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A and B are points on the circumference of the circle with c

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Carcass

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Joined: 18 Apr 2015

Posts: 25502

A and B are points on the circumference of the circle with c [#permalink]

16 Oct 2018, 09:58

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A and B are points on the circumference of the circle with center O (not shown). The length of chord AB is 15.

Quantity A	Quantity B
Circumference of circle O	$12\pi$

Quantity A is greater.
Quantity B is greater.
The two quantities are equal.
The relationship cannot be determined from the information given.

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GreenlightTestPrep

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Re: A and B are points on the circumference of the circle with c [#permalink]

16 Oct 2018, 13:24

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Carcass wrote:

A and B are points on the circumference of the circle with center O (not shown). The length of chord AB is 15.

Quantity A	Quantity B
Circumference of circle O	$12\pi$

Quantity A is greater.
Quantity B is greater.
The two quantities are equal.
The relationship cannot be determined from the information given.

KEY CONCEPT: If the length of chord AB is 15, then the diameter of the circle is AT LEAST 15 (this occurs when the chord IS the diameter).

Circumference = (π)(diameter)
So, if the diameter is 15, then the circumference 15π
So, the circumference of the circle is AT LEAST 15π

We get:
Quantity A: AT LEAST 15π
Quantity B: 12π

Answer: A

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harishsridharan

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Joined: 04 Jan 2019

Posts: 61

A and B are points on the circumference of the circle [#permalink]

Updated on: 20 Oct 2020, 20:54

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A and B are points on the circumference of the circle with center O (not shown). The length of the chord AB is 15.

Quantity A	Quantity B
Circumference of the circle	$ 12\pi $

A) Quantity A is greater.
B) Quantity B is greater.
C) The two quantities are equal.
D) The relationship cannot be determined from the information given.

Originally posted by harishsridharan on 20 Oct 2020, 11:10.
Last edited by harishsridharan on 20 Oct 2020, 20:54, edited 10 times in total.

cote

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Joined: 11 Aug 2020

Posts: 45

Re: A and B are points on the circumference of the circle [#permalink]

20 Oct 2020, 18:27

harishsridharan wrote:

A and B are points on the circumference of the circle with center O (not shown). The length of the chord AB is 15.

A chord is the straight line BX (in the figure). We know that the length of the maxium chord we can construct is closest to the diameter of the circle. In an extreme case, lets suppose that the length of the chord is the diameter of the circle . In that case, we have:

$diameter = 15$
therefore,
$r = 7.5$
In conclusion, the length of the circumference is given by:
$C = 2\pi r$
$C = 15\pi$

In this case, A > B, option A.

Now, lets suppose that the chord is less than the diameter. In this situation, we are completely sure that the diameter is more than 15, therefore, the length of the circumference is more than $15\pi$. In conclusion, A > B, Option A.

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Papist

Manager

Joined: 25 Jul 2020

Posts: 75

Re: A and B are points on the circumference of the circle [#permalink]

30 Oct 2020, 13:57

1) All diameters are chords but not all chords are diameters
2) The diameter is the longest line in the circle

Using these two rules, we can conclude that the diameter of our circle is equal to or greater than 15, and its circumference is thus equal to or greater than 15*pi. Therefore Quantity A will always be greater.

BelalHossain

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Joined: 23 Dec 2019

Posts: 50

Concentration: Finance, Economics

GMAT 1: 690 Q47 V38

GRE 1: Q165 V155

Re: A and B are points on the circumference of the circle with c [#permalink]

30 Mar 2021, 08:59

The diameter is the largest chord.
if chord= 15, diameter is 15 or more than 15.
so, circumference is 15 pi or more than 15pi.

So, Q A is greater.

witamar

Intern

Joined: 02 Jul 2020

Posts: 26

Re: A and B are points on the circumference of the circle with c [#permalink]

15 Apr 2022, 13:30

Piece of cake.
If the chord AB is the diameter of the circunsference, its perimeter is 15π which is larger than 12π.
If the chord AB isn´t the diameter of the circunsference, its perimeter is larger than 15π which is larger than 12π.

Answer A