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In the figure, AD and BC are lines intersecting at O. What is the valu

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In the figure, AD and BC are lines intersecting at O. What is the valu  [#permalink]

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New post 09 Oct 2018, 00:03
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A
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Question Stats:

73% (02:08) correct 27% (02:35) wrong based on 49 sessions

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In the figure, AD and BC are lines intersecting at O. What is the value of a ?


(A) 15

(B) 30

(C) 45

(D) 60

(E) 135


Attachment:
lines (1).jpg
lines (1).jpg [ 20.85 KiB | Viewed 550 times ]

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Re: In the figure, AD and BC are lines intersecting at O. What is the valu  [#permalink]

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New post 09 Oct 2018, 02:22
Bunuel wrote:
Image
In the figure, AD and BC are lines intersecting at O. What is the value of a ?

(A) 15
(B) 30
(C) 45
(D) 60
(E) 135

Attachment:
lines (4).jpg


Vertically Opposite angles are equal
5x + 5a = 5y/2

i.e. 2x + 2a = y

Also, 5x + 5a + 2x + 30 = 180

i.e. 7x + 5a = 150

Also, y = 2x + 30

i.e. 2x + 2a = 2x + 30

i.e. a = 15

Answer: Option A
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Re: In the figure, AD and BC are lines intersecting at O. What is the valu  [#permalink]

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New post 09 Oct 2018, 03:37
Bunuel wrote:
Image
In the figure, AD and BC are lines intersecting at O. What is the value of a ?

(A) 15
(B) 30
(C) 45
(D) 60
(E) 135

Attachment:
lines (4).jpg


5x+5a=5y/2
2x+30=y

Substitute value of y

10x+10a= 10x+150
10a=150
A=15

Answer A.


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Re: In the figure, AD and BC are lines intersecting at O. What is the valu  [#permalink]

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New post 09 Oct 2018, 16:43
Bunuel wrote:
Image
In the figure, AD and BC are lines intersecting at O. What is the value of a ?


(A) 15

(B) 30

(C) 45

(D) 60

(E) 135


a) \(y+\frac{5y}{2}=180\) or, y=360/7 (Angles on one side of a straight line always add to 180 degrees)
b) y=2x+30 or, \(x=\frac{75}{7}\) (opposite angles are congruent)
c) 5x+5a+2x+30=180 or, 7x+5a=150 or, 5a=150-75=75 or, a=15

Ans. (A)
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Re: In the figure, AD and BC are lines intersecting at O. What is the valu  [#permalink]

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New post 15 Oct 2018, 23:51
1
Bunuel wrote:
Image
In the figure, AD and BC are lines intersecting at O. What is the value of a ?

(A) 15
(B) 30
(C) 45
(D) 60
(E) 135

Attachment:
lines (4).jpg


Dear Moderator,
Same question seems to have been duplicated in the link below , you may wish to merge the same, Thank you.

https://gmatclub.com/forum/in-the-figur ... l#p2148445
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- Stne

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Re: In the figure, AD and BC are lines intersecting at O. What is the valu  [#permalink]

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New post 15 Oct 2018, 23:53
stne wrote:
Bunuel wrote:
Image
In the figure, AD and BC are lines intersecting at O. What is the value of a ?

(A) 15
(B) 30
(C) 45
(D) 60
(E) 135

Attachment:
lines (4).jpg


Dear Moderator,
Same question seems to have been duplicated in the link below , you may wish to merge the same, Thank you.

https://gmatclub.com/forum/in-the-figur ... l#p2148445


________________
Merged. Thank you.
_________________

New to the Math Forum?
Please read this: Ultimate GMAT Quantitative Megathread | All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:
GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | Tricky questions from previous years.

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.


What are GMAT Club Tests?
Extra-hard Quant Tests with Brilliant Analytics

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Re: In the figure, AD and BC are lines intersecting at O. What is the valu  [#permalink]

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New post 16 Oct 2018, 09:39
we can say, 5x+5a=5y/2
=>5(x+a)=5y/2
=>2x+2a=y

again, y=2x+30
=>2x+2a=2x+30
=>a=15
Ans A

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Re: In the figure, AD and BC are lines intersecting at O. What is the valu   [#permalink] 16 Oct 2018, 09:39
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