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

 It is currently 20 Oct 2019, 14:34 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 figure above, what is the value of x?

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

Hide Tags

Manager  Joined: 09 Feb 2013
Posts: 111
In the figure above, what is the value of x?  [#permalink]

Show Tags

10
10 00:00

Difficulty:   95% (hard)

Question Stats: 45% (02:23) correct 55% (02:52) wrong based on 230 sessions

HideShow timer Statistics

Attachment: 1.gif [ 2.64 KiB | Viewed 6674 times ]
In the figure above, what is the value of x?

(1) AD = AE = BE = CD = BC
(2) x = y

_________________
Kudos will encourage many others, like me.
Good Questions also deserve few KUDOS.

Originally posted by emmak on 25 Mar 2013, 22:57.
Last edited by Bunuel on 26 Mar 2013, 01:22, edited 1 time in total.
Edited the question.
Manager  Joined: 06 Jun 2012
Posts: 119
Re: In the figure above, what is the value of x?  [#permalink]

Show Tags

5
1
A little simpler way

Statement 1:

Angle BEC = z; As AE = EB = CD ==> we have Angle EBD = Angle ECD =x (Isosceles Triangle)
z = 2x (exterior angle theorem)
As BE = BC ==> z = x+y ==> 2x = x + y; means y =x

For Triangle ABC, Angle ACB + Angle CBA + Angle BAC = 180
(x+y) + (x+y) + x = 180
as x = y ==> x =y = 36
Statement 1 sufficient

Statement 2: clearly insufficient

Ans A
_________________
Please give Kudos if you like the post
General Discussion
GMAT Tutor G
Status: Tutor - BrushMyQuant
Joined: 05 Apr 2011
Posts: 622
Location: India
Concentration: Finance, Marketing
Schools: XLRI (A)
GMAT 1: 700 Q51 V31 GPA: 3
WE: Information Technology (Computer Software)
Re: In the figure above, what is the value of x?  [#permalink]

Show Tags

2
1
emmak wrote:
Attachment:
The attachment 1.gif is no longer available
In the figure above, what is the value of x?

(1) AD = AE = BE = CD = BC
(2) x = y

Figure attached
STAT1.

Consider Triangle BCD
sum of all three angles = 180
so, y + b + d + e = 180

Also, BC = CD
=> b = d + e

so, equation becomes
y + d + e + d + e = 180
y + 2d + 2e= 180 ... (1)

Consider traingle BCE
sum of all three angles = 180
so, a + c+ y + e = 180

Also, BC = BE
so, a = c+y
so, equation becomes

y + c + y+ c+ y = 180
3y + 2c = 180 ...(2)

Consider traingle ABC
sum of all three angles = 180
so, x + y + c+ d + e = 180 ...(3)

Consider traingle AEB
AE = EB
so, x = d ...(4)

so, x = c ...(5)

putting d=x (1) becomes
2x + y + 2e = 180 ...(6)

putting c=x in (2) becomes
2x + 3y = 180 ...(7)

putting c=x and d=x in (3) we have
3x+y+e=180 ...(8)

mutiply (8) by 2 and subtract from (6) we have
4x + y = 180 ...(9)

equating (7) and (9) we have
2x+ 3y = 4x+y
=> 2y = 2x
or x=y
putting x=y in (7) we have
5x= 180
x= 36

So, STAT1 is sufficient

STAT2
STAT2 is not sufficient as we dont have relationship between any other angles.

So, Answer will be A.
Will reply in sometime with a smaller and more geometric solution if i get in sometime!

Hope it helps!
Attachments figure.png [ 14.6 KiB | Viewed 6466 times ]

_________________
Manager  Status: Trying.... & desperate for success.
Joined: 17 May 2012
Posts: 55
Location: India
Schools: NUS '15
GPA: 2.92
WE: Analyst (Computer Software)
Re: In the figure above, what is the value of x?  [#permalink]

Show Tags

emmak wrote:
Attachment:
1.gif
In the figure above, what is the value of x?

(1) AD = AE = BE = CD = BC
(2) x = y

Good question and quite a learning...

