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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.

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Solution

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 16 of an hour, you are being asked if the shaded region is equal to more than 16 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 10π. You can rephrase the question as,"Is the are a of the shaded region more than one-sixth of 100π?" You can simplify 16 of 100π as such:

100π6=50π3=16.¯¯¯6π

Thus, the question can be rephrased as, "Is the area of the shaded region more than 16.¯¯¯6π?" 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 16π. By itself, this does not tell you anything about whether the area of the sector is more than 16 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 100π, and the area of the sector is "more than 16π."

Since 16 of the area of the circle is actually 16.¯¯¯6π, knowing that the area of the sector is "more than 16π" is still insufficient-the area of the sector could be 16.1π or something much larger.

The correct answer is (E).

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 16 of an hour, you are being asked if the shaded region is equal to more than 16 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 10π. You can rephrase the question as,"Is the are a of the shaded region more than one-sixth of 100π?" You can simplify 16 of 100π as such:

100π6=50π3=16.¯¯¯6π

Thus, the question can be rephrased as, "Is the area of the shaded region more than 16.¯¯¯6π?" 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 16π. By itself, this does not tell you anything about whether the area of the sector is more than 16 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 100π, and the area of the sector is "more than 16π."

Since 16 of the area of the circle is actually 16.¯¯¯6π, knowing that the area of the sector is "more than 16π" is still insufficient-the area of the sector could be 16.1π or something much larger.

The correct answer is (E).

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