Is ABCD a rectangle? (1) The perimeter of ABCD is equal to twice the

Question

Is ABCD a rectangle?

(1) The perimeter of ABCD is equal to twice the length of one side plus twice the length of any adjacent side.
(2) AC bisects BD

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yashikaaggarwal · Answer

To Find: Is ABCD a rectangle?

(1) The perimeter of ABCD is equal to twice the length of one side plus twice the length of any adjacent side.
=> Square, Rectangle, Rhombus, Parallelogram all satisfy the above constraint. 
(Insufficient)

(2) AC bisects BD.
=> paralellogram, rectangle, rhombus, square all diagonals bisect each other. (Insufficient)

1&2 together: We have four quadrilaterals satisfying both constraints, so can't conclude that it is rectangle specifically.

IMO E

rajatchopra1994 · Answer

Explanation:
Is ABCD is rectangle

Statement 1: The perimeter of ABCD is equal to twice the length of one side plus twice the length of any adjacent side.
let one side is x, adjacent side is y
so, Perimeter is 2x + 2y.

But still, we don't know anything about the angles of ABCD.

Not Sufficient

Statement 2: AC bisects BD
It can or cannot be a rectangle. don't know anything about the angles of ABCD

Not Sufficient

From 1 & 2, 
Still don't know anything about the angles of ABCD, as it is required for rectangle confirmation.

IMO-E

IanStewart · Answer

Statements 1 and 2 together are true for rectangles, but also for rhombuses, say (or for parallelograms generally) so the answer is E.

I have never seen a single official question which even mentions diagonals that "bisect" other diagonals, incidentally.

GMATinsight · Answer

Properties of Rectangle :
1) Opposite sides are equal
2) All angles are 90º
3) Diagonal are equal and they bisect each other
4) Diagonals are not perpendicular essentially but they may be and that case would become a square

STatement 1: The perimeter of ABCD is equal to twice the length of one side plus twice the length of any adjacent side.

The condition confirms even for a   parallelogram   but every parallelogram is NOT essentially a rectangle hence

NOT SUFFICIENT

STatement 2: AC bisects BD 
Diagonals are bisectors even in case of a   parallelogram   but every parallelogram is NOT essentially a rectangle hence

NOT SUFFICIENT

Combining the statements

Still the give information confirm that the quadrilateral is a Parallelo  parallelogram   but every parallelogram is NOT essentially a rectangle hence

NOT SUFFICIENT

Answer: Option E

sambitspm · Answer

Kindly see the attachment.
IMO E

vipulshahi · Answer

ABCD is rectangle = ?

Statement 1 : The perimeter of ABCD is equal to twice the length of one side plus twice the length of any adjacent side.
In Rectangle, Square, Rombhus, Parallelogram all have the above properties 
Not Sufficient.

Statement 2: AC bisects BD.
Above properties hold in square , rhombus , Parallelogram 
Not Sufficient.

Statement 1 & Statement 2 : 
Still not reach at single quadrilateral.
Not Sufficient.

Answer : E

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Is ABCD a rectangle? (1) The perimeter of ABCD is equal to twice the

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