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

Question

https://gmatclub.com/forum/download/file.php?id=47158 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 6bc7311ff3d3544995cdcaf4af10e95b690b3f22.png

Archit3110 · Answer

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

anshkool4u · Answer

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

Posted from my mobile device

GMATinsight · Answer

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

Archit3110 · Answer

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

...

Fdambro294 · Answer

Each area of 1 square is 1 unit squared (each square has dimensions of 1 by 1)

The area of the 5 squares thus ——-> 5 units squared

And the Slant Line creates an Area ——> (1/2) * 5 = 5/2

If we add one more square in on the bottom to complete the shaded triangle, it would add more 1 more unit squared of Area.

Thus, we would have a right Triangle with Area = 5/2 + 1 = 7/2

The height would be given by the Y coordinate of 3

The base would be given by: (3) - (a) =
Base——-> call this B

Area of Triangle = (1/2) * B * 3 = 7/2

B = 7/3

Plug in the value of the Base and find a

7/3 = (3) - (a)

a = 2/3

Posted from my mobile device

bumpbot · Answer

Automated notice from GMAT Club BumpBot: 

A member just gave Kudos to this thread, showing it’s still useful. I’ve bumped it to the top so more people can benefit. Feel free to add your own questions or solutions.

 This post was generated automatically.

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

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards

GMAT Problem Solving (PS) Questions

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

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards