Is the Quadrilateral ABCD a rectangle?

Question

GMATBusters’ Quant Quiz Question -10

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Is the Quadrilateral ABCD a rectangle?
1) AC and BD are perpendicular.
2) AC = BD

Archit3110 · Answer

Is the Quadrilateral ABCD a rectangle?
1) AC and BD are perpendicular.
2) AC = BD
for a llogram ABCD can be a square or rectangle
#1
AC and BD are perpendicular.
it can be a square, rectangle or rhombus
insufficient
#2AC = BD
i.e length of digonal is same so here again it can be square or rectangle
insufficient
from 1 &2
we do not know the sides of llogram whether all sides are same or we have rectangle with length & bredth
so insufficient
IMO E

ashwini2k6jha · Answer

State:1 Not sufficient
Square and rhombus also have same feature
State:2 not sufficient
Kite can also have same property ie diagonal equal
state1+2 not sufficient
kite and square have same propery

Raxit85 · Answer

Is the Quadrilateral ABCD a rectangle?

For rectangle, all angles have to be equal (hence, 90) and opposite sides should be equal. or rectangle is a quadrilateral with four right angles which is necessary and sufficient condition for quadrilateral to be a rectangle.

1) AC and BD are perpendicular. - Not sufficient as we cant prove about other three angles.

2) AC = BD - not sufficient.

1)+ 2) not sufficient

Ans. E

Kinshook · Answer

Asked: Is the Quadrilateral ABCD a rectangle?

1) AC and BD are perpendicular.
Is diagonals AC & BD are perpendicular.
The resulting quadrilateral ABCD may or may not be a rectangle
NOT SUFFICIENT

Attachment:

Screenshot 2020-04-26 at 9.48.36 AM.png [ 22.49 KiB | Viewed 5675 times ]

2) AC = BD
Is diagonals AC & BD are equal.
The resulting quadrilateral ABCD may or may not be a rectangle
NOT SUFFICIENT

Attachment:

Screenshot 2020-04-26 at 9.51.18 AM.png [ 24.68 KiB | Viewed 5624 times ]

(1) + (2)
1) AC and BD are perpendicular.
2) AC = BD
If diagonals are equal and perpendicular and do not bisect each other.
The resulting quadrilateral ABCD may or may not be a rectangle.
NOT SUFFICIENT

Attachment:

Screenshot 2020-04-26 at 9.56.54 AM.png [ 23.82 KiB | Viewed 5561 times ]

IMO E

SR71Blackbird · Answer

The answer to this question is E.

Statement 1: AC and BD are perpendicular, these could be diagonals of any quadrilateral like rhombus, square, rectangle. 
Statement 2: AC = BD, these two lines can cut at any angle on each other. making trapezium and many other shapes.

Combined, we get these line bisect each other perpendicular and equal length but can cut each other anywhere. Imagine, AC to be X axis and the line BD can be perpendicular at X=1 X=2 X=3 with various lengths above and below x axis and so on making different quadrilateral shapes.

kapilagarwal · Answer

ANS : E Both insufficient, since ABCD could be a square also

Posted from my mobile device

uc26 · Answer

(1) ABCD could be a kite or a rhombus or a square for example. Since all squares are rectangles, ABCD might or might not be a rectangle. Not sufficient.

(2) Not enough information to determine if ABCD is a rectangle. Not sufficient.

(1)+(2) Not enough information on the sides and angles of the quadrilateral to prove that it is a rectangle. We do not know if the four sides meet at right angles and we do not know if opposite sides are equal. Not sufficient.

Answer: E.

lacktutor · Answer

Is the Quadrilateral ABCD a rectangle?
Rectangle = a figure with four . straight sides and four right angles

(Statement1): AC and BD are perpendicular.
The diagonals of the Square are perpendicular (yes) 
The diagonals of the Rhombus are perpendicular. ( No) Rhombus is not a rectangle. 
Insuffcient

(Statement2): AC = BD 
The diagonals of the square are congruent. (Yes) 
The diagonals of an isosceles trapezium are congruent( No) 
Insufficient

Taken together 1&2, 
If it’s a square, ABCD is a rectangle. 
If it’s an isosceles trapezium, ABCD cannot be a rectangle. 
Insuffcient

Answer (E)

Posted from my mobile device

zs2 · Answer

Is the Quadrilateral ABCD a rectangle?
1) AC and BD are perpendicular.
2) AC = BD

From 1 we cannot be sure because even diagonals of rhombus are perpendicular to each other. Not sufficient.

From 2- Diagonals are equal , which ensures it to be a rectangle. It can be a square but square is also a special type of rectangle , hence sufficient

Answer B

GMATinsight · Answer

Properties of Rectangle 
- Opposite sides are equal
- All angles are 90º
- Diagonals are equal 
- Diagonal Bisect each other but not Essentially @ 90º

STatement 1 : AC and BD are perpendicular.

The figure could be a Square (which is a Rectangle YES) or a Kite (which is NOT a rectangle)

NOT SUFFICIENT

Statement 2 : AC = BD

DIagonals are equal in Rectangle (YES) as well as in an Isosceles Trapezium (NOT a rectangle)

NOT SUFFICIENT

Combining the statements:

We still have a Square and a Kite with equal Diagonals which are not bisecting hence

NOT SUFFICIENT

Answer: Option E

See the video explanation here:
 https://www.youtube.com/watch?v=9DQoolnUeOM

jrk23 · Answer

option A- not possible because it can be a rhombus.
Option B- Alone not possible.

Combining both possible. therefore, c is the answser

1BlackDiamond1 · Answer

Statement 1)
this tells us that the diagonals cut each other at middle of each other at 90°
The diagonals can be of different sizes..
So it is surely a RHOMBUS but cannot say if it is rectangle/square
Insufficient

Statement 2)
Diagonals are equal cannot alone suffice if it's a rectangle..

Combined
It is a square and each square is also a rectangle..
Sufficient
C

Tommy6e · Answer

Answer is E is correct.

Is the Quadrilateral ABCD a rectangle?

Statement 1:
1) AC and BD are perpendicular.
Two scenarios:
Scenario 1 - this shape can be a kite (see figure A)
Scenario 2 - this shape can be a rectangle

Statement 2:
2) AC = BD
This shape can be a trapeze (see figure B)
Scenario 2 - this shape can be a rectangle

Both statements:
Scenario 1 - this shape can be a kite (see figure C)
Scenario 2 - this shape can be a rectangle
This shape can still be a kite. We do not have enough information to decide whether ABCD is a rectangle.

firas92 · Answer

Combining both equations, the quadeilateral could still be square or a "kite"

Not sufficient

Answer is (E)

Posted from my mobile device

knevagi · Answer

I am confused. Aren't the diagonals of a rectangle never perpendicular to each other? So shouldn't the first statement be enough to determine if the quadrilateral is a rectangle or not?

Bunuel · Answer

A square is a special type of a rectangle: all squares are rectangles but not vise-versa. So, if a rectangle is a square, then its diagonals are perpendicular bisectors of each other.

GMATinsight · Answer

Hi knevagi Please check my explanation above for properties of rectangles https://gmatclub.com/forum/gmatbusters- ... l#p2505350 A rectangle does NOT essentially have perpendicular diagonals But if the diagonals of a rectangle are perpendicular then the rectangle will be square.

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Is the Quadrilateral ABCD a rectangle?

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Is the Quadrilateral ABCD a rectangle?

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