Circle 3

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karthikpandian19: Legendary Member; Posts: 1665; Joined: Thu Nov 03, 2011 7:04 pmFollowed by: 70 members; Thanked: 165 times

by karthikpandian19 » Mon Dec 26, 2011 9:37 pm

P is a circle with radius r. If AB is a chord in circle P, is AB<6?

(1) r=5

(2) The height from the center of P to AB is smaller than 4.

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Source: Beat The GMAT — Data Sufficiency | Mon Dec 26, 2011 9:37 pm

rijul007: Legendary Member; Posts: 588; Joined: Sun Oct 16, 2011 9:42 amFollowed by: 9 members; Location: New Delhi, India; Thanked: 130 times; GMAT Score:720

by rijul007 » Mon Dec 26, 2011 9:58 pm

karthikpandian19 wrote:P is a circle with radius r. If AB is a chord in circle P, is AB<6?

(1) r=5

(2) The height from the center of P to AB is smaller than 4.

(1) r=5

The longest chord in a circle is it diameter

0 < AB < 10

Not sufficient

(2) The height from the center of P to AB is smaller than 4.

a < 4
r = ?
length of AB depends on the value of both a and r

Insufficient

Combining (1) & (2)

r = 5
a < 4

for largest legth of AB,
a = 0
x = âˆš25 = 5
AB = 2x = 10

smallest length of AB,
a = 3.99999999 = 4 approx
x = âˆš(25 - 16) = 3
AB = 6

6 < AB < 10

This answers the ques "Is AB<6? " with a NO

Option C[/b]

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arpan20690: Junior | Next Rank: 30 Posts; Posts: 13; Joined: Thu Dec 08, 2011 10:39 pm

by arpan20690 » Tue Dec 27, 2011 12:43 am

I would like to Change the last part of rijul007's post i.e combining 1) and 2).
let AB = 2x
if we apply right angle formula for the triangle
then x^2 + a^2 = 5^2 ; a^2 = 25 - x^2
and also a^2 < 4^2.
so 25 - x^2 < 16
; x^2 > 9
; x > 3
AB = 2x > 6
So we can answer that AB is not less than 6. So, data SUFFICIENT.

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karthikpandian19: Legendary Member; Posts: 1665; Joined: Thu Nov 03, 2011 7:04 pmFollowed by: 70 members; Thanked: 165 times

by karthikpandian19 » Tue Dec 27, 2011 9:29 pm

OA is C

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