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A parallelogram is drawn in the xy-coordinate plane. Is the parallelog

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A parallelogram is drawn in the xy-coordinate plane. Is the parallelog  [#permalink]

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New post 26 Feb 2015, 16:11
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A parallelogram is drawn in the xy-coordinate plane. Is the parallelogram's area, in square units, an integer?

(1) The x- and y-coordinates of each of the parallelogram's four vertices are integers.

(2) The parallelogram has four sides of equal length.
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Re: A parallelogram is drawn in the xy-coordinate plane. Is the parallelog  [#permalink]

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New post 26 Feb 2015, 16:59
1
Question: A=b*h, where b is the base and h is the height.

(1) Sufficient. Draw a parallelogram in the xy-coordinate plane and you see that if all of the vertices of the parallelogram have integer coordinates, then the coordinates of the height will be integers as well. That is, the point of one end of the height will have the same coordinates as one of the vertices, hence, integers. And the point of the other end the height (where it meets the base) will have the same x-coordinate as one of the vertices and the y-coordante that will be the same as the y-coordinate of the other vertex. When you'll be calculating the length of the height (h), you care only about its y-coordinates (which are integers). The difference of two integers will give you an integer (h). The length of the base will be an integer too. Area= integer*integer= integer.
(2) Insufficient. The lengths of the height and base could be anything.
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Re: A parallelogram is drawn in the xy-coordinate plane. Is the parallelog  [#permalink]

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New post 17 Dec 2016, 09:03
santorasantu wrote:
A parallelogram is drawn in the xy-coordinate plane. Is the parallelogram's area, in square units, an integer?

(1) The x- and y-coordinates of each of the parallelogram's four vertices are integers.

(2) The parallelogram has four sides of equal length.

Please give me a shortcut to solve this within 2 minutes

I didn't get how statement 1 is sufficient? Can you please help me to grasp it,expert?
Thank you...
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Re: A parallelogram is drawn in the xy-coordinate plane. Is the parallelog  [#permalink]

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New post 17 Dec 2016, 20:01
iMyself wrote:
santorasantu wrote:
A parallelogram is drawn in the xy-coordinate plane. Is the parallelogram's area, in square units, an integer?

(1) The x- and y-coordinates of each of the parallelogram's four vertices are integers.

(2) The parallelogram has four sides of equal length.

Please give me a shortcut to solve this within 2 minutes

I didn't get how statement 1 is sufficient? Can you please help me to grasp it,expert?
Thank you...



iMyself

try drawing any parallelogram having integer coordinates

(2,3) (3,8) (6,8) (5,3)
here H=5 and B=3
Area=5*3=15 integer...thus suff...for any integer coordinates

whereas in statement 2 ,if cordinates are fractions then we get either H or B or both values in fraction
leading to any integer/fraction values..hence insuff..

Ans A
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Re: A parallelogram is drawn in the xy-coordinate plane. Is the parallelog  [#permalink]

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New post 26 Mar 2017, 04:45
rohit8865 wrote:
iMyself wrote:
santorasantu wrote:
A parallelogram is drawn in the xy-coordinate plane. Is the parallelogram's area, in square units, an integer?

(1) The x- and y-coordinates of each of the parallelogram's four vertices are integers.

(2) The parallelogram has four sides of equal length.

Please give me a shortcut to solve this within 2 minutes

I didn't get how statement 1 is sufficient? Can you please help me to grasp it,expert?
Thank you...



iMyself

try drawing any parallelogram having integer coordinates

(2,3) (3,8) (6,8) (5,3)
here H=5 and B=3
Area=5*3=15 integer...thus suff...for any integer coordinates

whereas in statement 2 ,if cordinates are fractions then we get either H or B or both values in fraction
leading to any integer/fraction values..hence insuff..

