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# M28-18

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Math Expert
Joined: 02 Sep 2009
Posts: 56300

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16 Sep 2014, 01:29
1
7
00:00

Difficulty:

65% (hard)

Question Stats:

48% (01:19) correct 52% (01:31) wrong based on 89 sessions

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What is the area of a region enclosed by $$|\frac{x}{3}|+|\frac{y}{9}|=10$$?

A. $$675$$
B. $$1350$$
C. $$2700$$
D. $$5400$$
E. $$10800$$

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Math Expert
Joined: 02 Sep 2009
Posts: 56300

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16 Sep 2014, 01:29
Official Solution:

What is the area of a region enclosed by $$|\frac{x}{3}|+|\frac{y}{9}|=10$$?

A. $$675$$
B. $$1350$$
C. $$2700$$
D. $$5400$$
E. $$10800$$

Find the $$x$$ and $$y$$ intercepts.

When $$y=0$$, then $$x=30$$ or $$x=-30$$.

When $$x=0$$, then $$y=90$$ or $$x=-90$$.

So, we have 4 points: (30, 0), (-30, 0) (0, 90), (0, -90). When joining these points we get the rhombus:

The area of a rhombus is $$\frac{d_1*d_2}{2}$$ (where $$d_1$$ and $$d_2$$ are the lengths of the diagonals), thus the area of the enclosed figure is $$\frac{60*180}{2}=5,400$$.

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Manager
Joined: 26 Apr 2012
Posts: 82
Location: India
Concentration: Entrepreneurship, General Management
GMAT 1: 640 Q48 V29
GMAT 2: 660 Q45 V35
GMAT 3: 680 Q48 V35
GPA: 2.8
WE: Information Technology (Computer Software)

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16 Oct 2016, 23:24
Hello,

Why we not considered the figure square ?

Is it because,in square, the four pieces of diagonals from the point of intersections are all equal. But here they are not ?

Thanks
Math Expert
Joined: 02 Sep 2009
Posts: 56300

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17 Oct 2016, 03:12
karant wrote:
Hello,

Why we not considered the figure square ?

Is it because,in square, the four pieces of diagonals from the point of intersections are all equal. But here they are not ?

Thanks

If you refer to the image you'd see that the figure is NOT a square (the diagonals are not equal).
_________________
Manager
Joined: 26 Apr 2012
Posts: 82
Location: India
Concentration: Entrepreneurship, General Management
GMAT 1: 640 Q48 V29
GMAT 2: 660 Q45 V35
GMAT 3: 680 Q48 V35
GPA: 2.8
WE: Information Technology (Computer Software)

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17 Oct 2016, 09:56
Bunuel wrote:
karant wrote:
Hello,

Why we not considered the figure square ?

Is it because,in square, the four pieces of diagonals from the point of intersections are all equal. But here they are not ?

Thanks

If you refer to the image you'd see that the figure is NOT a square (the diagonals are not equal).

Got it. Thanks Bunuel !!
Manager
Joined: 02 Jan 2016
Posts: 124

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11 May 2018, 22:46
Hi Karan,

More reliable way to find out whether this is square or not is to know the fact that, when the Rise/Run is equal i.e 10/10 or 25/25 in otherwords where the Slope is 1, we end up with 45-45-90 triangle. we add up all the four 45-45-90 triangle we end up with square, in this example clearly the Rise/Run is not 1. Hence it is a Rhombus and not a square.
Intern
Joined: 07 May 2018
Posts: 3
GMAT 1: 660 Q39 V41

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01 Nov 2018, 09:49
1
In case you don't have the equation for the area of a rhombus memorized, you could have also multiplied the area of a triangle by 4. This figure is made up of 4 equal triangles.
Area of triangle = 1/2bh
Area of our figure=4*(1/2*30*90)=5400
M28-18   [#permalink] 01 Nov 2018, 09:49
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# M28-18

Moderators: chetan2u, Bunuel