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

It is currently 23 Oct 2019, 14:12

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

In the figure above, if BD is perpendicular to AC and AC = 21, then AD

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

Hide Tags

Find Similar Topics 
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 58464
In the figure above, if BD is perpendicular to AC and AC = 21, then AD  [#permalink]

Show Tags

New post 25 Feb 2019, 02:46
00:00
A
B
C
D
E

Difficulty:

  25% (medium)

Question Stats:

83% (01:22) correct 17% (01:51) wrong based on 36 sessions

HideShow timer Statistics

VP
VP
User avatar
D
Joined: 31 Oct 2013
Posts: 1468
Concentration: Accounting, Finance
GPA: 3.68
WE: Analyst (Accounting)
CAT Tests
Re: In the figure above, if BD is perpendicular to AC and AC = 21, then AD  [#permalink]

Show Tags

New post 25 Feb 2019, 03:01
Bunuel wrote:
Image
In the figure above, if BD is perpendicular to AC and AC = 21, then AD =

A. 12
B. 13
C. 20
D. 21
E. 25

Attachment:
2019-02-25_1345.png



\(BD^2 = 13^2 - 5^2\)

\(BD^2 = 144\)

BD = 12.

Given ,

AC = 21

BC = 5

AB = 16.

\(AD^2 = BD^2 + AB^2\)

\(AD^2 = 12^2 + 16^2\)

\(AD^2 = 144 + 256\)

\(AD^2 = 400\)

AD = 20.

C is the correct answer.
Director
Director
User avatar
D
Joined: 28 Jul 2016
Posts: 614
Location: India
Concentration: Finance, Human Resources
GPA: 3.97
WE: Project Management (Investment Banking)
Reviews Badge
Re: In the figure above, if BD is perpendicular to AC and AC = 21, then AD  [#permalink]

Show Tags

New post 25 Feb 2019, 20:39
Triangle BCD is a right angle triangle
thus \(BD^2\)=\(CD^2\)-\(BC^2\)
hence \(13^2\)-\(5^2\) =144
BD=12

now considering other right angle triangle ABD
\(BD^2+ AB^2 = AD^2\)
\(12^2 +(21-5)^2 = 12^2+16^2 = 400\)
thus AD =20

Answer C
e-GMAT Representative
User avatar
V
Joined: 04 Jan 2015
Posts: 3092
Re: In the figure above, if BD is perpendicular to AC and AC = 21, then AD  [#permalink]

Show Tags

New post 25 Feb 2019, 22:22

Solution


Given:
    • In the given figure, BD is perpendicular to AC
    • AC = 21

To find:
    • The length of AD

Approach and Working:
As BD is perpendicular to AC, we can say triangle DBC and triangle DBA are both right-angled triangles.

In triangle DBC,
    • DC = 13 and BC = 5
    • Therefore, from Pythagoras Theorem, we can say DB = \(\sqrt{13^2 – 5^2}\) = 12

In triangle DBA,
    • DB = 12 and BA = 21 – 5 = 16
    • Therefore, from Pythagoras Theorem, we can say AD = \(\sqrt{12^2 + 16^2}\) = 20

Hence, the correct answer is option C.

Answer: C

Image

_________________
Veritas Prep GMAT Instructor
User avatar
V
Joined: 16 Oct 2010
Posts: 9705
Location: Pune, India
Re: In the figure above, if BD is perpendicular to AC and AC = 21, then AD  [#permalink]

Show Tags

New post 26 Feb 2019, 01:15
Bunuel wrote:
Image
In the figure above, if BD is perpendicular to AC and AC = 21, then AD =

A. 12
B. 13
C. 20
D. 21
E. 25

Attachment:
2019-02-25_1345.png


Use pythagorean triplets:

Triangle BCD is a right triangle. Since hypotenuse is 13 and one leg is 5, the other leg BD = 12 (since 5-12-13 is a pythagorean triplet)

Triangle ABD is also a right triangle such that AB = 21 - 5 = 16 and BD = 12. The two legs are 12 and 16 (in the ratio 3:4). So this is a multiple of pythagorean triplet 3-4-5 with a multiplier of 4. The hypotenuse AD will be 5*4 = 20

Answer (C)
_________________
Karishma
Veritas Prep GMAT Instructor

Learn more about how Veritas Prep can help you achieve a great GMAT score by checking out their GMAT Prep Options >
GMAT Club Bot
Re: In the figure above, if BD is perpendicular to AC and AC = 21, then AD   [#permalink] 26 Feb 2019, 01:15
Display posts from previous: Sort by

In the figure above, if BD is perpendicular to AC and AC = 21, then AD

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





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