It is currently 24 Feb 2018, 08:11

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

Events & Promotions

Events & Promotions in June
Open Detailed Calendar

If AB=20 and BC=25, what is the length of AD in the figure above?

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

Hide Tags

Expert Post
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 43896
If AB=20 and BC=25, what is the length of AD in the figure above? [#permalink]

Show Tags

New post 01 Aug 2017, 12:21
Expert's post
1
This post was
BOOKMARKED
00:00
A
B
C
D
E

Difficulty:

  25% (medium)

Question Stats:

82% (02:15) correct 18% (02:02) wrong based on 89 sessions

HideShow timer Statistics

Image
If AB=20 and BC=25, what is the length of AD in the figure above?

A. 6
B. 9.6
C. 12
D. 20
E. 24


[Reveal] Spoiler:
Attachment:
T6019.png
T6019.png [ 4.76 KiB | Viewed 956 times ]
[Reveal] Spoiler: OA

_________________

New to the Math Forum?
Please read this: Ultimate GMAT Quantitative Megathread | All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:
GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | Tricky questions from previous years.

Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


What are GMAT Club Tests?
Extra-hard Quant Tests with Brilliant Analytics

Intern
Intern
avatar
B
Joined: 03 Jul 2015
Posts: 9
Schools: INSEAD Jan '17
Re: If AB=20 and BC=25, what is the length of AD in the figure above? [#permalink]

Show Tags

New post 01 Aug 2017, 13:00
ADxBC = AC x AB
ADx25=15x20
AD=13

Sent from my MotoG3-TE using GMAT Club Forum mobile app
1 KUDOS received
BSchool Forum Moderator
User avatar
V
Joined: 26 Feb 2016
Posts: 2089
Location: India
GPA: 3.12
Premium Member CAT Tests
If AB=20 and BC=25, what is the length of AD in the figure above? [#permalink]

Show Tags

New post 01 Aug 2017, 19:21
1
This post received
KUDOS
1
This post was
BOOKMARKED
Image

Given data:AB = 20, BC = 25

Since the triangle is a right angled triangle,
Using Pythagoras theorem
\(BC^2 = AB^2 + AC^2\) => \(AC^2 = BC^2 - AB^2\)
\(AC^2 = 625 - 400\)
\(AC = \sqrt{225} = 15\)

The area of the triangle is 1/2 * AC * BD
The area if also equal to 1/2 * BC * AD
Therefore, AC*BD = BC*AD

Let AD be x
\(20*15 = 25*x\)

Solving for x, \(x = \frac{20*15}{25}\)= 12(Option C)
_________________

Stay hungry, Stay foolish

2017-2018 MBA Deadlines

Class of 2020: Rotman Thread | Schulich Thread
Class of 2019: Sauder Thread

VP
VP
avatar
P
Joined: 22 May 2016
Posts: 1350
Premium Member CAT Tests
If AB=20 and BC=25, what is the length of AD in the figure above? [#permalink]

Show Tags

New post 02 Aug 2017, 07:10
1
This post was
BOOKMARKED
Bunuel wrote:
Image
If AB=20 and BC=25, what is the length of AD in the figure above?

A. 6
B. 9.6
C. 12
D. 20
E. 24
[Reveal] Spoiler:
Attachment:
T6019.png

These triangles (ABC and DAB) are similar 3-4-5 right triangles.

Both have one 90° angle, and angle B is common to both. If two angles are equal, the third is equal. (AA = AAA = similar triangles.)

Whenever a right triangle has longer leg length that is a multiple of 4 (20), and a hypotenuse that is a multiple of 5 (25), the figure is a 3-4-5 right triangle.

Or find AC, and the 3x-4x-5x ratio will be clear. Let AC = a, AB = b, and BC = c. By Pythagorean theorem, \(a^2 + b^2 = c^2\)

\(a^2 + 20^2 = 25^2\)
\(a^2 + 400 = 625\)
\(a^2 = 225\)
\(a = 15\) = AC

15-20-25 divided by 5 throughout = 3-4-5 side ratio

Smaller triangle DAB must also be a 3-4-5 right triangle. Its hypotenuse AB = 20. To find length of shorter leg AD, find multiplier, using hypotenuse AB. 3x: 4x: 5x --> 5x is hypotenuse, 3x is shorter leg.

5x = 20
x = 4 = multiplier
AD corresponds with AC. Both are the shorter leg, i.e., 3x.

3x = (3)(4) = 12

Answer C
_________________

At the still point, there the dance is. -- T.S. Eliot
Formerly genxer123

If AB=20 and BC=25, what is the length of AD in the figure above?   [#permalink] 02 Aug 2017, 07:10
Display posts from previous: Sort by

If AB=20 and BC=25, what is the length of AD in the figure above?

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


GMAT Club MBA Forum Home| About| Terms and Conditions| GMAT Club Rules| Contact| Sitemap

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

Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.