metallicafan wrote:
If A, B, and C are distinct points, do line segments AB and BC have the same length?
(1) Together with point D, A, B, and C form a rectangle.
(2) AB is not equal to AC
Source:
https://www.gmathacks.comWe need to know whether AB = BC.
Statement 1So the four points A, B, C, D form a rectangle. We are not given any particular order first of all, so we dont know whether we should make this rectangle as ABCD or ACDB or something else.
Even if we make the cyclic order ABCD, then in that case opposite sides AB and CD will be equal, but whether adjacent sides AB and BC are equal is something that depends on whether this rectangle is also a square. This is not given. So we cannot conclude in this case whether AB = BC.
If we cannot conclude in this one case then there is no point in taking other cases like ACDB etc. So
not sufficient.
Statement 2AB is not equal to AC, but this doesnt tell us anything about AB and BC. So
not sufficient.
Combining the two statements,
I) If we take a rectangle in this order: ABCD - here opposite sides AB=CD and AD=BC. Now if its adjacent sides are equal (its a square) then AB=BC. We are given from statement 2, AB is not equal to AC. But AB and AC can anyway not be equal because AB is a side and AC is a diagonal. Diagonal > Side anyway. We are not given whether its a square or just a rectangle so we cannot conclude whether AB=BC or not.
We can take other order for rectangle also: ADCB or ACBD but that is not required because for order ABCD only we are unable to conclude anything about the question asked. So this is
not sufficient.
Hence
E answer