Oct 22 09:00 AM PDT  10:00 AM PDT Watch & learn the Do's and Don’ts for your upcoming interview Oct 22 08:00 PM PDT  09:00 PM PDT On Demand for $79. For a score of 4951 (from current actual score of 40+) AllInOne Standard & 700+ Level Questions (150 questions) Oct 23 08:00 AM PDT  09:00 AM PDT Join an exclusive interview with the people behind the test. If you're taking the GMAT, this is a webinar you cannot afford to miss! Oct 26 07:00 AM PDT  09:00 AM PDT Want to score 90 percentile or higher on GMAT CR? Attend this free webinar to learn how to prethink assumptions and solve the most challenging questions in less than 2 minutes. Oct 27 07:00 AM EDT  09:00 AM PDT Exclusive offer! Get 400+ Practice Questions, 25 Video lessons and 6+ Webinars for FREE.
Author 
Message 
TAGS:

Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 58402

In the diagram above, ∠A = ∠ABC, ∠CBD = ∠BDC, and ∠CBE =90°. If AE =
[#permalink]
Show Tags
26 Feb 2015, 06:48
Question Stats:
80% (03:02) correct 20% (03:08) wrong based on 107 sessions
HideShow timer Statistics
Attachment:
differenceofsquares.png [ 18.25 KiB  Viewed 2732 times ]
In the diagram above, ∠A = ∠ABC, ∠CBD = ∠BDC, and ∠CBE =90°. If AE = 16 and DE = 4, what is the length of BE? (A) 7 (B) 8 (C) 9 (D) 10 (E) 11 Kudos for a correct solution.
Official Answer and Stats are available only to registered users. Register/ Login.
_________________



Manager
Status: single
Joined: 19 Jan 2015
Posts: 84
Location: India
GPA: 3.2
WE: Sales (Pharmaceuticals and Biotech)

Re: In the diagram above, ∠A = ∠ABC, ∠CBD = ∠BDC, and ∠CBE =90°. If AE =
[#permalink]
Show Tags
26 Feb 2015, 11:30
in triangle abc Angle A= Angle ABC. Both sides are equal. put angle a = X ANGLE C 180 2X In triangle BDC. ANGLE B= ANGLE D.put angle B = Y anlge C 1802Y. Angle C supplementary ,1802x+1802y=180 2x+2y=180 x+y =90 In trianlge BDE ANGLE B 90y. angle D 180y anlge E 2Y90= 2yxy =yx. so y >=x if y = 45 degree , then in Tri BDE , ang B =45, ang D 135 can"t satisfy If y = 50 degree , ang B 40, ang D 130, ange E 10. hen In Triangle ABC ang A 40, angle B 130, angle C 10
If y = 55 degree, ang B 35, ang D 125 , ang E35 cant satisfy.
if y = 60 degre, ang B 30, ang D 120, ang E 30 satisfy. only y = 50 ,60, 70 ,80 satisfy. then Here also Angle A 30, angle B 120, Angle C = 30. Triangle ABC and Triangle BDE are congruent.
BE/AE = DE/BE => BE^2=AE*DE= 16*4=64. BE = 8.
Answer is B.



SVP
Status: The Best Or Nothing
Joined: 27 Dec 2012
Posts: 1747
Location: India
Concentration: General Management, Technology
WE: Information Technology (Computer Software)

In the diagram above, ∠A = ∠ABC, ∠CBD = ∠BDC, and ∠CBE =90°. If AE =
[#permalink]
Show Tags
26 Feb 2015, 18:59
Answer = B = 8 Refer diagram below Attachment:
differenceofsquares.png [ 25.12 KiB  Viewed 2652 times ]
∠A = ∠ABC = ∠CBD = ∠BDC (Angles are same, so corresponding lengths are same & viceversa) AC = CB = CD = 6 BE \(= \sqrt{(6+4)^2  6^2} = \sqrt{64} = 8\)
_________________
Kindly press "+1 Kudos" to appreciate



Math Expert
Joined: 02 Sep 2009
Posts: 58402

Re: In the diagram above, ∠A = ∠ABC, ∠CBD = ∠BDC, and ∠CBE =90°. If AE =
[#permalink]
Show Tags
02 Mar 2015, 05:35
Bunuel wrote: Attachment: differenceofsquares.png In the diagram above, ∠A = ∠ABC, ∠CBD = ∠BDC, and ∠CBE =90°. If AE = 16 and DE = 4, what is the length of BE? (A) 7 (B) 8 (C) 9 (D) 10 (E) 11 Kudos for a correct solution. MAGOOSH OFFICIAL SOLUTION:This is a tricky one. Remember, it’s a diagram drawn to scale, so if all else fails, you can estimate (see this post). But, let’s solve this with math. The fact that ∠A = ∠ABC tells us triangle ABC is isosceles, with AC = BC. The fact that ∠CBD = ∠BDC tells us triangle BCD is isosceles, with BC = CD. The fact that ∠CBE = 90° means that (BC)2 + (BE)2 = (CE)2. This means (BE)^2 = (CE)^2  (BC)^2 = (CE + BC)(CE  BC) = (CE + AC)(CE  CD) (substitutions from the two isosceles triangles) = (AE)(DE) = (16)(4) = 64 > BE = 8 Answer = B.
_________________



Intern
Joined: 12 May 2017
Posts: 13

Re: In the diagram above, ∠A = ∠ABC, ∠CBD = ∠BDC, and ∠CBE =90°. If AE =
[#permalink]
Show Tags
18 Jun 2017, 07:05
I've got another way to solve the problem.
You know line segment DE is 4. First step: Form a triangle with a line with an angle of 30 degrees, from point D, to line segment BE. Let's call this new point, point F. Point F now has 2 right angles. Second step: Triangle DEF is a triangle with angles of 306090, so proportions are x : xscrt3 : 2x Fill in (since 2x is 4), 2 : 2sqrt3 : 4 (In triangle DEF, line segment DF is the long leg) Now you now that line segment DF is 2sqrt3. Third step: Triangle BDF also has a right triangle and you know the short leg is 2sqrt3. (notice how the long leg from DEF is the short leg in BDF) Same proportions x : xsqrt3 : 2x Fill in to find the long leg: (2sqrt3)*sqrt3=6 Last step: Add up line segments BF and EF > 6+2= 8



Intern
Joined: 30 Dec 2018
Posts: 2

Re: In the diagram above, ∠A = ∠ABC, ∠CBD = ∠BDC, and ∠CBE =90°. If AE =
[#permalink]
Show Tags
02 Mar 2019, 13:05
PareshGmat wrote: Answer = B = 8 Refer diagram below Attachment: differenceofsquares.png ∠A = ∠ABC = ∠CBD = ∠BDC (Angles are same, so corresponding lengths are same & viceversa) AC = CB = CD = 6 BE \(= \sqrt{(6+4)^2  6^2} = \sqrt{64} = 8\) Isn't it wrong to assume that ∠A = ∠ABC = ∠CBD = ∠BDC We know their corresponding sides are equal, but that does not necessarily mean they are equal. Also, since it is drawn to scale, it is evident they are not equal, since if they were, the triangles would be congruent based on AAS rule. Another confirmation they are not equal is because if they were, then they would each have to be equal to 45oC,which means ∠ACB = 90 and ∠BCD =90 which is evidently wrong




Re: In the diagram above, ∠A = ∠ABC, ∠CBD = ∠BDC, and ∠CBE =90°. If AE =
[#permalink]
02 Mar 2019, 13:05






