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# If equation |x/2| + |y/2| = 5 enclose a certain region

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Intern
Joined: 29 May 2015
Posts: 10
Re: If equation |x/2| + |y/2| = 5 enclose a certain region  [#permalink]

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22 Sep 2015, 23:35
I think there is a pattern for this sort of problem.

1. x<0 and y<0 --> −x−y=10 --> y=−10−x;

2. x<0 and y≥0 --> −x+y=10 --> y=10+x;

3. x≥0 and y<0 --> x−y=10 --> y=x−10;

4. x≥0 and y≥0 --> x+y=10 --> y=10−x;

From above, we see that 1 & 4 are parallel, since they have the same slope, as this would be the case for 2 & 4.
From above, we see that intersection points on x and y-axis is -10 and 10.

If you get to this far, you know it is a sqaure.

Afterwards, as written by many ppl, it is just finding an area of a square, 200.
Manager
Joined: 18 Apr 2018
Posts: 93
Re: If equation |x/2| + |y/2| = 5 enclose a certain region  [#permalink]

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09 Jul 2018, 05:16
Hi guys, really good explanation. Totally get it. I have a question though, Is it possible to solve this in less than 3 mins because I spent about 5mins on it.

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Intern
Joined: 10 Jun 2019
Posts: 9
Re: If equation |x/2| + |y/2| = 5 enclose a certain region  [#permalink]

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17 Jun 2019, 04:55
Approach the question by trying to find the intercept of the equations.
So when y=0 => |x/2|=5 => x = 10 and -10.
Similarly, when x=0 => |y/2|=5 => y = 10 or -10.
So we get an area bounded by the above intercepts and symmetrical about the x-y axis.
Therefore we can find the area of 1 region and multiply by 4 to get the total area.
Area of one region = 1/2*10*10 = 50.
Total area = 50*4 = 200. Option D is the right answer.
Re: If equation |x/2| + |y/2| = 5 enclose a certain region   [#permalink] 17 Jun 2019, 04:55

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