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What is the area of a triangle?

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What is the area of a triangle?  [#permalink]

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New post 31 Aug 2018, 01:12
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A
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C
D
E

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[Math Revolution GMAT math practice question]

What is the area of a triangle?

1) The triangle is isosceles.
2) Two sides of the triangle are 10.

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Re: What is the area of a triangle?  [#permalink]

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New post 31 Aug 2018, 01:15
MathRevolution wrote:
[Math Revolution GMAT math practice question]

What is the area of a triangle?

1) The triangle is isosceles.
2) Two sides of the triangle are 10.


S1 - Unable to find area. No sides are given.
Insufficient.

S2 - Even with 2 sides given, the area can differ.
Insufficient.

Combining, also gives no addition information than S2.
Answer E.
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Re: What is the area of a triangle?  [#permalink]

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New post 31 Aug 2018, 01:31
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(1) : No side measurements given, thus not sufficient

(2) : The triangle could be an equilateral triangle or an isosceles one (further in the case of which, the height, length of the base, and thus the area have multiple possibilities) : Not Sufficient

Combined : Also not sufficient

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What is the area of a triangle?  [#permalink]

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New post 31 Aug 2018, 08:19
MathRevolution wrote:
[Math Revolution GMAT math practice question]

What is the area of a triangle?

1) The triangle is isosceles.
2) Two sides of the triangle are 10.


The image below shows our GEOMETRIC BIFURCATION for (1+2), one of our most powerful tools when dealing with Geometry-related Data Sufficiency problems!

This solution follows the notations and rationale taught in the GMATH method.
Attachments

31Ago18_4w.gif
31Ago18_4w.gif [ 23.82 KiB | Viewed 259 times ]


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Re: What is the area of a triangle?  [#permalink]

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New post 31 Aug 2018, 08:34
Excerpt from the awesome GMAT Math book from the Triangles section.

Area The number of square units it takes to exactly fill the interior of a triangle.

Usually called "half of base times height", the area of a triangle is given by the formula below.
• \(A=\frac{hb}{2}\)

Other formula:
• \(A=\frac{P*r}{2}\)

• \(A=\frac{abc}{4R}\)

Where \(b\) is the length of the base, \(a\) and \(c\) the other sides; \(h\) is the length of the corresponding altitude; \(R\) is the Radius of circumscribed circle; \(r\) is the radius of inscribed circle; P is the perimeter

• Heron's or Hero's Formula for calculating the area \(A = \sqrt{s(s-a)(s-b)(s-c)}\) where \(a,b,c\) are the three sides of the triangle and \(s = \frac{a+b+c}{2}\) which is the semi perimeter of the triangle.


Clearly, we need either base and height of the triangle or the three sides to calculate the area, and both the statements individually, or even when combined, fail to give that essential information. Hence, the correct answer should be (E)

MathRevolution wrote:
[Math Revolution GMAT math practice question]

What is the area of a triangle?

1) The triangle is isosceles.
2) Two sides of the triangle are 10.



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Re: What is the area of a triangle?  [#permalink]

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New post 02 Sep 2018, 18:47
=>

Forget conventional ways of solving math questions. For DS problems, the VA (Variable Approach) method is the quickest and easiest way to find the answer without actually solving the problem. Remember that equal numbers of variables and independent equations ensure a solution.

When we apply the VA (Variable Approach) method to a triangle, we have 3 variables corresponding to the side-lengths of the triangle. Since each condition provides only one equation, E is most likely to be the answer. So, we should consider conditions 1) & 2) together first. After comparing the number of variables and the number of equations, we can save time by considering conditions 1) & 2) together first.

Conditions 1) & 2):

Attachment:
9.3.png
9.3.png [ 11.02 KiB | Viewed 133 times ]


If the triangle is a right-angled isosceles triangle with two legs of length \(10\), then its area is \((\frac{1}{2})10*10 = 50\).
If the triangle is an equilateral triangle with all sides of length \(10\), then its area is \((\frac{√3}{4})10^2 = 25√3.\)
Since we don’t have a unique solution, both conditions are not sufficient, when taken together.

Therefore, E is the answer.

Answer: E

In cases where 3 or more additional equations are required, such as for original conditions with “3 variables”, or “4 variables and 1 equation”, or “5 variables and 2 equations”, conditions 1) and 2) usually supply only one additional equation. Therefore, there is an 80% chance that E is the answer, a 15% chance that C is the answer, and a 5% chance that the answer is A, B or D. Since E (i.e. conditions 1) & 2) are NOT sufficient, when taken together) is most likely to be the answer, it is generally most efficient to begin by checking the sufficiency of conditions 1) and 2), when taken together. Obviously, there may be occasions on which the answer is A, B, C or D.
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Re: What is the area of a triangle? &nbs [#permalink] 02 Sep 2018, 18:47
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