In the figure above, is quadrilateral GHJK a rectangle?

Question

https://gmatclub.com/forum/download/file.php?id=54719 In the figure above, is quadrilateral GHJK a rectangle? (1) p = q = r = s (2) GH = KJ and GK = HJ DS21259 Are You Up For the Challenge: 700 Level Questions 1.png

karan12345 · Answer

By statement 1, we can get all angles of the quadrilateral are equal.
We know, sum of angles of a quadrilateral is = 360
So, each angle is = 90.
Thus the figure is a rectangle.
 The statement alone is sufficient.

By statement 2, we get both opposite sides of quadrilateral are equal.
But it can be a rectangle or a parallelogram
 Thus statement 2 alone is insufficient

Hence, OA is A.

Manasvi1 · Answer

Statement 1 - 
p = q = r = s
which are liner pairs to interior angles of quadrilateral
and sum of angles of quadrilateral = 360 (Angle sum property of a quadrilateral)
=> all angles of quadrilateral are equal and equal to 90
So it may be a square or a rectangle and a square is also a rectangle  (sufficient)
 
Statement 2 - 
This statement gives opposite sides as equal 
 Therefore, this can be a parallelogram or a rectangle
  Hence, Insufficient

Hence OA is (A)

Aman1204 · Answer

IMO E

1) p==q==r==s
=> p=q=r=s=90 degrees
=> The figure can be either of rectangle or of Square
Not sufficient

2) GH=KJ and GK=HJ
No relationship between GK and GH is provided.
Hence if, GK=GH, then it can be either a rhombus or a square
also, if GH is not equal to GK, then it can be a rectangle.

Not sufficient

1 + 2
Can either be a rectangle or be a square.

Not sufficient. Hence E is the answer

arora1 · Answer

in some official questions, i have seen square being considered a different entity than rectangle. 
In this question, the quadrilateral can well be a square.

Papist · Answer

S1: This can only be true if the four angles are equal to 90 degrees. SUFFICIENT.

S2: This means that GHJK is a parallelogram. However, we cannot say it's a rectangle without knowing anything about the angles. NOT SUFFICIENT.

ANSWER: A

ABCDEFU · Answer

I answered C considering:

1) Gave us: Could be a square or a rectangle

2) Gave us: Could be a parallelogram or a rectangle

(1+2) Gave us: Rectangle as all angles are =90degree & opposite sides are equal.

OA says it's A. Why do we consider square as a rectangle as well? Is this to be assumed for all questions on the GMAT as a rule of thumb?

Manasvi1 · Answer

Conditions for a quadrilateral to be a rectangle are:
 1) Each angle = 90 degree
 2) Opposite sides are equal

And in a square,
 Each angle = 90 degree &
 Opposite sides are equal.
  Hence, a square is a rectangle.

Basshead · Answer

OE:

In the figure above, the interior angles of quadrilateral GHJK have degree measures (180 – p), (180 – q), (180 – r), and (180 – s). Since the sum of the degree measures of the interior angles of a quadrilateral is 360, it follows that (180 – p) + (180 – q) + (180 – r) + (180 – s) = 360 or 720 – (p + q + r + s) = 360, so p + q + r + s = 360.

(1) Given that p = q = r = s, from the remarks above, p = q = r = s = 90 and GHJK is a rectangle; SUFFICIENT.
(2) Given that GH = KJ and GK = HJ, it is not possible to determine if GHJK is a rectangle. If each interior angle of GHJK has degree measure 90, then GHJK is a rectangle. If each interior angle of GHJK does not have degree measure 90, such as is the case for a rhombus or diamond, then GHJK is not a rectangle; NOT sufficient.

The correct answer is A;
statement 1 alone is sufficient.

Anki111 · Answer

Can any expert explain this one. The explanation given doesn't suffice the properties.

SnorLax_7 · Answer

Every square is a rectangle, hence once we get that each angle = 90 degree, we can infer that it is atleast a rectangle.

Experts, Pls correct me if I am wrong.

Thanks !

In the figure above, is quadrilateral GHJK a rectangle?

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