GMAT Question of the Day - Daily to your Mailbox; hard ones only

It is currently 24 Aug 2019, 13:54

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

O is the center of the circle. If line segment DC has length 5, and si

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:

Hide Tags

Find Similar Topics 
CEO
CEO
User avatar
V
Joined: 12 Sep 2015
Posts: 3922
Location: Canada
O is the center of the circle. If line segment DC has length 5, and si  [#permalink]

Show Tags

New post Updated on: 08 Aug 2019, 13:57
1
Top Contributor
00:00
A
B
C
D
E

Difficulty:

  85% (hard)

Question Stats:

39% (03:10) correct 61% (04:01) wrong based on 18 sessions

HideShow timer Statistics

Image

O is the center of the circle. If line segment DC has length 5, and side AB has length \(\sqrt{24}\), what is the length of x?

A) \(\sqrt{15}\)

B) \(2\sqrt{5}\)

C) \(2\sqrt{6}\)

D) \(\sqrt{30}\)

E) \(6\)

Aside: I posted a nearly-identical question a few minutes ago, and realized there was a flaw. So, I deleted the question and posted this corrected version.
Sorry to those who attempted my first post.


Well, it turns out I wasn't finished making flawed questions!! :cry:
Please see my explanation (as to why this is a flawed question) below.

Attachment:
LmRAOvn.png
LmRAOvn.png [ 7.25 KiB | Viewed 409 times ]

_________________
Test confidently with gmatprepnow.com
Image

Originally posted by GMATPrepNow on 08 Aug 2019, 08:00.
Last edited by GMATPrepNow on 08 Aug 2019, 13:57, edited 1 time in total.
GMAT Club Legend
GMAT Club Legend
User avatar
D
Joined: 18 Aug 2017
Posts: 4534
Location: India
Concentration: Sustainability, Marketing
GPA: 4
WE: Marketing (Energy and Utilities)
GMAT ToolKit User Premium Member CAT Tests
Re: O is the center of the circle. If line segment DC has length 5, and si  [#permalink]

Show Tags

New post Updated on: 08 Aug 2019, 11:59
1
GMATPrepNow
giving a try
I solved the question using given answer choices for x
let side OD = a
so radius of circle = 5+a
for ∆ ABD we can say
(√24)^2= ( x)^2+ ( 5+2a)^2 ------(1)
substituting values of x we can clearly see that options c,d,e wont be valid as in that case the relation (1) wont be valid
amongst a & b
I checked with x=\(\sqrt{15}\) & \(2\sqrt{5}\) ; there in value of a is coming out to be -ve...
I am not sure whether which one would be correct.. as value of a is coming an integer for option A ( -4,-1) and fraction for option B ( -7/2,-3/2)
IMO A ;


GMATPrepNow wrote:
Image

O is the center of the circle. If line segment DC has length 5, and side AB has length \(\sqrt{24}\), what is the length of x?

A) \(\sqrt{15}\)

B) \(2\sqrt{5}\)

C) \(2\sqrt{6}\)

D) \(\sqrt{30}\)

E) \(6\)

Aside: I posted a nearly-identical question a few minutes ago, and realized there was a flaw. So, I deleted the question and posted this corrected version.
Sorry to those who attempted my first post.



Attachment:
LmRAOvn.png

_________________
If you liked my solution then please give Kudos. Kudos encourage active discussions.

Originally posted by Archit3110 on 08 Aug 2019, 11:07.
Last edited by Archit3110 on 08 Aug 2019, 11:59, edited 1 time in total.
Director
Director
avatar
P
Joined: 20 Jul 2017
Posts: 637
Location: India
Concentration: Entrepreneurship, Marketing
WE: Education (Education)
Re: O is the center of the circle. If line segment DC has length 5, and si  [#permalink]

Show Tags

New post 08 Aug 2019, 11:56
2
GMATPrepNow wrote:
Image

O is the center of the circle. If line segment DC has length 5, and side AB has length \(\sqrt{24}\), what is the length of x?

A) \(\sqrt{15}\)

B) \(2\sqrt{5}\)

C) \(2\sqrt{6}\)

D) \(\sqrt{30}\)

E) \(6\)

Aside: I posted a nearly-identical question a few minutes ago, and realized there was a flaw. So, I deleted the question and posted this corrected version.
Sorry to those who attempted my first post.



