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What is the cost of fencing the triangular field PQR?

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What is the cost of fencing the triangular field PQR?  [#permalink]

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New post 10 Mar 2018, 09:21
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What is the cost of fencing the triangular field PQR?

(1) The sides PQ and PR are in ratio 10:9 while the cost of fencing along the PQ & PR is 760$ at the rate of 20$ per meter?
(2) The angle PQR = 60 deg.

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Re: What is the cost of fencing the triangular field PQR?  [#permalink]

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New post 10 Mar 2018, 09:51
If angle QPR would have been 60 degrees, then one might have selected C.

But both statements are insufficient.

Therefore, E.

Posted from my mobile device
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Re: What is the cost of fencing the triangular field PQR?  [#permalink]

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New post 10 Mar 2018, 09:57
gmatbusters wrote:
What is the cost of fencing the triangular field PQR?

(1) The sides PQ and PR are in ratio 10:9 while the cost of fencing along the PQ & PR is 760$ at the rate of 20$ per meter?
(2) The angle PQR = 60 deg.

OA will be provided tomorrow.


To calculate the cost, we need to know the length of the perimeter and the cost per unit length.
We'll look for statements that give us this information, a Logical approach.

(1) This gives us information on the lengths of 2 of the 3 sides of the triangle.
Insufficient!

(2) This does not give us the information we need.
Insufficient!

Combined: (2) gives us the angle in front of PR and (1) tells us that PQ is larger than PR.
That is, we have a Side-Side-Angle pattern (PR-PQ-PQR) where the 'middle' side is longer than the 'outer' one (PQ>PR)
There are 2 triangles that fulfill the given conditions so we cannot calculate the perimeter.

(E) is our answer.

**Note: as far as I know, this is out of the scope of standard GMAT material... if you want to see more see the Wikipedia entry on law of sines and skip to the 'ambiguous solution' part
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Re: What is the cost of fencing the triangular field PQR?  [#permalink]

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New post 13 Mar 2018, 07:11
vtexcelgmat wrote:
If angle QPR would have been 60 degrees, then one might have selected C.

But both statements are insufficient.

Therefore, E.

Posted from my mobile device



Even if PRQ is given, we can have unique triangle
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What is the cost of fencing the triangular field PQR?  [#permalink]

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New post 13 Mar 2018, 07:17
That would depend on the value of the angle PRQ,
If angle PRQ is 90 degree or obtuse, then it would be a unique triangle, but if angle PRQ is acute, triangle is not unique.

See this. https://gmatclub.com/forum/what-is-the- ... l#p2027164

itisSheldon wrote:
vtexcelgmat wrote:
If angle QPR would have been 60 degrees, then one might have selected C.

But both statements are insufficient.

Therefore, E.

Posted from my mobile device



Even if PRQ is given, we can have unique triangle

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What is the cost of fencing the triangular field PQR?  [#permalink]

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New post 13 Mar 2018, 07:33
gmatbusters wrote:
That would depend on the value of the angle PRQ,
If angle PRQ is 90 degree or obtuse, then it would be a unique triangle, but if angle PRQ is acute, triangle is not unique.

See this. https://gmatclub.com/forum/what-is-the- ... l#p2027164

itisSheldon wrote:
vtexcelgmat wrote:
If angle QPR would have been 60 degrees, then one might have selected C.

But both statements are insufficient.

Therefore, E.

Posted from my mobile device



Even if PRQ is given, we can have a unique triangle


You are right
But in this case since PR is always less than PQ, even when PRQ is acute angle we can have a unique triangle

Correct me if i am wrong :thumbup:
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What is the cost of fencing the triangular field PQR?  [#permalink]

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New post 13 Mar 2018, 07:50
SSA does not prove congruence when the angle is acute and the opposite side is shorter than the
known adjacent side but longer than the sine of the angle times the adjacent side. This is the ambiguous case. In
all other cases with corresponding equalities, SSA proves congruence.

In this particular question, sides are 18, 20 and non included angle is 60.
Here 20sin 60<18<20. Hence it is not congruent.



Posted from my mobile device[/quote]


Even if PRQ is given, we can have a unique triangle[/quote][/quote]

You are right
But in this case since PR is always less than PQ, even when PRQ is acute angle we can have a unique triangle

Correct me if i am wrong :thumbup:[/quote]
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What is the cost of fencing the triangular field PQR? &nbs [#permalink] 13 Mar 2018, 07:50
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