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Five unit squares are arranged in the coordinate plane as shown, with

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Five unit squares are arranged in the coordinate plane as shown, with  [#permalink]

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New post 29 Mar 2019, 00:38
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Five unit squares are arranged in the coordinate plane as shown, with the lower left corner at the origin. The slanted line, extending from (a,0) to (3,3), divides the entire region into two regions of equal area. What is a?

(A) 1/2
(B) 3/5
(C) 2/3
(D) 3/4
(E) 4/5

Attachment:
6bc7311ff3d3544995cdcaf4af10e95b690b3f22.png
6bc7311ff3d3544995cdcaf4af10e95b690b3f22.png [ 26.46 KiB | Viewed 336 times ]

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Five unit squares are arranged in the coordinate plane as shown, with  [#permalink]

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New post Updated on: 30 Mar 2019, 00:35
Bunuel wrote:
Image
Five unit squares are arranged in the coordinate plane as shown, with the lower left corner at the origin. The slanted line, extending from (a,0) to (3,3), divides the entire region into two regions of equal area. What is a?

(A) 1/2
(B) 3/5
(C) 2/3
(D) 3/4
(E) 4/5

Attachment:
6bc7311ff3d3544995cdcaf4af10e95b690b3f22.png


total area of the square region = 1*1*5 ; 5
line (a,0) to (3,3) forms a triangle and its area
1/2 * (3-a) * 3 ----(1)
a 6th square will be a part of this triangle so we need to subtract it from (1)

1/2 *9-3a -1
7-3a / 1/2 --(B)
given that line The slanted line, extending from (a,0) to (3,3), divides the entire region into two regions of equal area viz.
area of triangle is equal to half the area of 5 squares
i.e
7-3a / 1/2 = 1/2 * 5 *1*1
solve for a
a = 2/3
IMO C
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Originally posted by Archit3110 on 29 Mar 2019, 07:28.
Last edited by Archit3110 on 30 Mar 2019, 00:35, edited 1 time in total.
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Five unit squares are arranged in the coordinate plane as shown, with  [#permalink]

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New post 29 Mar 2019, 08:16
The area of entire figure is 5 unit^2.
The area of shaded region will be half of the area of entire figure= 5/2=2.5 unit^2.

Now,area of shaded figure can also be thought of as 0.5*3*(3-a) -1 unit^2 = 3.5-1.5a ( we can consider the shaded area as comprising of one more unit square ,which makes the shaded region a right angled triangle.Later to find the area of actual shaded region,subtract the area of that additional square)

Therefore,2.5=3.5-1.5a
Hence ,a=1/1.5= 2/3

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Five unit squares are arranged in the coordinate plane as shown, with  [#permalink]

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New post 29 Mar 2019, 22:31
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Archit3110 wrote:
Bunuel wrote:
Image
Five unit squares are arranged in the coordinate plane as shown, with the lower left corner at the origin. The slanted line, extending from (a,0) to (3,3), divides the entire region into two regions of equal area. What is a?

(A) 1/2
(B) 3/5
(C) 2/3
(D) 3/4
(E) 4/5

Attachment:
6bc7311ff3d3544995cdcaf4af10e95b690b3f22.png


not able to completely solve the question
the side of each square side = 1
so total area = 5 of all squares
the tricky part is of determing the shaded area and non shaded area of each square
GMATinsight ; sir kindly advise on how to solve this question..

Archit3110

Let's assume there is a sixth square block at the right bottom corner as well which makes the shaded region a triangle with base (3-a) units long and height of 3 units

Shaded area = Area of Triangle with base (3-a) and height 3 - area of assumed sixth square = (1/2)*area of five squares

i.e. Shaded Area = (1/2)*(3-a)*3 - 1*1 = (1/2)*1*1*5 (half of the area of five squares of dimension 1 unit each)

i.e. 9 - 3a - 2 = 5

i.e. 7 - (5) = 3a

i.e. 2 = 3a

i.e. a = 2/3

Answer: Option C
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Re: Five unit squares are arranged in the coordinate plane as shown, with  [#permalink]

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New post 30 Mar 2019, 00:30
GMATinsight ; thank you sir for the solution..
two things I had done wrong while initially solving the question.
1. i did not subtract the area of triangle with area of square
2. I overlooked the question , where it says that line (a,0) to (3,3) divides the area of region equally :( ...





GMATinsight wrote:
Archit3110 wrote:
Bunuel wrote:
Image
Five unit squares are arranged in the coordinate plane as shown, with the lower left corner at the origin. The slanted line, extending from (a,0) to (3,3), divides the entire region into two regions of equal area. What is a?

(A) 1/2
(B) 3/5
(C) 2/3
(D) 3/4
(E) 4/5

Attachment:
6bc7311ff3d3544995cdcaf4af10e95b690b3f22.png


not able to completely solve the question
the side of each square side = 1
so total area = 5 of all squares
the tricky part is of determing the shaded area and non shaded area of each square
GMATinsight ; sir kindly advise on how to solve this question..

Archit3110

Let's assume there is a sixth square block at the right bottom corner as well which makes the shaded region a triangle with base (3-a) units long and height of 3 units

Shaded area = Area of Triangle with base (3-a) and height 3 - area of assumed sixth square = (1/2)*area of five squares

i.e. Shaded Area = (1/2)*(3-a)*3 - 1*1 = (1/2)*1*1*5 (half of the area of five squares of dimension 1 unit each)

i.e. 9 - 3a - 2 = 5

i.e. 7 - (5) = 3a

i.e. 2 = 3a

i.e. a = 2/3

Answer: Option C

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Re: Five unit squares are arranged in the coordinate plane as shown, with   [#permalink] 30 Mar 2019, 00:30
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Five unit squares are arranged in the coordinate plane as shown, with

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