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Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.  If E is the midpoint of AD, what is the length of EB?

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Math Expert V
Joined: 02 Sep 2009
Posts: 58400
If E is the midpoint of AD, what is the length of EB?  [#permalink]

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Difficulty:   45% (medium)

Question Stats: 56% (01:06) correct 44% (01:13) wrong based on 149 sessions

HideShow timer Statistics If E is the midpoint of AD, what is the length of EB?

(1) ∠D = 60°
(2) DC = 4

Attachment: 2017-05-21_2155.png [ 6.28 KiB | Viewed 1985 times ]

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Retired Moderator P
Joined: 22 Aug 2013
Posts: 1430
Location: India
Re: If E is the midpoint of AD, what is the length of EB?  [#permalink]

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Since both EB and DC are perpendicular on the same line, EB is parallel to DC.
Thus angle AEB = angle ADC (corresponding angles)

Also by mid point theorem of a triangle, since E is the mid point of AD and EB||DC,
B must be the mid point of AC and EB = DC/2

Statement 1. angle ADC = 60 , so angle AEB is also = 60
Triangle AEB is a 30-60-90 triangle. So we know the ratio of sides of this triangle.
But since none of the three sides is given, we cannot find anything. So Insufficient

Statement 2. DC = 4, so EB = DC/2 = 2 (mid point theorem)
Sufficient

Hence answer is B
Manager  B
Status: Preparing
Joined: 05 May 2016
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Location: India
Concentration: International Business, Finance
Re: If E is the midpoint of AD, what is the length of EB?  [#permalink]

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Bunuel wrote: If E is the midpoint of AD, what is the length of EB?

(1) ∠D = 60°
(2) DC = 4

Attachment:
2017-05-21_2155.png

I think b alone is sufficient as it provides measure of a side.
Triangles AEB and ADC are similar(Angle A is common, Angle b and c are 90 degrees, angle E and D will be equal)
AE/ED=EB/DC
1/2=EB/4
EB=2.

Please correct me if i am wrong.
Director  S
Joined: 21 Mar 2016
Posts: 509
Re: If E is the midpoint of AD, what is the length of EB?  [#permalink]

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stat1: gives info about angles..no info on length ..not suff

stat2: EB and DC are parallel,,, using Basic proprtionality theorem,, EB = 1/2 DC,...suff

ans B
Director  S
Joined: 12 Nov 2016
Posts: 701
Location: United States
Schools: Yale '18
GMAT 1: 650 Q43 V37 GRE 1: Q157 V158 GPA: 2.66
Re: If E is the midpoint of AD, what is the length of EB?  [#permalink]

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Bunuel wrote: If E is the midpoint of AD, what is the length of EB?

(1) ∠D = 60°
(2) DC = 4

Attachment:
2017-05-21_2155.png

If we understand that these are similar triangles and that EB is the midline, then we can clearly see that EB must be half of AD in order to maintain similarity and proportionality.

B Re: If E is the midpoint of AD, what is the length of EB?   [#permalink] 06 Sep 2017, 22:23
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If E is the midpoint of AD, what is the length of EB?

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