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

 It is currently 15 Oct 2019, 00:16 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

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.  In the diagram below, triangle ABC is right-angled at B. What is the

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

Hide Tags

Math Expert V
Joined: 02 Sep 2009
Posts: 58339
In the diagram below, triangle ABC is right-angled at B. What is the  [#permalink]

Show Tags 00:00

Difficulty:   55% (hard)

Question Stats: 60% (02:38) correct 40% (02:38) wrong based on 47 sessions

HideShow timer Statistics

In the diagram below, triangle ABC is right-angled at B. What is the measure of ∠BAC? (1) BD = BC and AE = AD.
(2) BE = DE.

Attachment: 2017-07-18_1030.png [ 6.99 KiB | Viewed 2080 times ]

_________________
Senior Manager  P
Joined: 24 Jun 2012
Posts: 365
Location: Pakistan
Concentration: Strategy, International Business
GPA: 3.76
Re: In the diagram below, triangle ABC is right-angled at B. What is the  [#permalink]

Show Tags

i have tried every possible thing to get the answer but knowing that two sides are same, i cant get the angle of the other side. I cant find the relationship between the two small triangles even...so E for me
_________________
Push yourself again and again. Don't give an inch until the final buzzer sounds. -Larry Bird
Success isn't something that just happens - success is learned, success is practiced and then it is shared. -Sparky Anderson
-S
Manager  P
Joined: 14 Oct 2015
Posts: 244
GPA: 3.57
In the diagram below, triangle ABC is right-angled at B. What is the  [#permalink]

Show Tags

1
Bunuel wrote:
In the diagram below, triangle ABC is right-angled at B. What is the measure of ∠BAC? (1) BD = BC and AE = AD.
(2) BE = DE.

Attachment:
The attachment 2017-07-18_1030.png is no longer available

It should be C

Statement 1: Insufficient
(1) BD = BC and AE = AD.

This tells us both top and bottom triangles are isosceles but it does not provide us any information about the central triangle.

Statement 2: Insufficient
This tells us central triangle is an isosceles but it does not give out information about the angles.

Lets combined 1 and 2.

From 1, Since $$BD = BC$$, we know $$∠BDC = ∠BCD$$. Let us call this angle x. In the triangle $$BDC$$, third angle $$∠CBD$$ would be equal to $$180 - 2x$$.

Since triangle ABC is right angled at B, $$∠EBD = 90 - (180 - 2x) = -90 + 2x$$

From 2, we know $$BE = DE$$, hence $$∠EBD = ∠EDB = -90 + 2x$$

The third angle in the central triangle would be $$180 - 2 (-90 + 2x) = 360 - 4x$$

Lets name the two equal angles from triangle $$AED = y$$

At point D, we have

$$x + (-90 + 2x) + y = 180$$
$$3x + y = 270$$ --- (1)

At point E, we have

$$360 - 4x + y = 180$$
$$4x - y = 180$$ --- (2)

Solving the two equations, we get the value of y and since two angles in triangle AED are y, the third $$∠BAC$$ can be calculated using $$180 - 2y$$.

Edit: resizing diagram as it was too large.
Attachments diagram.jpg [ 28.2 KiB | Viewed 1727 times ]

_________________
Please hit Kudos if this post helped you inch closer to your GMAT goal.
Procrastination is the termite constantly trying to eat your GMAT tree from the inside.
There is one fix to every problem, working harder!
Director  S
Joined: 21 Mar 2016
Posts: 513
Re: In the diagram below, triangle ABC is right-angled at B. What is the  [#permalink]

Show Tags

anybody can solve this a simpler way?
Math Expert V
Joined: 02 Aug 2009
Posts: 7958
In the diagram below, triangle ABC is right-angled at B. What is the  [#permalink]

Show Tags

Bunuel wrote:
In the diagram below, triangle ABC is right-angled at B. What is the measure of ∠BAC? (1) BD = BC and AE = AD.
(2) BE = DE.

Hi...
A simpler way as someone has asked
COMBINED..
Angle DBC=angle DCB=x
EBD=EDB=r
Now the equations..
1) from angle ABC=90..
r+x=90.....(i)
2) from triangle AED and ∆EBD
y=2R.....(ii)
3) from ∆ADB and ∆BDC..
r+y=2x.....(iii)

Three variables x,y and r.... Three equations above..
Sufficient

C
_________________
Senior Manager  P
Joined: 24 Jun 2012
Posts: 365
Location: Pakistan
Concentration: Strategy, International Business
GPA: 3.76
Re: In the diagram below, triangle ABC is right-angled at B. What is the  [#permalink]

Show Tags

Yes it should be C...Bunuel You are giving Good questions at least your questions are building my concepts....i am able to apply all the rules that i have learned so far...Thanks
_________________
Push yourself again and again. Don't give an inch until the final buzzer sounds. -Larry Bird
Success isn't something that just happens - success is learned, success is practiced and then it is shared. -Sparky Anderson
-S
Manager  P
Joined: 14 Oct 2015
Posts: 244
GPA: 3.57
Re: In the diagram below, triangle ABC is right-angled at B. What is the  [#permalink]

Show Tags

mohshu wrote:
anybody can solve this a simpler way?

Yes, instead of calculating Y, you can calculate X and since we know angle B in the larger triangle ABC is 90, knowing X, we can simply calculate required ∠BAC by 180 - 90 - x. This would not require you to calculate Y.
_________________
Please hit Kudos if this post helped you inch closer to your GMAT goal.
Procrastination is the termite constantly trying to eat your GMAT tree from the inside.
There is one fix to every problem, working harder!
Senior Manager  P
Status: Gathering chakra
Joined: 05 Feb 2018
Posts: 433
Re: In the diagram below, triangle ABC is right-angled at B. What is the  [#permalink]

Show Tags

chetan2u confused by your explanation, see highlighted below

chetan2u wrote:
Hi...
A simpler way as someone has asked
COMBINED..
Angle DBC=angle DCB=x shouldn't it be ∠BDC = ∠DCB? since prompt is DB=BC
EBD=EDB=r
Now the equations..
1) from angle ABC=90..
r+x=90.....(i)
2) from triangle AED and ∆EBD
y=2R.....(ii)
3) from ∆ADB and ∆BDC..
r+y=2x.....(iii)

Three variables x,y and r.... Three equations above..
Sufficient

C Re: In the diagram below, triangle ABC is right-angled at B. What is the   [#permalink] 27 Feb 2019, 13:54
Display posts from previous: Sort by

In the diagram below, triangle ABC is right-angled at B. What is the

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

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