lying on the same

[sanju09]

If A, B, C and D are all points in the coordinate plane; then what is the ratio of the distance from B to C to the distance from C to D?

(1) The distance from A to C is twice the distance from C to D and three times the distance from B to D.

(2) The four points, A, B, C and D, all lie on a straight line.

[onedayi'll]

IMO E....

Let AC = 6; then CD = 3, with D on either side of C. BD=2, but B could be on either side of D,
we have no way of knowing length BC.
ratio BC/CD cannot be determined.

[Stuart@KaplanGMAT]

What is the value of the ratio BC/CD?

(1) AC = 2 CD = 3 BD.

(2) A, B, C, and D are the points lying on the same straight line.

This is an impossible question.

From (2), each letter represents a pair of coordinate points. From (1), each letter represents a single number. These two facts are contradictory.

While variables can certainly represent multiple things in the same question (e.g. we could have n workers who each get paid $n per hour), they cannot represent mutually exclusive concepts.

[fibbonnaci]

Stuart, I do not understand why this is an impossible question.
2) gives the coordinate points, i agree. but 1) states the distances between those points.

what is wrong in that?

[Stuart@KaplanGMAT]

Stuart, I do not understand why this is an impossible question.
2) gives the coordinate points, i agree. but 1) states the distances between those points.

what is wrong in that?

I suppose that's one interpretation; but without statement (2), how do we know that they're points on the coordinate plane?

The common interpretation of (1) would be that a*c = 2*c*d = 3*b*d

On the actual GMAT, we never have to guess at what's going on - we're given all the information we need to interpret the question.

[kstv]

In the straight line AC = 2 CD = 3 BD. Then AC: CD: BD = 6: 3 : 2. Starting with AC which is 6 units, the point D can be (6-3) 3 units from A i.e in the order A D C in the st. line or (6+3) 9 units from A i.e. A C D. Similarly pt. B can be on either side of pt D at a distance of 2 units. Therefore the ratio can be 1/3 or 5/3.

[sanju09]

What is the value of the ratio BC/CD?

(1) AC = 2 CD = 3 BD.

(2) A, B, C, and D are the points lying on the same straight line.

This is an impossible question.

From (2), each letter represents a pair of coordinate points. From (1), each letter represents a single number. These two facts are contradictory.

While variables can certainly represent multiple things in the same question (e.g. we could have n workers who each get paid $n per hour), they cannot represent mutually exclusive concepts.

If I merely swap the statements, will it be fine then? It'll cost a single redo to me.

[gmatmachoman]

Stuart, I do not understand why this is an impossible question.
2) gives the coordinate points, i agree. but 1) states the distances between those points.

what is wrong in that?

IMO C

I tried plugging in some random values :

CD= 3
---> BD= 2

CD+DB= 5= CB or BC

BC/CD=(5/3)

The straight line is formed by A,C,D,B points

Am i correct??

[Stuart@KaplanGMAT]

If I merely swap the statements, will it be fine then? It'll cost a single redo to me.

So is this a made-up question? Please always post the source!

Swapping the statements doesn't help, since the order is irrelevant; when we look at each statement individually, it needs to be able to exist in the absence of the other statement.

If fibbonnaci's interpretation is correct, then the question stem should read:

If A, B, C and D are all points in the coordinate plane, then what is the ratio of the distance from B to C to the distance from C to D?

and statement (1) should also be unambiguous:

(1) The distance from A to C is twice the distance from C to D and three times the distance from B to D.

finally, statement (2) should be slightly refined:

(2) A, B, C and D all lie on a straight line.

[sanju09]

If I merely swap the statements, will it be fine then? It'll cost a single redo to me.

So is this a made-up question? Please always post the source!

Swapping the statements doesn't help, since the order is irrelevant; when we look at each statement individually, it needs to be able to exist in the absence of the other statement.

If fibbonnaci's interpretation is correct, then the question stem should read:

If A, B, C and D are all points in the coordinate plane, then what is the ratio of the distance from B to C to the distance from C to D?

and statement (1) should also be unambiguous:

(1) The distance from A to C is twice the distance from C to D and three times the distance from B to D.

finally, statement (2) should be slightly refined:

(2) A, B, C and D all lie on a straight line.

Absolutely perfect. Thanks