Ans A

:) This question is from Manhattan GMAT challenge question, so I thought it will be difficult to make the solution and I scared about it. But, this question is more easier, i think. It may take just 30 seconds to solve this problem. Anyway Thank you rohit8865. Goodluck man...
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Re: A parallelogram is drawn in the xy-coordinate plane. Is the parallelog  [#permalink]

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New post 26 Mar 2017, 13:00
Hi,

Even if all the vertices of a parallelogram are integers, the parallelogram might be tilted on XY plane and in that case the lengths of height and base might be fractions. You can try with a rectangle since it is a parallelogram on XY plane. So I guess the ans should be E.
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Re: A parallelogram is drawn in the xy-coordinate plane. Is the parallelog  [#permalink]

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New post 01 May 2018, 10:10
Bunuel .... could you pls help on this
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Re: A parallelogram is drawn in the xy-coordinate plane. Is the parallelog  [#permalink]

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New post 19 Nov 2018, 10:04
The area of a parallelogram is base multiplied by height that is base * height. If the x coordinates and y coordinates are integers then the multiplication of the base (an integer) and height (an integer) will result in an integer. Hence A is sufficient.

From B we do not know if the base and height are integers or not. Hence, the multiplication of base and height may or may not result in an integer.
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Re: A parallelogram is drawn in the xy-coordinate plane. Is the parallelog  [#permalink]

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New post 05 Mar 2019, 04:39
anant327 wrote:
The area of a parallelogram is base multiplied by height that is base * height. If the x coordinates and y coordinates are integers then the multiplication of the base (an integer) and height (an integer) will result in an integer. Hence A is sufficient.

From B we do not know if the base and height are integers or not. Hence, the multiplication of base and height may or may not result in an integer.



even if the base and height coordinates are integers..........base and height lengths may or may not be integers.......Try tilting the parallelogram in the XY plane..........

Thoughts on this Bunuel
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Re: A parallelogram is drawn in the xy-coordinate plane. Is the parallelog  [#permalink]

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New post 09 Mar 2019, 06:21
Can anyone explain with diagram?
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Re: A parallelogram is drawn in the xy-coordinate plane. Is the parallelog  [#permalink]

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New post 18 Mar 2019, 09:05
avikroy wrote:
anant327 wrote:
The area of a parallelogram is base multiplied by height that is base * height. If the x coordinates and y coordinates are integers then the multiplication of the base (an integer) and height (an integer) will result in an integer. Hence A is sufficient.

From B we do not know if the base and height are integers or not. Hence, the multiplication of base and height may or may not result in an integer.



even if the base and height coordinates are integers..........base and height lengths may or may not be integers.......Try tilting the parallelogram in the XY plane..........

Thoughts on this Bunuel


Can you please tell me an example of 4 coordinates which has integer x and y coorfinates but has a decimal length ?

Posted from my mobile device
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Re: A parallelogram is drawn in the xy-coordinate plane. Is the parallelog  [#permalink]

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New post 19 Mar 2019, 06:52
anant327 wrote:
avikroy wrote:
anant327 wrote:
The area of a parallelogram is base multiplied by height that is base * height. If the x coordinates and y coordinates are integers then the multiplication of the base (an integer) and height (an integer) will result in an integer. Hence A is sufficient.

From B we do not know if the base and height are integers or not. Hence, the multiplication of base and height may or may not result in an integer.



even if the base and height coordinates are integers..........base and height lengths may or may not be integers.......Try tilting the parallelogram in the XY plane..........

Thoughts on this Bunuel


Can you please tell me an example of 4 coordinates which has integer x and y coorfinates but has a decimal length ?

Posted from my mobile device




For easier calculation, lets take one of the vertices is the origin (0,0)
Another vertices of parallelogram be (7, 3) and the line passes through these points be a length

Length of this side of parallelogram = \(\sqrt{7^2+3^2}\) = \(\sqrt{58}\) --> not an integer

Width of parallelogram can be any integer, it will not give area in integer.

Thus i feel answer should be E.

Am I missing something?
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Re: A parallelogram is drawn in the xy-coordinate plane. Is the parallelog   [#permalink] 19 Mar 2019, 06:52
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