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In a triangle ABC point D lies on segment AC. Is the area of triangle

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Manager
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Joined: 14 Oct 2014
Posts: 66
Location: United States
GMAT 1: 500 Q36 V23
In a triangle ABC point D lies on segment AC. Is the area of triangle  [#permalink]

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New post 19 Dec 2014, 19:45
1
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A
B
C
D
E

Difficulty:

  55% (hard)

Question Stats:

62% (00:50) correct 38% (01:22) wrong based on 98 sessions

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In a triangle ABC point D lies on segment AC. Is the area of triangle ABD greater than the area of triangle BDC?

(1) DC > AD
(2) BC > AB
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Location: India
Concentration: Finance, Marketing
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GMAT 1: 700 Q51 V31
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Re: In a triangle ABC point D lies on segment AC. Is the area of triangle  [#permalink]

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New post 19 Dec 2014, 22:53
[Figure Attached]

Area of triangle ABD = (1/2)*AD*BE
Area of triangle BDC = (1/2)*DC*BE

So if we know a relationship between AD and DC then we can say whether the area of triangle ABD greater than the area of triangle BDC or not.

STAT1
DC > AD
Multiply with (1/2)*BE on both the sides we get
(1/2)*DC*BE > (1/2)*AD*BE
So, the area of triangle ABD is NOT greater than the area of triangle BDC.
SO, SUFFICIENT

STAT2
BC > AB
We do not know anything about D. D can be anywhere on AC and so the the area of triangle ABD can be greater than,less than or equal to the area of triangle BDC
So, INSUFFICIENT

So, answer will be A

Hope it helps!

greater than the area of triangle BDC?
viktorija wrote:
In a triangle ABC point D lies on segment AC. Is the area of triangle ABD greater than the area of triangle BDC?
(1) DC > AD
(2) BC > AB

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Re: In a triangle ABC point D lies on segment AC. Is the area of triangle  [#permalink]

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New post 22 Jan 2018, 23:16
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viktorija wrote:
In a triangle ABC point D lies on segment AC. Is the area of triangle ABD greater than the area of triangle BDC?
(1) DC > AD
(2) BC > AB


If suppose D was the mid-point of AD, then AD would become median and in that case areas of two triangles ABD and BDC would be equal (thats a property of median). But instead if D is closer to A than C, then area of ABD would be less than BDC. And similarly if D is closer to C, then area of ABD would be more than BDC.

(1) DC > AD
This clearly tells us that D is closer to A, so area of ABD is lesser, or NOT greater than that of BDC. Thus Sufficient.

(2) BC > AB
This just gives us the comparison between two sides of this triangle. No information about the location of D, or anything else. So not sufficient.

Hence A answer
Re: In a triangle ABC point D lies on segment AC. Is the area of triangle &nbs [#permalink] 22 Jan 2018, 23:16
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