attitude.freak4u wrote:A triangle has three corners A,B and C. A line parallel to BC connects the sides AB and AC. What is the ratio of DE:BC?
1) AD=DB
2) Height of ADE = Height of ABC

This question has just one thing missing and that is the line parallel to BC connects the sides AB and AC in D and E respectively.

This uses the BPT (Basic Proportionality Theorem) in triangles. must revise we all

(1) When AD = DB, the problem reduces from the BPT (Basic Proportionality Theorem) to MPT (Mid Point Theorem) in triangles, and in that case a side of the bigger of the two similar triangles so obtained is twice of the corresponding side of the smaller of the two similar triangles so obtained, and hence, DE:BC = 1:2. Sufficient

(2) Ambiguity starts from here, this is possible only when the bases DE and BC are coinciding, DE:BC = 1:1. Seems sufficient, but it contradicts with (1)

[spoiler]D, if contradiction within the statements could be overlooked by a mass[/spoiler]

I would say both are sufficient on their own in order to find DE:BC. I'm just starting my studying for the GMAT - and as the earlier poster noted the two conditions would lead to different results for DE:BC - so is that a problem or would the answer still be D - EACH statement ALONE is sufficient?

Can a straight line be considered as two parallel lines?

frank1 wrote:Can a straight line be considered as two parallel lines?

We can otherwise say that when two or more lines parallel to a line l are each at zero distance from the line l, then these are all coinciding with the line l, and hence it could collectively be treated as the same line l.

sanju09 wrote:

frank1 wrote:Can a straight line be considered as two parallel lines?

We can otherwise say that when two or more lines parallel to a line l are each at zero distance from the line l, then these are all coinciding with the line l, and hence it could collectively be treated as the same line l.

is it yes or no?
you mean to say, it can happen when we take two lines and another point as reference...or two parallel line can overlap?

my logic is then why a single line cannot be considered as two paralle lines

frank1 wrote:

sanju09 wrote:

frank1 wrote:Can a straight line be considered as two parallel lines?

We can otherwise say that when two or more lines parallel to a line l are each at zero distance from the line l, then these are all coinciding with the line l, and hence it could collectively be treated as the same line l.

is it yes or no?
you mean to say, it can happen when we take two lines and another point as reference... (how can I mean something that I myself didn't really get?)or two parallel lineS can overlap (yes, it can)?

my logic is then why a single line cannot be considered as two paralle lines

Dear frank1, my answer to your chief query would then be, not exactly! Why a straight line be considered as only two parallel lines, why not 3, 4, 5 or more? It's analogous to the statement, a zero can be considered as the sum of so many zeros, or a 1 can be considered as the product of so many 1s, etc. Please, reconsider my previous post, it perhaps answers the chief doubt of yours, before hand. Thanks for writing in.

KatieB wrote:I would say both are sufficient on their own in order to find DE:BC. I'm just starting my studying for the GMAT - and as the earlier poster noted the two conditions would lead to different results for DE:BC - so is that a problem or would the answer still be D - EACH statement ALONE is sufficient?

Yes KatieB, that is a problem from the GMAT perspective, GMAT openly slams AMBIGUOUS tag on so many other situations, few of those similar to the one in hand, and no one would ever find on GMAT DS, the two statements, no matter which one suffices or which one not, contradicting one another in one way or the other.

That's why I noted

[spoiler]D, if contradiction within the statements could be overlooked by a mass[/spoiler]

keep writing