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

It is currently 16 Dec 2018, 00:38

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 in December
PrevNext
SuMoTuWeThFrSa
2526272829301
2345678
9101112131415
16171819202122
23242526272829
303112345
Open Detailed Calendar
  • FREE Quant Workshop by e-GMAT!

     December 16, 2018

     December 16, 2018

     07:00 AM PST

     09:00 AM PST

    Get personalized insights on how to achieve your Target Quant Score.
  • Free GMAT Prep Hour

     December 16, 2018

     December 16, 2018

     03:00 PM EST

     04:00 PM EST

    Strategies and techniques for approaching featured GMAT topics

Triangle ABC is right angled at B, while triangle ACD is right angled

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

Hide Tags

DS Forum Moderator
avatar
P
Joined: 21 Aug 2013
Posts: 1412
Location: India
Premium Member
Triangle ABC is right angled at B, while triangle ACD is right angled  [#permalink]

Show Tags

New post 22 Nov 2018, 22:38
2
00:00
A
B
C
D
E

Difficulty:

  85% (hard)

Question Stats:

30% (01:32) correct 70% (01:38) wrong based on 54 sessions

HideShow timer Statistics

Triangle ABC is right angled at B, while triangle ACD is right angled at C. Is the length of CD > length of AB?

(1) Angle BAC = 45 degrees.

(2) Angle ADC = 45 degrees.
Math Expert
User avatar
V
Joined: 02 Aug 2009
Posts: 7108
Re: Triangle ABC is right angled at B, while triangle ACD is right angled  [#permalink]

Show Tags

New post 23 Nov 2018, 19:02
1
amanvermagmat wrote:
Triangle ABC is right angled at B, while triangle ACD is right angled at C. Is the length of CD > length of AB?

(1) Angle BAC = 45 degrees.

(2) Angle ADC = 45 degrees.



So we have a triangle ABC where AC is the hypotenuse and in other triangle AC is a side.
1) angle BAC =45
So triangle BAC is isosceles right angled triangle.
Nothing about D, we could take D to any length
Insufficient

2) angle ADC is 45
So triangle ADC is a right angled triangle with AC=CD
But in other triangle AC is the hypotenuse so it is >the side AB..
Therefore CD is also greater than AB
Sufficient

B
Attachments

PicsArt_11-24-08.27.50.jpg
PicsArt_11-24-08.27.50.jpg [ 35.33 KiB | Viewed 295 times ]


_________________

1) Absolute modulus : http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html
3) effects of arithmetic operations : https://gmatclub.com/forum/effects-of-arithmetic-operations-on-fractions-269413.html


GMAT online Tutor

Director
Director
User avatar
S
Affiliations: CrackVerbal
Joined: 03 Oct 2013
Posts: 533
Location: India
GMAT 1: 780 Q51 V46
Re: Triangle ABC is right angled at B, while triangle ACD is right angled  [#permalink]

Show Tags

New post 29 Nov 2018, 00:10
Top Contributor
Hello,

Since the triangles mentioned in the problem are right-angled triangles, it is natural to think that applying the Pythagoras theorem will help us solve the problem. However, we just need to know the concept that the Hypotenuse is the longest side in a right-angled triangle, to be able to solve this problem.

Using statement 1 alone,

We can say that triangle ABC is an isosceles right-angled triangle and hence, AB = BC. However, this is grossly insufficient to find out a relationship between CD and AB, since we know neither the lengths of the sides of the triangle ACD nor the angles. Hence, statement I alone is insufficient.

Using statement II alone,

We can deduce that triangle ACD is now an isosceles right-angled triangle and hence, CD = AC. Now, in triangle ABC, AC represents the hypotenuse and is, therefore, the longest side in triangle ABC. Hence, it has to be longer than AB; so we can say that CD is definitely longer than AB. Statement II alone is sufficient.

Therefore, the answer option is B.

In such questions, a good thing to do is to draw a diagram and try to put in as many values as possible, before analysing it further. Also, a point to remember about DS questions on Geometry is that any data that gives you a UNIQUE figure/diagram is the data that is going to be sufficient and vice versa.

Hope this helps!

Cheers,
CrackVerbal Academics Team
Attachments

Triangle ABC is right angled at B, while triangle ACD is right angled - 2.jpg
Triangle ABC is right angled at B, while triangle ACD is right angled - 2.jpg [ 63.51 KiB | Viewed 161 times ]

Triangle ABC is right angled at B, while triangle ACD is right angled - 1.jpg
Triangle ABC is right angled at B, while triangle ACD is right angled - 1.jpg [ 73.46 KiB | Viewed 161 times ]


_________________

For more info on GMAT and MBA, follow us on @AskCrackVerbal

Register for the Free GMAT Video Training Course : https://crackverbal.com/MBA-Through-GMAT-2019-Registration

Intern
Intern
avatar
B
Joined: 05 Oct 2018
Posts: 25
Location: United States
Schools: Wharton Exec '21
GMAT 1: 770 Q49 V47
GPA: 3.95
WE: General Management (Other)
Re: Triangle ABC is right angled at B, while triangle ACD is right angled  [#permalink]

Show Tags

New post 29 Nov 2018, 08:34
amanvermagmat wrote:
Triangle ABC is right angled at B, while triangle ACD is right angled at C. Is the length of CD > length of AB?

(1) Angle BAC = 45 degrees.

(2) Angle ADC = 45 degrees.


Need to draw a picture to answer this question.

S1) Easy to see from the image that point D can be moved anywhere you want, so length of CD can be anything. Insufficient
S2) ACD is a 45:45:90, so CD = AC. AC is hypotenuse of ABC so AC > AB. Therefore CD > AB. Answer definitively is yes. Sufficient

Answer B.
GMAT Club Bot
Re: Triangle ABC is right angled at B, while triangle ACD is right angled &nbs [#permalink] 29 Nov 2018, 08:34
Display posts from previous: Sort by

Triangle ABC is right angled at B, while triangle ACD is right angled

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


Copyright

GMAT Club MBA Forum Home| About| Terms and Conditions and Privacy Policy| 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®.