Attachment:
LmRAOvn.png


Angle in a semicircle is 90
—> ∠B = 90

Triangles ADB & BDC are similar
—> DB/AB = CD/BC
—> x/√24 = 5/√(5^2 + x^2)
Squaring on both sides,
—> x^2/24 = 25/(5^2 + x^2)
—> 25x^2 + x^4 = 600
—> x^4 + 25x^2 - 600 = 0
—> x^4 + 40x^2 - 15x^2 - 600 = 0
—> (x^2 + 40)(x^2 - 15) = 0
—> x = √15

IMO Option A

Pls Hit kudos if you like the solution

Posted from my mobile device
Senior Manager
Senior Manager
User avatar
P
Joined: 16 Jan 2019
Posts: 426
Location: India
Concentration: General Management
WE: Sales (Other)
Re: O is the center of the circle. If line segment DC has length 5, and si  [#permalink]

Show Tags

New post 08 Aug 2019, 12:38
1
A perpendicular drawn from the right angle to the hypotenuse in a right traingle divides the triangle into two similar triangles each of which are also similar to the original triangle

By this property, since AC is the diameter which makes ABC a right angled triangle,

ABC, ADB and BDC are similar triangles

From BDC, \(BC=\sqrt{x^2+25}\)

From ABC and BDC

\(\frac{AB}{BC}=\frac{BD}{DC}\)
\(\frac{√24}{\sqrt{x^2+25}}=\frac{x}{5}\)

\(\frac{24}{x^2+25}=\frac{x^2}{25}\)

\(x^4+25x^2-600=0\)
\((x^2+40)(x^2-15)=0\)

\(x^2=15\)
\(x=\sqrt{15}\)

Answer is (A)

Posted from my mobile device
CEO
CEO
User avatar
V
Joined: 12 Sep 2015
Posts: 3922
Location: Canada
Re: O is the center of the circle. If line segment DC has length 5, and si  [#permalink]

Show Tags

New post 08 Aug 2019, 13:54
Top Contributor
Archit3110 wrote:
GMATPrepNow
giving a try
I solved the question using given answer choices for x
let side OD = a
so radius of circle = 5+a
for ∆ ABD we can say
(√24)^2= ( x)^2+ ( 5+2a)^2 ------(1)
substituting values of x we can clearly see that options c,d,e wont be valid as in that case the relation (1) wont be valid
amongst a & b
I checked with x=\(\sqrt{15}\) & \(2\sqrt{5}\) ; there in value of a is coming out to be -ve...
I am not sure whether which one would be correct.. as value of a is coming an integer for option A ( -4,-1) and fraction for option B ( -7/2,-3/2)
IMO A ;


GMATPrepNow wrote:
Image

O is the center of the circle. If line segment DC has length 5, and side AB has length \(\sqrt{24}\), what is the length of x?

A) \(\sqrt{15}\)

B) \(2\sqrt{5}\)

C) \(2\sqrt{6}\)

D) \(\sqrt{30}\)

E) \(6\)

Aside: I posted a nearly-identical question a few minutes ago, and realized there was a flaw. So, I deleted the question and posted this corrected version.
Sorry to those who attempted my first post.



Attachment:
LmRAOvn.png


This is a great approach. In fact, if I had used that approach, I would have seen that the diagram I created cannot exist in our Universe.

When creating the question, I used the similar triangles approach used by Dillesh4096 and firas92 asmd and my calculations yielded an answer of \(\sqrt{15}\) (answer choice A)
However, this means my diagram makes no sense whatsoever.
Notice that, if \(x=\sqrt{15}\), then we can use the Pythagorean Theorem to see that side BC has length \(\sqrt{40}\)
And all of this means that side AC has length 8
In other words, the diameter of the circle is 8, which means the radius is 4.
This is where things get ugly. If the radius is 4, how can side DC = 5?

Ughh!!!!!!
That said, the above solutions are great/valid.
The only issue is that diagram is nonsensical.
My apologies.

Kudos for everyone!!!

Cheers,
Brent
_________________
Test confidently with gmatprepnow.com
Image
GMAT Club Bot
Re: O is the center of the circle. If line segment DC has length 5, and si   [#permalink] 08 Aug 2019, 13:54
Display posts from previous: Sort by

O is the center of the circle. If line segment DC has length 5, and si

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  





cron

Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne