both statements together is not sufficient.
• E. Neither of the Statement I or II is sufficient

Answer 1

The correct option is E Neither of the Statement I or II is sufficient

First, note that this is a Yes/No Data Sufficiency question.
The question "Does the shaded sector of the clock represent more than 10 minutes?" is really asking you about the area of a sector of a circle.
Since 10 minutes is $\frac{1}{6}$ of an hour, you are being asked if the shaded region is equal to more than $\frac{1}{6}$ of the area of the circle.
(1) INSUFFICIENT: The "clock hand" is equal to the radius. Knowing that the radius equals 10 is enough to tell you that the entire area of the circle is equal to $10\pi$. You can rephrase the question as,"Is the are a of the shaded region more than one-sixth of $100\pi$?" You can simplify $\frac{1}{6}$ of $100\pi$ as such:
$\frac{100\pi }{6}=\frac{50\pi }{3}=16.\overline{6}\pi$
Thus, the question can be rephrased as, "Is the area of the shaded region more than $16.\overline{6}\pi$?" However, you don't know anything about the area of the shaded region from this statement alone.
(2) INSUFFICIENT: The area of the sector is more than $16\pi$. By itself, this does not tell you anything about whether the area of the sector is more than $\frac{1}{6}$ the area of the circle, since you do not know the area of the entire circle.
(1) AND (2) INSUFFICIENT: The area of the entire circle is $100\pi$, and the area of the sector is "more than $16\pi$."
Since $\frac{1}{6}$ of the area of the circle is actually $16.\overline{6}\pi$, knowing that the area of the sector is "more than $16\pi$" is still insufficient-the area of the sector could be $16.1\pi$ or something much larger.
The correct answer is (E).