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The figure above shows a portion of a road map on which the measures

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The figure above shows a portion of a road map on which the measures  [#permalink]

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New post 26 Apr 2019, 07:48
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A
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The figure above shows a portion of a road map on which the measures of certain angles are indicated. If all lines shown are straight and intersect as shown, is road PQ parallel to road RS ?

(1) b = 2a
(2) c = 3a


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Re: The figure above shows a portion of a road map on which the measures  [#permalink]

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New post 26 Apr 2019, 11:11
The Logical approach to this question would start with the fact that each of the triangles and the point in which they 'touch' (T) all provide the same equation: a+b+c=180. We'll use the Logical rule that when there are more variables than equations, there's an infinite number of possible solutions. Now, since each of the two statements only eliminates one of the variables, we'll need both of them to find the exact size of the angles.
Note: there's no need to find what this size is, since with the exact value we can definitely answer the question (either 'Yes!' or 'No!'), so there's enough information.

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New post Updated on: 21 Jul 2019, 13:32
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The Precise approach would start off using the equations a+b+c=180 and b=2a.This gives us: a+2a+c=180, which is not enough to find neither a nor c. Answer choices (A) and (D) are eliminated.
In the same way, if we take a+b+c=180 and c=3a,we'll get a+b+3a=180, which is not enough to find neither a nor b. Answer choice (B) is eliminated.
Using both statements we'll get a+2a+3a=180, so 6a=180, and thus a=30. Now, since c=90 the lines are indeed parallel (the sum of the two adjacent angles, both c, is 180). This means that both statements together are enough.

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Originally posted by DavidTutorexamPAL on 26 Apr 2019, 11:23.
Last edited by DavidTutorexamPAL on 21 Jul 2019, 13:32, edited 1 time in total.
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Re: The figure above shows a portion of a road map on which the measures  [#permalink]

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New post 21 Jul 2019, 12:25
If PQ and RS are two parallel lines, thus making the line across them a transversal line, then the sum of the two adjacent angels must be equal,
=> c=180–c
=> 2c=180
=>c=90
Thus, if c=90, PQ and RS must be parallel.

So, we have to check if c=90.

1) No way to find the value of c.
2) No way to find the value of c.
3) Using 1) and 2) we can find the value of c, which comes out to be 90. Thus, C is the answer.
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Re: The figure above shows a portion of a road map on which the measures  [#permalink]

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New post 27 Jul 2019, 12:35
We can prove two lines are parallel if we know Angle C i.e. if C=90 then parallel else No

1. b=2a. No info about c. Not Sufficient
2. c=3a. No infor about b. Not Sufficient

On combining, we can get values of all a,b and c
Sufficient.

Hence C
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Re: The figure above shows a portion of a road map on which the measures   [#permalink] 27 Jul 2019, 12:35
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