GMAT Question of the Day - Daily to your Mailbox; hard ones only

 It is currently 15 Dec 2019, 02:47

GMAT Club Daily Prep

Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

For how many of the following types of quadrilaterals does there exist

Author Message
TAGS:

Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 59726
For how many of the following types of quadrilaterals does there exist  [#permalink]

Show Tags

14 May 2019, 00:04
00:00

Difficulty:

85% (hard)

Question Stats:

33% (01:40) correct 67% (01:24) wrong based on 51 sessions

HideShow timer Statistics

For how many of the following types of quadrilaterals does there exist a point in the plane of the quadrilateral that is equidistant from all four vertices of the quadrilateral?

a square
a rectangle that is not a square
a rhombus that is not a square
a parallelogram that is not a rectangle or a rhombus
an isosceles trapezoid that is not a parallelogram

A. 1
B. 2
C. 3
D. 4
E. 5

_________________
VP
Joined: 19 Oct 2018
Posts: 1177
Location: India
Re: For how many of the following types of quadrilaterals does there exist  [#permalink]

Show Tags

24 May 2019, 06:52
If there exist a point in the plane of the quadrilateral that is equidistant from all four vertices of the quadrilateral, then it must be cyclic.
Square, a rectangle that is not a square, and an isosceles trapezoid that is not a parallelogram are cyclic quadrilaterals.

Proof that Only parallelograms that are rectangle can be cyclic.
If ABCD is a parallelogram, then ∠A=∠C. If it is cyclic then [∠A+∠C=180]
Hence ∠A=90 and ∠C=90
Hence all cyclic parallelograms are rectangle.
Similarly we can prove that all cyclic rhombus are squares.
Manager
Joined: 07 May 2018
Posts: 61
Re: For how many of the following types of quadrilaterals does there exist  [#permalink]

Show Tags

25 May 2019, 02:54
Bunuel wrote:
For how many of the following types of quadrilaterals does there exist a point in the plane of the quadrilateral that is equidistant from all four vertices of the quadrilateral?

a square
a rectangle that is not a square
a rhombus that is not a square
a parallelogram that is not a rectangle or a rhombus
an isosceles trapezoid that is not a parallelogram

A. 1
B. 2
C. 3
D. 4
E. 5

Hi Could you please explain how you got 3 as the answer?
Intern
Joined: 23 Mar 2019
Posts: 3
Re: For how many of the following types of quadrilaterals does there exist  [#permalink]

Show Tags

30 May 2019, 17:49
Square, Rectangle - Center 2
Rhombus sym - diag diff, Paralleogram - diagonals different,
Isosceles trapezoid - diag same / symmetry of sides - 1

For the visually inclined, take a square and stretch out the bottom.
The point equidistant from each vertex follows the axis.
Easiest to visualize is three equilateral triangles together

C - 3
Re: For how many of the following types of quadrilaterals does there exist   [#permalink] 30 May 2019, 17:49
Display posts from previous: Sort by