Last visit was: 23 Jul 2024, 05:43 It is currently 23 Jul 2024, 05:43
Close
GMAT Club Daily Prep
Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track
Your Progress

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History
Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.
Close
Request Expert Reply
Confirm Cancel
SORT BY:
Date
Tags:
Show Tags
Hide Tags
Math Expert
Joined: 02 Sep 2009
Posts: 94580
Own Kudos [?]: 643207 [2]
Given Kudos: 86728
Send PM
User avatar
Manager
Manager
Joined: 03 Oct 2013
Status:Kitchener
Posts: 64
Own Kudos [?]: 47 [1]
Given Kudos: 144
Location: Canada
Concentration: Finance, Finance
GPA: 2.9
WE:Education (Education)
Send PM
avatar
Manager
Manager
Joined: 25 Mar 2014
Posts: 108
Own Kudos [?]: 126 [0]
Given Kudos: 48
Location: India
Concentration: Operations, Finance
GMAT Date: 05-10-2015
GPA: 3.51
WE:Programming (Computer Software)
Send PM
User avatar
Manager
Manager
Joined: 05 Mar 2015
Status:A mind once opened never loses..!
Posts: 172
Own Kudos [?]: 676 [0]
Given Kudos: 258
Location: India
MISSION : 800
WE:Design (Manufacturing)
Send PM
Re: In the diagram above, O is the center of the circle. What is the leng [#permalink]
Hi

Statement i >> insufficient
We don't know the radius.

Statement ii >> insufficient
We don't know the length of the other two chords, we just can calculate the diameter

Statement i + ii >> sufficient

Answer C
Senior Manager
Senior Manager
Joined: 28 Feb 2014
Posts: 269
Own Kudos [?]: 325 [1]
Given Kudos: 132
Location: United States
Concentration: Strategy, General Management
Send PM
Re: In the diagram above, O is the center of the circle. What is the leng [#permalink]
Bunuel wrote:
Attachment:
cpotg_img4-300x285.png
In the diagram above, O is the center of the circle. What is the length of chord AC?

(1) chord BC = 14
(2) the circle has an area of \(625\pi\)

Kudos for a correct solution.


The triangle formed is a right triangle, we just need to figure out 2 of the sides.

Statement 1: Only 1 side is given
Insufficient

Statement 2: Only 1 side is given
Insufficient

Combined, we have 2 sides and can use pythagorean theorem.
Sufficient

Answer: C
Math Expert
Joined: 02 Sep 2009
Posts: 94580
Own Kudos [?]: 643207 [1]
Given Kudos: 86728
Send PM
Re: In the diagram above, O is the center of the circle. What is the leng [#permalink]
1
Kudos
Expert Reply
Bunuel wrote:

In the diagram above, O is the center of the circle. What is the length of chord AC?

(1) chord BC = 14
(2) the circle has an area of \(625\pi\)

Kudos for a correct solution.


MAGOOSH OFFICIAL SOLUTION:

The fact that AB is a diameter guarantees that angle C = 90º. If we had two sides of right triangle ABC, we could find the third using the Pythagorean Theorem.

Statement #1: this gives us only one side of a right triangle: not helpful. This statement, alone and by itself, is not sufficient.

Statement #2: this allows us to solve for the radius and, hence, the diameter, so we can determine side AB. Nevertheless, this gives us only one side of a right triangle: also not helpful. This statement, alone and by itself, is not sufficient.

Combined statements: We get the length of BC from the first statement, and the length of AB from the second. Now, we have two sides of the right triangle, so we can use the Pythagorean Theorem to solve for the third side, AC. Combined, the statements are sufficient.

Answer = (C)
Manager
Manager
Joined: 13 Dec 2013
Posts: 100
Own Kudos [?]: 128 [0]
Given Kudos: 122
Location: United States (NY)
Concentration: General Management, International Business
GMAT 1: 710 Q46 V41
GMAT 2: 720 Q48 V40
GPA: 4
WE:Consulting (Consulting)
Send PM
Re: In the diagram above, O is the center of the circle. What is the leng [#permalink]
23a2012 wrote:
the answer is C

from the question we know that AB is the diameter and the tringle ACB is right tringle 90-60-30

statment 1 insuff where we can not find AC with no information about the other side AB
statment 2 insuff it allow us just to find AB=50 where no information about other side CB
from 1&2 we have AB&CB so we can find AC



Don't think you can assume it's a 30-60-90 triangle. Flawed reasoning here.
GMAT Club Legend
GMAT Club Legend
Joined: 12 Sep 2015
Posts: 6804
Own Kudos [?]: 30852 [4]
Given Kudos: 799
Location: Canada
Send PM
In the diagram above, O is the center of the circle. What is the leng [#permalink]
2
Kudos
2
Bookmarks
Expert Reply
Top Contributor
Bunuel wrote:
Attachment:
cpotg_img4-300x285.png
In the diagram above, O is the center of the circle. What is the length of chord AC?

(1) chord BC = 14
(2) the circle has an area of \(625\pi\)

Kudos for a correct solution.


Target question: What is the length of chord AC?

Given: O is the center of the circle
If O is the center of the circle, then AB is the circle's DIAMETER
If AB is the DIAMETER, then ∠C = 90°, because ∠C is an inscribed angle containing ("holding") the diameter.
So, let's first add this information to the diagram


Statement 1: chord BC = 14
Notice that the length of chord BC has no bearing on the length of chord AC.
In fact, here are two diagrams that satisfy statement 1:


In the left-hand diagram, the answer to the target question is chord AC has length 20
In the right-hand diagram, the answer to the target question is chord AC has length 30
Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT

Statement 2: the circle has an area of 625π
Area of circle = πr²
So, we can write: πr² = 625π
Divide both sides by π to get: r² = 625
Solve: r = 25
So, the circle's radius = 25, which means the DIAMETER AB has length 50.

This time the length of the diameter has little bearing on the length of chord AC.
In fact, here are two diagrams that satisfy statement 2:


In the left-hand diagram, the answer to the target question is chord AC has length 30
In the right-hand diagram, the answer to the target question is chord AC has length 40
Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT

Statements 1 and 2 combined
When we combine the two statements, we see that we know the lengths of two sides of a RIGHT triangle


So, we COULD apply the Pythagorean Theorem to write: 14² + x² = 50²,
And we COULD solve the equation to get x = 48.
However, performing all of those calculations would be a waste of the time, since we need only show that we COULD answer the target question with certainty.
Since we COULD answer the target question with certainty, the combined statements are SUFFICIENT

Answer: C

Cheers,
Brent

RELATED VIDEO

Originally posted by BrentGMATPrepNow on 07 Feb 2019, 12:19.
Last edited by BrentGMATPrepNow on 17 May 2021, 08:35, edited 1 time in total.
User avatar
Non-Human User
Joined: 09 Sep 2013
Posts: 34048
Own Kudos [?]: 853 [0]
Given Kudos: 0
Send PM
Re: In the diagram above, O is the center of the circle. What is the leng [#permalink]
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
GMAT Club Bot
Re: In the diagram above, O is the center of the circle. What is the leng [#permalink]
Moderator:
Math Expert
94580 posts