A triangle ABC has points D and E which lie on sides AB and AC respect

Question

A triangle ABC has points D and E which lie on sides AB and AC respectively. Length of AD is 6 units and length of EC is 3 units. What is the length of AE?

(1) If points D and E are joined to each other, line DE will be parallel to side BC of triangle ABC.

(2) Length of BD is 2 units.

PKN · Answer

Given, AD=6 unit, EC=3 unit

Question stem, AE=?

Property:-
  
Any line parallel to one side of a triangle divides the other two sides proportionally.

Statement-1
Here, DE is drawn parallel to BC, it would divide sides AB and AC proportionally, i.e.,
 \frac{AD}{DB} = \frac{AE}{EC} 
Or,  \frac{6}{DB} = \frac{AE}{3} -----------------(1)
We can't find the length of AE as the length of DB is not known.
Hence, insufficient.

Statement-2
Given, BD=2 unit, So what? No other relevant info is available.(No info on the positioning of D & E)

Clearly, insufficient.

Now combining st1 & st2, we have from (1),
 \frac{6}{DB} = \frac{AE}{3} (substituting the value of BD from st2)
 Or, \frac{6}{2}=\frac{AE}{3} 
Or,3= \frac{AE}{3} 
Or, AE=9 unit

Clearly sufficient,though the highlighted portion needn't to be computed,

Diagram affixed for reference.(Not to scale)

Ans. C

Shishou · Answer

When 2 points on two different sides of a triangle are joined ,they can either be parallel or not.
If they are then we have two similar triangles and we can thus use the properties of similar triangles to solve the problem.

Statement 1: We know they the line joining the two sides are parallel but we do not know the ratio of the sides.If the midpoints of the 2 sides had been joined, then the ratio of the sideof the larger triangle to the smaller one would be a 2:1 ratio.We don't know that 
Insufficient

Statement 2: clearly insufficient .So many triangles can be drawn with such a criteria.

Together : we know AD is 6 and DB is 2.The ratio of the sides of the two triangles is 8:6
Hence we can find AE

A triangle ABC has points D and E which lie on sides AB and AC respect

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GMAT Data Sufficiency (DS) Questions

A triangle ABC has points D and E which lie on sides AB and AC respect

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