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# The area of region ABCD

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The area of region ABCD [#permalink]  15 Dec 2016, 02:23
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00:00

Question Stats:

63% (00:41) correct 36% (00:36) wrong based on 22 sessions
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#GREpracticequestion ABCD is a parallelogram.jpg [ 5.26 KiB | Viewed 949 times ]

ABCD is a parallelogram

 Quantity A Quantity B The area of the region ABCD 24

A)The quantity in Column A is greater.
B)The quantity in Column B is greater.
C)The two quantities are equal.
D)The relationship cannot be determined from the information given.
[Reveal] Spoiler: OA

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Re: The area of region ABCD [#permalink]  29 Dec 2016, 13:45
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Carcass wrote:

ABCD is a parallelogram

 Quantity A Quantity B The area of the region ABCD 24

First notice that IF a RECTANGLE had lengths the same as the parallelogram...

...then the area of that rectangle would be 24 (since area = base x height = 4x6 = 24)

However, the given quadrilateral is NOT a rectangle.
Instead, the rectangle has been "pushed" over.

Notice that if we "push" the rectangle far enough, then its measurements will be the same as in the given diagram/

Most importantly, the height is now less than 6
The area of a parallelogram = base x height
So, the area = 4 x (some number that's less than 6) = some value that's less than 24

ASIDE: We need not find the actual height of the parallelogram; we need only recognize that it will be less than 6.

We have:
Quantity A: some value that's less than 24
Quantity B: 24

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Re: The area of region ABCD [#permalink]  03 Dec 2018, 20:45
Carcass..if not above logic , what could be the other solution.
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Re: The area of region ABCD [#permalink]  05 Dec 2018, 13:41
Expert's post
Sorry, In this particular case your geometry notions applied to the figure would lead to the right answer pretty fast.

I do not see any other strategy such as picking numbers, not here at least.

Regards
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Re: The area of region ABCD [#permalink]  05 Dec 2018, 13:43
Expert's post
Sorry, In this particular case your geometry notions applied to the figure would lead to the right answer pretty fast.

I do not see any other strategy such as picking numbers, not here at least.

Regards
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Re: The area of region ABCD [#permalink]  05 Dec 2018, 19:54
Expert's post
msk0657 wrote:
Carcass..if not above logic , what could be the other solution.

see what can be the area of the given parallelogram..
The area of a parallelogram is Base * Height.
Base is 4 and height is a, which will be less than 6 as 6 is the hypotenuse and thus he largest side of right angled triangle.
therefore area will be < 4*6 or <24.
hence B>A.

B
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1. Arithmetic and Geometric progressions : https://greprepclub.com/forum/progressions-arithmetic-geometric-and-harmonic-11574.html#p27048
2. Effect of Arithmetic Operations on fraction : https://greprepclub.com/forum/effects-of-arithmetic-operations-on-fractions-11573.html?sid=d570445335a783891cd4d48a17db9825
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5. Absolute Modulus and Inequalities : https://greprepclub.com/forum/absolute-modulus-a-better-understanding-11281.html

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Re: The area of region ABCD [#permalink]  06 Dec 2018, 01:13
It's quite simple.
The area of a parallelogram will be 6x4xSin125. That's 24Sin125. The value of Sin125 should be less than 1. That will reduce the area below 24. So 24 is more than 24 Sin125.
It's B
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Re: The area of region ABCD [#permalink]  14 Feb 2019, 12:46
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Carcass wrote:
Attachment:
#GREpracticequestion ABCD is a parallelogram.jpg

ABCD is a parallelogram

 Quantity A Quantity B The area of the region ABCD 24

A)The quantity in Column A is greater.
B)The quantity in Column B is greater.
C)The two quantities are equal.
D)The relationship cannot be determined from the information given.

Here's a different approach:

The area of a parallelogram = (base)(height)

We know the base has length 4...

...however, we don't know the height:

However, if we recognize that we have a RIGHT TRIANGLE hiding in our diagram...

... we can use the fact that the hypotenuse is always the longest side in a RIGHT TRIANGLE.
Since the hypotenuse in the above triangle has length 6, we know that the other sides of the right triangle are LESS THAN 6

This means the triangle's height is less than 6

It also means the height of the parallelogram is less than 6

The area of a parallelogram = (base)(height)
= (4)(some number less than 6)
= some number less than 24

So, we get:
QUANTITY A: some number less than 24
QUANTITY B: 24

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Re: The area of region ABCD   [#permalink] 14 Feb 2019, 12:46
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