In the figure above, if lines r and s are parallel, what is the value

Question

https://gmatclub.com/forum/download/file.php?id=53418 In the figure above, if lines r and s are parallel, what is the value of a + b? (1) c − a = 25 (2) a − d = 15 2020-03-24_1718.png

ShankSouljaBoi · Answer

chetan2u  Hi !!!!

Could you please help with this one ?

Regards

Posted from my mobile device

GMATWhizTeam · Answer

Solution:

Step 1:  
 • In the given figure, it’s given that line r and s are parallel to each other (shown in diagram below). 
• From the diagram, we can infer the following:
 o Notice the vertically possible angle, i.e. angle “a”
o Also, a = b (corresponding angles)
o And c + d = 180 (straight line angle)..........(i)
  Note, using the parallel line information, we are just able to infer that a = b. The remaining two information are general angle/straight line properties.

We need to find the value of a + b or in other words, we need to find the value of either a or b, since both are equal.

https://www.dropbox.com/s/wfyij47ys8b9qrh/Answer1.png?dl=1 
  Step 2:

Statement 1 : c – a = 25
 • We already know that c + d = 180 or c = 180 – d.........(i)
• Also, c – a = 25 or c = 25 + a
 o Equating c, we get
  25 + a = 180 – d or a + d = 155  
• But we cannot find the value of a.
 o Hence, statement 1 is not sufficient.  
 Statement 2 : a – d = 15.
 • Using this information also, we cannot find the value of a.
• Hence, statement 2 is also not sufficient.

Step 3:

• On combining both statements, we have:
 o a + d = 155 and 
o a – d = 15 
• So, we can find the value of a and that in turn will help us find the value of a + b.

Hence, the correct answer is Option C.

Probable mistakes, that a student can make: 
They may end up assuming the other two lines are parallel too.
 • That will lead them to believe that a = d and a + c = 180
 o This in turn will lead them to think that the answer will be Option A or D, which is incorrect.

chetan2u · Answer

ShankSouljaBoi ,

Most important  -- Understand the sketch..

Now the opposite angle to a will also be a, as shown in the attached figure
Since r || s, the  \angle a  would be equal to  \angle b  ---  Corresponding angles

What about measure of a, b, c and d ? - It can be anything as nothing is known about them.

Requirement  - value of a+b or a+a=2a....So we require to know a or b

(1) c − a = 25
a is dependent on c, so a could be anything.

(2) a − d = 15
a is dependent on d, so a could be anything.

Combined..
The moment you see a in both the statements, you should think if there is any way of handling c and d.
 Now c and d are supplementary angles, that is they are a pair equaling 180. 
So you have to get c+d from above statements.
If you subtract statement 2 from 1, you get 
 c − a -(a − d )= 25-15......(c+d)-2a=10......180-2a=10....2a=180-10=170....a=85 
Suff

C

deepak.brijendra · Answer

Hi

(c-d)-(a-d)= 25-15
c+d=10

Whereas C+D has to be 180

I see a fundamental flaw in this problem

Nabneet · Answer

It is:
(c- a )-(a-d)= 25-15
c+d -2a=10
2a=170

Bi mistake you have written wrong statement1 while solving.

In the figure above, if lines r and s are parallel, what is the value

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