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M28-18

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M28-18 [#permalink]

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New post 16 Sep 2014, 01:29
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Question Stats:

61% (00:49) correct 39% (02:16) wrong based on 28 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. \(10800\)
Spoiler: OA

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M28-18 [#permalink]

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New post 16 Sep 2014, 01:29
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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:

Image

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 \(\frac{60*180}{2}=5,400\).


Answer: D
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Re: M28-18 [#permalink]

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New post 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 ?

Please explain the reasoning.

Thanks
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Re: M28-18 [#permalink]

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New post 17 Oct 2016, 03:12
Expert's post
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 ?

Please explain the reasoning.

Thanks


If you refer to the image you'd see that the figure is NOT a square (the diagonals are not equal).
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Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


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Re: M28-18 [#permalink]

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New post 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 ?

Please explain the reasoning.

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 !!
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Re: M28-18 [#permalink]

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New post 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.
Re: M28-18   [#permalink] 11 May 2018, 22:46
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