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What is the area of quadrilateral ABCD? (1) The diagonals of the quad

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What is the area of quadrilateral ABCD? (1) The diagonals of the quad  [#permalink]

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New post 08 Apr 2020, 02:11
00:00
A
B
C
D
E

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  55% (hard)

Question Stats:

41% (00:56) correct 59% (00:53) wrong based on 38 sessions

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Re: What is the area of quadrilateral ABCD? (1) The diagonals of the quad  [#permalink]

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New post 08 Apr 2020, 02:27
1) rectangle, square
2) rhombus, square
1+2 => square, so 10*10=100
ans C
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Re: What is the area of quadrilateral ABCD? (1) The diagonals of the quad  [#permalink]

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New post 08 Apr 2020, 03:04
Answer is supposedly B.
Since statement one is drawing out two conclusion that either the quadrilateral is a rhombus or square because both of them have their diagonal perpendicular bisect each other. But that doesn't give any specific value.
(Not sufficient)
Statement 2 is again staring the quadrilateral be either rhombus or square. But with the given sides.
We can easily put out the area of Quadrilateral. Which is 100 in both cases.
Square=10^2=100
And rhombus= diaonalA*diagonalB/2 (diagonal is drawn by using Pythagoras theorem)
10√2*10*√2/2=100 (sufficient)
So B should be the OA

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Re: What is the area of quadrilateral ABCD? (1) The diagonals of the quad  [#permalink]

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New post 08 Apr 2020, 04:31
1
Quote:
What is the area of quadrilateral ABCD?

(1) The diagonals of the quadrilateral are perpendicular bisectors of each other.

(2) The length of each side of the quadrilateral is 10 cm.


Question: Area of ABCD = ?

Statement 1: The diagonals of the quadrilateral are perpendicular bisectors of each other

i.e. ABCD is a square or a Rhombus

Dimensions are unknown also it's uncertain whether it's a rhombus or a square (a type of rhombus) hence

NOT SUFFICIENT

Statement 2: The length of each side of the quadrilateral is 10 cm.

It could be a square as well as a non-square rhombus and the area will be different in two cases hence

NOT SUFFICIENT

Combining the two statements

It could be a square of side 10 and area 100 as well as a non-square rhombus with area less than 100 hence

NOT SUFFICIENT

Answer: Option E
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Re: What is the area of quadrilateral ABCD? (1) The diagonals of the quad  [#permalink]

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New post 08 Apr 2020, 04:32
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Q) What is the area of quadrilateral ABCD?
(1) The diagonals of the quadrilateral are perpendicular bisectors of each other.
(2) The length of each side of the quadrilateral is 10 cm.

A) In order to evaluate the area of the quadrilateral ABCD, we need to know the following :
a) Type of quadrilateral b) Dimensions required to compute the area

Considering statement (1) alone, we can infer that the quadrilateral can be either a rhombus or a square. But since the dimensions are unknown, we cannot find its area. Hence INSUFFICIENT

Considering statement (2) alone, we are given the dimensions of the quadrilateral but do not know which quadrilateral it is. Hence INSUFFICIENT

Considering both the statements (1) and (2), we know that the quadrilateral is either a rhombus or a square of length 10cm. Since, the area of a rhombus and square are not equal, we cannot find the required area. Hence INSUFFICIENT

Hence E is the right option answer.
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What is the area of quadrilateral ABCD? (1) The diagonals of the quad  [#permalink]

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New post Updated on: 09 Apr 2020, 01:35
(1)
If the diagonals of a quadrilateral are perpendicular bisectors of each other, the quadrilateral must be a square or a rhombus. However, no length dimension is given, so we cannot calculate area of ABCD.
NOT SUFFICIENT

(2)
Equal length on its four sides, the quadrilateral could be a square or a rhombus or a kite.
- If it is square, then the area is 10*10 = 100 cm^2
- If it is either a rhombus or a kite, then the area is < 100cm^2, depending on the angle between the horizontal and the vertical sides.
NOT SUFFICIENT

(1)+(2)
We are uncertain whether the quadrilateral is a square or a rhombus. Thus, the area of ABCD is either 10*10 = 100 cm^2 or less.
NOT SUFFICIENT

FINAL ANSWER IS (E)

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Originally posted by chondro48 on 08 Apr 2020, 05:27.
Last edited by chondro48 on 09 Apr 2020, 01:35, edited 1 time in total.
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Re: What is the area of quadrilateral ABCD? (1) The diagonals of the quad  [#permalink]

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New post 08 Apr 2020, 08:23
#1
The diagonals of the quadrilateral are perpendicular bisectors of each other.
it can be rhombus, rectangle or square insufficient
#2
The length of each side of the quadrilateral is 10 cm.
it can be a square or rhombus
insufficient
from 1 &2
we can say that the length of digonal will be 10√2 ie are equal so it will be a square or it can be a rhombus as well

IMO E ; sufficient

What is the area of quadrilateral ABCD?

(1) The diagonals of the quadrilateral are perpendicular bisectors of each other.

(2) The length of each side of the quadrilateral is 10 cm.
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Re: What is the area of quadrilateral ABCD? (1) The diagonals of the quad  [#permalink]

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New post 08 Apr 2020, 09:27
What is the area of quadrilateral ABCD?

(1) The diagonals of the quadrilateral are perpendicular bisectors of each other.
Whether quadrilateral is square or a rhombus, it's not given.
Areas may or may not differ but more importantly nothing as such is available to calculate them.

INSUFFICIENT.

(2) The length of each side of the quadrilateral is 10 cm.
Maximum area possible i.e. when it a square with these = 10*10 = 100
For other quadrilateral which is a rhombus the area would be less.

INSUFFICIENT.

Together 1 and 2
It is clear from both that the quadrilateral is a square.
Area = 10*10 = 100

SUFFICIENT.

Answer C.
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Re: What is the area of quadrilateral ABCD? (1) The diagonals of the quad  [#permalink]

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New post 08 Apr 2020, 12:55
Quote:
What is the area of quadrilateral ABCD?

(1) The diagonals of the quadrilateral are perpendicular bisectors of each other.

(2) The length of each side of the quadrilateral is 10 cm.


(1) insufic

(2) insufic
rhombus or a square

(1/2) insufic
diagonals of square and rhombus are perp bisect

Ans (E)
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Re: What is the area of quadrilateral ABCD? (1) The diagonals of the quad  [#permalink]

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New post 08 Apr 2020, 14:25
1
Statement 1 doesn't have any information with respect to dimension. Area cannot be found.

Statement 2 mentioned that all sides are equal. This could be a square or a rhombus. Insufficient.

Together,we still have no information regarding the angle of adjacent sides or size of the diagonals.

Answer E.

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Re: What is the area of quadrilateral ABCD? (1) The diagonals of the quad   [#permalink] 08 Apr 2020, 14:25

What is the area of quadrilateral ABCD? (1) The diagonals of the quad

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