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Is the quadrilateral ABCD a rectangle? (1) Mid points of AB, BC, CD

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Is the quadrilateral ABCD a rectangle? (1) Mid points of AB, BC, CD  [#permalink]

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New post 25 Jun 2018, 10:59
2
00:00
A
B
C
D
E

Difficulty:

  85% (hard)

Question Stats:

19% (01:44) correct 81% (01:25) wrong based on 50 sessions

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Is the quadrilateral ABCD a rectangle?

(1) Mid points of AB, BC, CD and AD are E, F, G and H respectively. Quadrilateral EFGH is a rhombus.

(2) Diagonals of quadrilateral ABCD bisect each other.
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Re: Is the quadrilateral ABCD a rectangle? (1) Mid points of AB, BC, CD  [#permalink]

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New post 25 Jun 2018, 11:55
amanvermagmat wrote:
Is the quadrilateral ABCD a rectangle?

(1) Mid points of AB, BC, CD and AD are E, F, G and H respectively. Quadrilateral EFGH is a rhombus.

(2) Diagonals of quadrilateral ABCD bisect each other.


statement 1 is insufficient alone, as the quadrilateral can be a square as well as a rectangle ( as per given info)
statement 2 is also insufficient alone as the quadrilateral can be a square as well as a rectangle ( as per given info)

combining statement will also not help in solving the problem as both square and rectangle satisfy the condition.

Hence E

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Re: Is the quadrilateral ABCD a rectangle? (1) Mid points of AB, BC, CD  [#permalink]

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New post 27 Jun 2018, 12:41
Can somebody please give an explanation to the question? The OA is C
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Re: Is the quadrilateral ABCD a rectangle? (1) Mid points of AB, BC, CD  [#permalink]

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New post 27 Jun 2018, 13:42
amanvermagmat wrote:
Is the quadrilateral ABCD a rectangle?

(1) Mid points of AB, BC, CD and AD are E, F, G and H respectively. Quadrilateral EFGH is a rhombus.

(2) Diagonals of quadrilateral ABCD bisect each other.



Amanverma Kindly give the answer with explanation. I think there is some more info needed for answer choice C to be OA
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Is the quadrilateral ABCD a rectangle? (1) Mid points of AB, BC, CD  [#permalink]

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New post 28 Jun 2018, 06:42
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ReadyPlayerOne wrote:
amanvermagmat wrote:
Is the quadrilateral ABCD a rectangle?

(1) Mid points of AB, BC, CD and AD are E, F, G and H respectively. Quadrilateral EFGH is a rhombus.

(2) Diagonals of quadrilateral ABCD bisect each other.


statement 1 is insufficient alone, as the quadrilateral can be a square as well as a rectangle ( as per given info)
statement 2 is also insufficient alone as the quadrilateral can be a square as well as a rectangle ( as per given info)

combining statement will also not help in solving the problem as both square and rectangle satisfy the condition.

Hence E

DONT FORGET TO KUDOS


Square is also a rectangle..
so if ABCD is a square, it means it is a rectangle.
ofcourse vice versa may not be true

also statement I will be true for an isosceles trapezium too along with rectangle..
and statement II will also be true for rhombus along with rectangle and any parallelogram for that matter

combined
it will be a rectangle ..
see attached figure
Attachments

quad-rectangle.png
quad-rectangle.png [ 10.14 KiB | Viewed 276 times ]


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1) Absolute modulus : http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html
3) effects of arithmetic operations : https://gmatclub.com/forum/effects-of-arithmetic-operations-on-fractions-269413.html


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Re: Is the quadrilateral ABCD a rectangle? (1) Mid points of AB, BC, CD  [#permalink]

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New post 28 Jun 2018, 08:19
chetan2u wrote:
ReadyPlayerOne wrote:
amanvermagmat wrote:
Is the quadrilateral ABCD a rectangle?

(1) Mid points of AB, BC, CD and AD are E, F, G and H respectively. Quadrilateral EFGH is a rhombus.

(2) Diagonals of quadrilateral ABCD bisect each other.


statement 1 is insufficient alone, as the quadrilateral can be a square as well as a rectangle ( as per given info)
statement 2 is also insufficient alone as the quadrilateral can be a square as well as a rectangle ( as per given info)

combining statement will also not help in solving the problem as both square and rectangle satisfy the condition.

Hence E

DONT FORGET TO KUDOS



Square is also a rectangle..
so if ABCD is a square, it means it is a rectangle.
ofcourse vice versa may not be true

also statement I will be true for an isosceles trapezium too along with rectangle..
and statement II will also be true for rhombus along with rectangle and any parallelogram for that matter

combined
it will be a rectangle ..
see attached figure












Nice explanation, but I want to know why the combination of the statement A and B cannot be a rohmbus. (it has bisecting diagonals and for that matter statement 1 is also true for a rohmbus.
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Re: Is the quadrilateral ABCD a rectangle? (1) Mid points of AB, BC, CD  [#permalink]

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New post 28 Jun 2018, 09:06
ReadyPlayerOne wrote:
chetan2u wrote:
amanvermagmat wrote:
Is the quadrilateral ABCD a rectangle?

(1) Mid points of AB, BC, CD and AD are E, F, G and H respectively. Quadrilateral EFGH is a rhombus.

(2) Diagonals of quadrilateral ABCD bisect each other.



Square is also a rectangle..
so if ABCD is a square, it means it is a rectangle.
ofcourse vice versa may not be true

also statement I will be true for an isosceles trapezium too along with rectangle..
and statement II will also be true for rhombus along with rectangle and any parallelogram for that matter

combined
it will be a rectangle ..
see attached figure












Nice explanation, but I want to know why the combination of the statement A and B cannot be a rohmbus. (it has bisecting diagonals and for that matter statement 1 is also true for a rohmbus.



Incase you have a rhombus which has all sides equal but angles are not 90..
If you join the midpoints of side of this rhombus, the parallelogram so formed will not be a rhombus as all four sides will not be equal. Only opposite sides will be equal
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1) Absolute modulus : http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html
3) effects of arithmetic operations : https://gmatclub.com/forum/effects-of-arithmetic-operations-on-fractions-269413.html


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Re: Is the quadrilateral ABCD a rectangle? (1) Mid points of AB, BC, CD &nbs [#permalink] 28 Jun 2018, 09:06
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