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# In Quadrilateral WXYZ, is XY perpendicular to YZ?

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Math Expert
Joined: 02 Sep 2009
Posts: 60647

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13 Nov 2019, 02:15
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Difficulty:

55% (hard)

Question Stats:

32% (01:18) correct 68% (01:24) wrong based on 37 sessions

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In Quadrilateral WXYZ, is XY perpendicular to YZ?

(1) WXY is a right angle

(2) WZY is a right angle

Are You Up For the Challenge: 700 Level Questions

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Joined: 02 Aug 2009
Posts: 8337

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13 Nov 2019, 06:46
Bunuel wrote:
In Quadrilateral WXYZ, is XY perpendicular to YZ?

(1) WXY is a right angle

(2) WZY is a right angle

Are You Up For the Challenge: 700 Level Questions

There are no restrictions on lengths or other two angles..
Now if two opposite angles, X and Z are 90 and if Y too is 90 then the quadrilateral is a rectangle. So the question can be said Is WXYZ a rectangle?
I) WXYZ can be a rectangle, then YES
2) WXYZ can be any quadrilateral but not a parallelogram, then NO

E

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Untitled.png [ 10.83 KiB | Viewed 499 times ]

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Location: India
GMAT 1: 580 Q43 V27
WE: Sales (Energy and Utilities)

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13 Nov 2019, 10:05
chetan2u wrote:
Bunuel wrote:
In Quadrilateral WXYZ, is XY perpendicular to YZ?

(1) WXY is a right angle

(2) WZY is a right angle

Are You Up For the Challenge: 700 Level Questions

There are no restrictions on lengths or other two angles..
I) WXYZ can be a rectangle, then YES
2) WXYZ can be any quadrilateral but not a parallelogram, then NO

E

chetan2u
Isn't as per the question X and Z are opposite to each other. And combining two statements means two opposite angles sum to 180 confirming that angles W and Y both are also 90 each.

Hence XY perpendicular to YZ.

Am i missing something.
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Ephemeral Epiphany..!

GMATPREP1 590(Q48,V23) March 6, 2019
GMATPREP2 610(Q44,V29) June 10, 2019
GMATPREPSoft1 680(Q48,V35) June 26, 2019
Math Expert
Joined: 02 Aug 2009
Posts: 8337

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13 Nov 2019, 10:21
lnm87 wrote:
chetan2u wrote:
Bunuel wrote:
In Quadrilateral WXYZ, is XY perpendicular to YZ?

(1) WXY is a right angle

(2) WZY is a right angle

Are You Up For the Challenge: 700 Level Questions

There are no restrictions on lengths or other two angles..
I) WXYZ can be a rectangle, then YES
2) WXYZ can be any quadrilateral but not a parallelogram, then NO

E

chetan2u
Isn't as per the question X and Z are opposite to each other. And combining two statements means two opposite angles sum to 180 confirming that angles W and Y both are also 90 each.

Hence XY perpendicular to YZ.

Am i missing something.

No all angles need not be 90. A pair of Opposite angles are 90 but the other pair could be anything. You can even draw 1 and 179 degrees or 80 and 100 degrees as there is no restriction on the length of sides
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13 Nov 2019, 10:40
chetan2u wrote:
lnm87 wrote:
Isn't as per the question X and Z are opposite to each other. And combining two statements means two opposite angles sum to 180 confirming that angles W and Y both are also 90 each.

Hence XY perpendicular to YZ.

Am i missing something.

No all angles need not be 90. A pair of Opposite angles are 90 but the other pair could be anything. You can even draw 1 and 179 degrees or 80 and 100 degrees as there is no restriction on the length of sides

Thank you ..!!
I got it.
I presumed sides part and asked such a silly question.
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Ephemeral Epiphany..!

GMATPREP1 590(Q48,V23) March 6, 2019
GMATPREP2 610(Q44,V29) June 10, 2019
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Director
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14 Nov 2019, 02:51
1
Bunuel wrote:
In Quadrilateral WXYZ, is XY perpendicular to YZ?

(1) WXY is a right angle

(2) WZY is a right angle

Are You Up For the Challenge: 700 Level Questions

Attachment:

Gmat DS.png [ 8.89 KiB | Viewed 343 times ]

Lets look at the figures above:

(1) WXY is a right angle -
IF you look at Fig.1 Answer is NO
IF you look at Fig.2 Answer is Yes
INSUFF.

(2) WZY is a right angle-
IF you look at Fig.1 Answer is NO
IF you look at Fig.2 Answer is Yes
INSUFF.

1+2

IF you look at Fig.1 Answer is NO
IF you look at Fig.2 Answer is Yes
INSUFF.

Ans- E
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In Quadrilateral WXYZ, is XY perpendicular to YZ?   [#permalink] 14 Nov 2019, 02:51
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