BTGmoderatorDC wrote: ↑

Thu May 28, 2020 6:29 pm

QWSA.jpg

In the figure shown above, O represents the center of a circular 60- minute timer. If the minute-hand moves through the shaded region shown, does the shaded region represent more than 10 minutes on the timer?

(1) The minute-hand has a length of 10.

(2) The area of the sector is greater than 16π

OA E

Source: Manhattan Prep

Given the information, if the minute had moved more than 10 minutes, then the area of the sector/shaded region must be greater than 10/60 = 1/6 of the area of the circle

Question rephrased: Is the area of the shaded region greater than 1/6 of the area of the circle?

Let's take each statement one by one.

(1) The minute-hand has a length of 10.

We can get the area of the circle = π*10^2 = 100π, but we do not have any information about the shaded region. Insufficient.

(2) The area of the sector is greater than 16π.

We have some information about the area of the shaded region, but we do not know the area of the circle. Insufficient.

(1) and (2) together

Case 1: If the area of the sector is almost 16π.

Ratio of area of shaded region / area of circle = 16π/100π = 1/(100/16) = 1/6.25

Since 1/6.25 < 1/6, the answer is no.

Case 2: If the area of the sector is much larger than 16π. Say it is 50π.

Ratio of area of shaded region / area of circle = 50π/100π = 1/2

Since 1/2 > 1/6, the answer is yes.

No unique answer. Insufficient.

The correct answer: E

Hope this helps!

-Jay
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