In the figure shown above, O represents the center of a circular 60

Question

https://gmatclub.com/forum/download/file.php?id=62974 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 Untitled.png

iridescent995 · Answer

Figure not provided

Bunuel · Answer

_________________________
Fixed. Thank you!

LamboWalker · Answer

For the minute hand to have moved at least 10 min, the shaded portion would have to be at least 2/12 or 1/6 of the total area of the circle.

Statement (1) 
Radium = 10cm. Clearly insufficient, no info about the shaded region.

Statement (2) 
Area of the sector given but nothing about how it compares to the total area of the circle. Insufficient.

(1) & (2)  
Area of timer =  100π 
For the shaded region to represent more than 10 min, area of the sector must be at least  \frac{100π}{6}  or  16.67π 
Even if the shaded region area is greater than  16π , it could be either  16.2π  (less than 10 min) or  17π  (more than 10 min).

No unique answer hence insufficient  (E) .

DHRJ0032 · Answer

question asks if angle covered by minute has is greater than 60 deg?
area of sector=(x/360)*pi r^2
1)r=10 units 
INSUFFICIENT.

2)area >16pi
(x/360)r^2>16
dont know about r.
INSUFFICIENT.

On combining,
x>57.6 degree

if x=59 NO
if x=61 YES

INSUFFICIENT

E it is.

Fdambro294 · Answer

Each 5 minutes of a 360 degree Circular Clock represents an Arc on the circumference = 30 degrees

10 minutes ——-> represents a 60 degree Arc

For the Shaded Sector Area to be greater than > 10 minutes

The Sector Area must be greater than > (60 / 360) * (Area of Circular Clock)

as a percentage, the question be rephrased as:

Is: (Shaded Sector Area) > (16.66%) of (Area) ?

s1: the length of the minute hand gives us the length of the radius, but we have no way to determine the Central Angle that defines the shaded Sector Area

Not sufficient

S2: shaded sector area > 16(pi)

However, we do not know how big the circular clock is.

We do not know if 16(pi) represents more or less than 16.66% of the Circular Area

Not sufficient

(1) + (2)

Given the Radius = 10 ———-> Area of Circular Face = 100(pi)

Now we can determine the sector area’s relative portion of the entire circle

Statement 2 says: Sector area > 16(pi)

As a percentage of the entire circular figure:

16(pi) / 100(pi) = 16/100 = 16% of Area

Thus we know that:

S2: Shaded Sector Area > (16%) of (Area)

Q: is shaded Sector Area > (16.66%) of (Area)?

Could be yes or no

E

Neither/nor

Posted from my mobile device

bumpbot · Answer

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In the figure shown above, O represents the center of a circular 60

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In the figure shown above, O represents the center of a circular 60

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