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What is the area of the parallelogram ABCD? (1) The sum of Angle C an

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What is the area of the parallelogram ABCD? (1) The sum of Angle C an  [#permalink]

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New post 02 Sep 2018, 22:11
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62% (00:48) correct 38% (01:10) wrong based on 29 sessions

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What is the area of the parallelogram ABCD?

(1) The sum of Angle C and Angle B is 180°
(2) The shortest possible distance from point A to line segment DC is 10.


Attachment:
image024.jpg
image024.jpg [ 1.5 KiB | Viewed 352 times ]

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Re: What is the area of the parallelogram ABCD? (1) The sum of Angle C an  [#permalink]

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New post 03 Sep 2018, 02:53
Bunuel wrote:
Image
What is the area of the parallelogram ABCD?

(1) The sum of Angle C and Angle B is 180°
(2) The shortest possible distance from point A to line segment DC is 10.


Attachment:
image024.jpg


Question : What is the area of the parallelogram ABCD?

Area of Parallelogram = Base * Height

We already have Base = 8 so we only need the Height of the Parallelogram i.e. perpendicular distance between AB and CD

Statement 1: The sum of Angle C and Angle B is 180°

This is a fact about any parallelogram hence Options A C D may be eliminated only options B and E remain

NOT SUFFICIENT

Statement 2: The shortest possible distance from point A to line segment DC is 10.

i.e. Height = 10 hence

Area of parallelogram = 8*10 = 80

SUFFICIENT

Answer: Option B
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Re: What is the area of the parallelogram ABCD? (1) The sum of Angle C an  [#permalink]

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New post 03 Sep 2018, 08:47
GMATinsight wrote:
Bunuel wrote:
Image
What is the area of the parallelogram ABCD?

(1) The sum of Angle C and Angle B is 180°
(2) The shortest possible distance from point A to line segment DC is 10.


Attachment:
image024.jpg


Question : What is the area of the parallelogram ABCD?

Area of Parallelogram = Base * Height

We already have Base = 8 so we only need the Height of the Parallelogram i.e. perpendicular distance between AB and CD

Statement 1: The sum of Angle C and Angle B is 180°

This is a fact about any parallelogram hence Options A C D may be eliminated only options B and E remain

NOT SUFFICIENT

Statement 2: The shortest possible distance from point A to line segment DC is 10.

i.e. Height = 10 hence

Area of parallelogram = 8*10 = 80

SUFFICIENT

Answer: Option B


Can we consider the height as 90 degrees because it says that the shortest distance from point A to line segment DB in this case is always going to be at 90 degrees?
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Re: What is the area of the parallelogram ABCD? (1) The sum of Angle C an  [#permalink]

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New post 03 Sep 2018, 12:42
Bunuel wrote:
Image
What is the area of the parallelogram ABCD?

(1) The sum of Angle C and Angle B is 180°
(2) The shortest possible distance from point A to line segment DC is 10.


The following are just "conceptual considerations", not a new solution to this problem.

As mentioned in a previous post, two consecutive internal angles of ANY parallelogram are always supplements (i.e., their sum is 180 degrees).

In other words, statement (1) adds NOTHING to the question stem (pre-statements) and, because of that, we are sure (1) is INSUFFICIENT (= no need for an explicit bifurcation).

The rationale above DOES take into account an important implicit rule of ANY Data Sufficiency, the following:

In any Data Sufficiency problem, the question stem pre-statements is ALWAYS not enough to answer the focus (=question asked) in a unique way.

I hope these considerations are useful.

Regards,
fskilnik.
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What is the area of the parallelogram ABCD? (1) The sum of Angle C an  [#permalink]

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New post 03 Sep 2018, 22:57
rajudantuluri wrote:
GMATinsight wrote:
Bunuel wrote:
Image
What is the area of the parallelogram ABCD?

(1) The sum of Angle C and Angle B is 180°
(2) The shortest possible distance from point A to line segment DC is 10.


Attachment:
image024.jpg


Question : What is the area of the parallelogram ABCD?

Area of Parallelogram = Base * Height

We already have Base = 8 so we only need the Height of the Parallelogram i.e. perpendicular distance between AB and CD

Statement 1: The sum of Angle C and Angle B is 180°

This is a fact about any parallelogram hence Options A C D may be eliminated only options B and E remain

NOT SUFFICIENT

Statement 2: The shortest possible distance from point A to line segment DC is 10.

i.e. Height = 10 hence

Area of parallelogram = 8*10 = 80

SUFFICIENT

Answer: Option B


Can we consider the height as 90 degrees because it says that the shortest distance from point A to line segment DB in this case is always going to be at 90 degrees?


Short distance between a point and a line is obtained when a perpendicular is dropped from the point on the line. Hence, Shortest distance is same as perpendicular distance.

I think your question is about considering the side as the height, which may/may not be the height so we are not even bringing the length of the other side of this parallelogram.

I hope this helps!!!

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What is the area of the parallelogram ABCD? (1) The sum of Angle C an &nbs [#permalink] 03 Sep 2018, 22:57
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