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# If O represents the center of a circular clock and the point of the cl

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Math Expert
Joined: 02 Sep 2009
Posts: 52182
If O represents the center of a circular clock and the point of the cl  [#permalink]

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23 Jun 2015, 22:08
1
4
00:00

Difficulty:

95% (hard)

Question Stats:

38% (02:18) correct 62% (01:53) wrong based on 154 sessions

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If O 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 more than $$16\pi$$.

Kudos for a correct solution.

Attachment:

2015-06-24_1004.png [ 15.92 KiB | Viewed 2739 times ]

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Re: If O represents the center of a circular clock and the point of the cl  [#permalink]

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24 Jun 2015, 02:05
1
Concept : Wall clock is a circular area with 12 sectors of 5 minute each.
Therefore the area of 10 min sector = π*r*r*(2/12)

Considering statement 1:
Radius = 10, Area of circle = πr^2 = 100π
Area of 10 min sector = 100π*(2/12) = 16.66π.
But we don't know if the shaded area is more than 16.66π or less than that.
Hence Insufficient !

Considering statement 2:
Area is more than 16π. But we don't know the radius.
Hence Insufficient

Using 1 & 2 both:
Area of sector is more than 16π
But, if the area is 16.22π, then it is less than 10 mins & if it is more than 16.86π then it is more than 10 mins.

Hence E !!
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If O represents the center of a circular clock and the point of the cl  [#permalink]

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24 Jun 2015, 04:38
1
1
Bunuel wrote:

If O 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 more than $$16\pi$$.

Kudos for a correct solution.

Attachment:
2015-06-24_1004.png

Total angle at the centre of the clock = 360
Total parts in which the angle 360 is divided equally = 12
Angle between any two adjacent numbers in clock (i.e. 1 gap) = 360/12 = 30 degree
Angular measurement of 10 minutes in a clock = Angle between two gaps = 30*2 = 60 degrees

Question REDEFINED : Does the shaded sector of the clock represent more than 60 degrees?

Statement 1: The clock hand has a length of 10

With Radius of the sector, we can't find the angle made by sector

Hence, NOT SUFFICIENT

Statement 2: The area of the sector is more than $$16\pi$$

Area of Sector > (Angle/360)*$$(/pi)r^2$$

But Radius of the sector is unknown, therefore, we can't find the angle made by sector

Hence, NOT SUFFICIENT

Combining the two statements

Area of Sector > $$16\pi$$
Area of Sector = (Angle/360)*$$(/pi)r^2$$
i.e. (Angle/360)*$$(/pi)r^2$$ > $$16\pi$$
i.e. (Angle) > $$16*360 / 10^2$$
i.e. (Angle) > $$57.6$$

i.e. Angle may or may not be Greater than 60 degrees

Hence, NOT SUFFICIENT

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Re: If O represents the center of a circular clock and the point of the cl  [#permalink]

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24 Jun 2015, 09:54
A clock can be divided in 12 equal parts, to find out the shaded region more than 10 minutes or not, we need radios of the clock and angle made by the clock for that region.

A) Radius =10 , shaded region angle is not given so insufficient
B) Area if given but angle and radius is not known, so insufficient

Together A+B) we have radius and area of the sector, so we can find out the angle of the sector, so Sufficient

Thanks,
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Re: If O represents the center of a circular clock and the point of the cl  [#permalink]

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24 Jun 2015, 10:12
lipsi18 wrote:
A clock can be divided in 12 equal parts, to find out the shaded region more than 10 minutes or not, we need radios of the clock and angle made by the clock for that region.

A) Radius =10 , shaded region angle is not given so insufficient
B) Area if given but angle and radius is not known, so insufficient

Together A+B) we have radius and area of the sector, so we can find out the angle of the sector, so Sufficient

Thanks,

Please check the highlighted part and Statement 2.

Statement 2 clearly tells us that that The area of the sector is more than 16π.

which doesn't tell us exact area but it just provides us the range of Areas and in such cases it's NECESSARY to check if the Range gives us a consistent answer or NOT.

Unfortunately the range doesn't provide a consistent answer and hence it's not sufficient
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Re: If O represents the center of a circular clock and the point of the cl  [#permalink]

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29 Jun 2015, 06:09
Bunuel wrote:

If O 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 more than $$16\pi$$.

Kudos for a correct solution.

Attachment:
2015-06-24_1004.png

MANHATTAN GMAT OFFICIAL SOLUTION:

First of all, 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 1/6 of an hour, you are being asked if the shaded region is equal to more than 1/6 of the area of the circle.

(1) INSUFFICIENT: The “clock hand” is equal to the radius. Knowing that the radius = 10 is enough to tell you that the entire area of the circle is equal to 100#. You can rephrase the question as, “Is the area of the shaded region more than one-sixth of $$100\pi$$?” You can simplify 1/6 of 100# as such:

$$\frac{100\pi}{6}=16.(6)\pi$$

Thus, the question can be rephrased as, “Is the area of the shaded region more than $$16.(6)\pi$$?” 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 $$16.(6)\pi$$. By itself, this does not tell you anything about whether the area of the sector is more than 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 $$16.(6)\pi$$.” Since 1/6 of the area of the circle is actually 16.6#, knowing that the area of the sector is “more than 16#” is still insufficient — the area of the sector could be $$16.1\pi$$ or something much larger.

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Re: If O represents the center of a circular clock and the point of the cl  [#permalink]

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24 Mar 2018, 04:52
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