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GMATinsight
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Schools: IIM (A) ISB '24
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Find the area bounded by the graphs 2x+y=10, x+2y=6 and y-x=6. A) 12 09 Aug 2023, 08:04
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Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!

Difficulty:

95% (hard)

Question Stats:

35% (02:37) correct 65% (03:06) wrong based on 43 sessions

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Find the area bounded by the graphs 2x+y=10, x+2y=6 and y-x=6.

A) 12 1/3
B) 12 2/3
C) 14 2/3
D) 16 2/3
E) 18 1/3

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D
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Find the area bounded by the graphs 2x+y=10, x+2y=6 and y-x=6. A) 12 13 Aug 2023, 03:03
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GMATinsight , I though managed to solve it but it took > 2mins
I hope that there is a way to solve in <2 mins as well..

below is my explanation


given are three line equations
2x+y-10=0
x+2y-6=0
-x+y-6=0
point of intersection of these three lines can be determined by
x= (b1c2-b2c1/ a1b2-a2b1)
y= ( a2c1-a1c2/ a1b2-a2b1)
we get
A = 4/3 , 22/3
B= 14/3 , 2/3
C= -2 , 4
∆ area will be
l ax(by-cy) + bx(cy-ay) +cx( ay-by)/2 l
solve we get
300/18 ; 16.6
option D 16 2/3

GMATinsight
Find the area bounded by the graphs 2x+y=10, x+2y=6 and y-x=6.

A) 12 1/3
B) 12 2/3
C) 14 2/3
D) 16 2/3
E) 18 1/3

Source: http://www.GMATinsight.com
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Find the area bounded by the graphs 2x+y=10, x+2y=6 and y-x=6. A) 12 13 Aug 2023, 06:59
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Once you get the intersection points, its easier to solve it through (area of larger triangle- area of smaller triangle). Its much faster.
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Find the area bounded by the graphs 2x+y=10, x+2y=6 and y-x=6. A) 12 26 Oct 2023, 05:43
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Can someone please give the solution to this problem Bunuel, KarishmaB, ScottTargetTestPrep.
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Find the area bounded by the graphs 2x+y=10, x+2y=6 and y-x=6. A) 12 26 Oct 2023, 08:34
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Could this question actually be asked on the GMAT ? I don't recall this formula for line intersection in the TTP course and it seems overly cumbersome even if it were testable material - perhaps there is some other more intuitive way?
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Find the area bounded by the graphs 2x+y=10, x+2y=6 and y-x=6. A) 12 26 Oct 2023, 22:03
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adityashinde88
Can someone please give the solution to this problem Bunuel, KarishmaB, ScottTargetTestPrep.
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Here is the solution. You use simultaneous equations to get the points of intersection.

Attachment:
Screenshot 2023-10-27 at 10.31.19 AM.png
Screenshot 2023-10-27 at 10.31.19 AM.png [ 100.85 KiB | Viewed 1457 times ]

Answer (D)
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Find the area bounded by the graphs 2x+y=10, x+2y=6 and y-x=6. A) 12 26 Oct 2023, 22:11
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FyodorPiketty
Could this question actually be asked on the GMAT ? I don't recall this formula for line intersection in the TTP course and it seems overly cumbersome even if it were testable material - perhaps there is some other more intuitive way?
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You can find the points of intersection by simply solving equations simultaneously and can solve for the area of the triangle by subtracting out from the big triangle as done in the figure above. You do not need to use any other formulas or matrices.

As for whether this question can be asked on the GMAT, the quick answer is 'No' but there is a whole lot more to it. When you go through the curriculum of a test prep, there are lots of concepts we need to make you understand. There are lots of pieces of the puzzle that we need to ensure you put in place. So we make many conceptual questions (I do in my curriculum too!) - the ones that will not be solved in under 2 mins but will help you understand the entire big picture or the process or the flow of data. In the actual test, you could get a question asking for the area of the bounded region but it will require far fewer steps and might have a trick or two. After you solve conceptual questions like this one, those will make more sense so these need to be taken in the right spirit. They are a part of the 'learning phase,' not the 'testing phase.'
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Find the area bounded by the graphs 2x+y=10, x+2y=6 and y-x=6. A) 12 01 Mar 2025, 23:58
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