It is currently 23 Oct 2017, 07:27

### 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

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

# In the semicircle above, the length of arc AC is equal to t

Author Message
TAGS:
Moderator
Joined: 18 Apr 2015
Posts: 2158
Followers: 30

Kudos [?]: 313 [1] , given: 1278

In the semicircle above, the length of arc AC is equal to t [#permalink]  19 Jun 2017, 11:52
1
KUDOS
Expert's post
00:00

Difficulty:

5% (low)

Question Stats:

0% (00:00) correct 0% (00:00) wrong based on 0 sessions

In the semicircle above, the length of arc AC is equal to the length of arc BD, and the length of arc AB is less than the length of arc BD.
 Quantity A Quantity B \frac{\text{the length of chord AB}}{\text{the length of chord CD}} \frac{1}{2}

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.
[Reveal] Spoiler: OA

_________________
Intern
Joined: 01 May 2017
Posts: 3
Followers: 0

Kudos [?]: 4 [1] , given: 0

Re: In the semicircle above, the length of arc AC is equal to t [#permalink]  26 Jul 2017, 15:52
1
KUDOS
Senior Manager
Joined: 03 Sep 2017
Posts: 409
Followers: 0

Kudos [?]: 121 [0], given: 64

Re: In the semicircle above, the length of arc AC is equal to t [#permalink]  03 Sep 2017, 08:22
Could someone post an explanation to this question? Would be very appreciated!
GRE Instructor
Joined: 10 Apr 2015
Posts: 638
Followers: 29

Kudos [?]: 450 [3] , given: 3

Re: In the semicircle above, the length of arc AC is equal to t [#permalink]  05 Sep 2017, 16:43
3
KUDOS
Expert's post
Carcass wrote:

In the semicircle above, the length of arc AC is equal to the length of arc BD, and the length of arc AB is less than the length of arc BD.
 Quantity A Quantity B \frac{\text{the length of chord AB}}{\text{the length of chord CD}} \frac{1}{2}

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.

Okay, so here's what we have so far...

As you can see, I've added the entire circle AND I've added the circle's center

Now the question tells us that the length of arc AB is less than the length of arc BD.
However, at this point, I want to investigate what would happen if it were the case that the length of arc AB is equal to the length of arc BD
We'd get something like this...

Notice that all 3 arcs (AC, AB, and BC) all have the SAME length.

This means that each CENTRAL ANGLE that "holds" these 3 equal arcs must also be equal...

Since all three angles are on the same line (the diameter to be exact), they must add to 180°, which means each angle must be 60°

Since OA and OB are the radii of the circle, we can conclude that ∠OAB and ∠OBA must both be equal, which means they both equal 60°

So, ∆OAB is an EQUILATERAL TRIANGLE, which means all 3 sides have equal length.
In fact all 3 sides are equal to the radius of the circle.

Since OC and OD are also radii, we can see that we have a BUNCH of line segments that are all the same length.

At this point, we can see that: (length of chord AB)/(length of chord CD) = 1/2 [since AB = the length of 1 radius, and CD = the length of 2 radii]

So, if it were the case that the length of arc AB is equal to the length of arc BD, then Quantities A and B would be EQUAL.

However, the original question tells us that the length of arc AB is less than the length of arc BD.
From this, we can conclude that chord AB is LESS THAN the radius of the circle.

This means (length of chord AB)/(length of chord CD) < 1/2

[Reveal] Spoiler:
B

RELATED VIDEO

_________________

Brent Hanneson – Founder of greenlighttestprep.com

Check out the online reviews of our course

Moderator
Joined: 18 Apr 2015
Posts: 2158
Followers: 30

Kudos [?]: 313 [0], given: 1278

Re: In the semicircle above, the length of arc AC is equal to t [#permalink]  06 Sep 2017, 03:47
Expert's post
Awesome.

Thank you so much.

Regards
_________________
Re: In the semicircle above, the length of arc AC is equal to t   [#permalink] 06 Sep 2017, 03:47
Display posts from previous: Sort by