Out of curiousity, can this sum be solved in less than 2mins that too under "GMAT exam" conditions that too at first sight??
Manager  Joined: 07 May 2012
Posts: 52
Location: United States
Re: In the figure above, what is the value of x?  [#permalink]

Show Tags

summer101 wrote:
A little simpler way

Statement 1:

Angle BEC = z; As AE = EB = CD ==> we have Angle EBD = Angle ECD =x (Isosceles Triangle)
z = 2x (exterior angle theorem)
As BE = BC ==> z = x+y ==> 2x = x + y; means y =x

For Triangle ABC, Angle ACB + Angle CBA + Angle BAC = 180
(x+y) + (x+y) + x = 180
as x = y ==> x =y = 36
Statement 1 sufficient

Statement 2: clearly insufficient

Ans A

Could you please elaborate on the highlighted one . As to , how did you arrive at Angle EBD = Angle ECD ??

Thanks,
Jyothi
_________________
Jyothi hosamani
Board of Directors P
Joined: 17 Jul 2014
Posts: 2509
Location: United States (IL)
Concentration: Finance, Economics
GMAT 1: 650 Q49 V30 GPA: 3.92
WE: General Management (Transportation)
Re: In the figure above, what is the value of x?  [#permalink]

Show Tags

this is my approach.
we can rewrite the sum of the big triangles as:
180=x+2z
where z = 180-2x.

based on statement 1, we can solve for x.
statement 2 doesn't tell us much.
Attachments Untitled.jpg [ 99.53 KiB | Viewed 3006 times ]

Intern  Joined: 18 Aug 2012
Posts: 9
GMAT 1: 730 Q50 V39 In the figure above, what is the value of x?  [#permalink]

Show Tags

Attachment: Pic.png [ 38.87 KiB | Viewed 2999 times ]

Detailed Solution

Step-I: Given Info

The question asks us to find the value of x as indicated in the figure, using the 2 statements given.

Step-II: Interpreting the Question Statement

To find the value of x from the given figure, we have to make use of different concepts of geometry based on the information given in the individual statements.
We will also modify the figure as per our convenience to be able to solve the problems easily.
The modified figure is attached as Pic.png(Attached), with all angles marked.

Step-III: Statement-I

Statement- I gives us the information that AD = AE = BE = CD = BC.

Now from the Pic.png(Attached) and using the information in statement 1, we know

Equation 1: x=t=z (Because AE=BE=AD) (Concept Used: Angles opposite to equal sides are equal)
Equation 2: v=t+s & w=z+y (Because BE=BC=CD) (Concept Used: Angles opposite to equal sides are equal)
Equation 3: w=x+t (Concept Used: Exterior angle of a traingle is equal to the Sum of Interior opposite angles)

Combining the results of the above 3 equations

By equation 2 and 3;

w=z+y=x+t.
From Equation 1 x=z=t, so we have x+y=2*x
This means y=x
Also combining this result with equation 1&2, we get y=x=z=t=s

Now considering Triangle ABC,
We know that Sum of Angles in a triangle is 180 degree,

So, $$x+z+y+t+s = 180$$

Since all these 5 angles are equal to each other, we have 5*x=180 or x=36

Hence, statement 1 is sufficient to answer the question.

Step-IV: Statement-II

Statement- II gives us information that x=y. We dis drive this result from statement 1, but it is not sufficient to answer the question since neither value of x or y is given nor any other condition of the triangle is given to come to a definite value of x.

Hence, statement 2 is not sufficient to answer this question.

Step-V: Combining Statements I & II

Since, we have a unique answer from Statement- I so, we don’t need to combine Statements- I & II.
Hence, the correct answer is Option A

Key Takeaways

1. Use of Property: Exterior angle of a triangle is equal to the sum of the interior opposite angles.
2. Use of Property: Angles opposite to equal sides are equal.
Non-Human User Joined: 09 Sep 2013
Posts: 13316
Re: In the figure above, what is the value of x?  [#permalink]

Show Tags

1
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________ Re: In the figure above, what is the value of x?   [#permalink] 30 Oct 2018, 23:57
Display posts from previous: Sort by

In the figure above, what is the value of x?

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

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