Is point Q the center of the circle?

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gmattesttaker2: Legendary Member; Posts: 641; Joined: Tue Feb 14, 2012 3:52 pmFollowed by: 8 members; Thanked: 11 times

by gmattesttaker2 » Mon Feb 03, 2014 10:15 pm

Hello,

Can you please assist with this:

Point Q lies in the interior of a particular circle. Is point Q the center of the circle?

(1) There exist points A, B, and C, all distinct points on the circle's circumference, such that the distances QA, QB, and QC are identical.

(2) At least two different diameters of the circle contain point Q.

OA: D

I tried to solve this as follows:

1) My understanding was that Q has to be the center of the circle in-order for the distances QA, QB and QC to be the same. Hence suff.

2) I was not sure if there can be 2 different diameters. I thought that there is only 1 diameter.

Thanks for your help,
Sri

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Source: Beat The GMAT — Data Sufficiency | Mon Feb 03, 2014 10:15 pm

sanju09: GMAT Instructor; Posts: 3650; Joined: Wed Jan 21, 2009 4:27 amFollowed by: 80 members; Location: India; Thanked: 267 times; GMAT Score:760

by sanju09 » Tue Feb 04, 2014 1:02 am

gmattesttaker2 wrote:Hello,

Can you please assist with this:

Point Q lies in the interior of a particular circle. Is point Q the center of the circle?

(1) There exist points A, B, and C, all distinct points on the circle's circumference, such that the distances QA, QB, and QC are identical.

(2) At least two different diameters of the circle contain point Q.

OA: D

I tried to solve this as follows:

1) My understanding was that Q has to be the center of the circle in-order for the distances QA, QB and QC to be the same. Hence suff.

2) I was not sure if there can be 2 different diameters. I thought that there is only 1 diameter.

Thanks for your help,
Sri

Two diameters of a circle always intersect at the center, hence Q is the center of the circle. There are infinitely many diameters to a circle.

The mind is everything. What you think you become. -Lord Buddha

Sanjeev K Saxena
Quantitative Instructor
The Princeton Review - Manya Abroad
Lucknow-226001

www.manyagroup.com

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Bill@VeritasPrep: GMAT Instructor; Posts: 1248; Joined: Thu Mar 29, 2012 2:57 pmFollowed by: 192 members; Location: Everywhere; Thanked: 503 times; GMAT Score:780

by Bill@VeritasPrep » Tue Feb 04, 2014 10:26 am

There is one length for the diameter, but you can draw it any number of ways by connecting different points on the circumference through the center of the circle.

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