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555-605 (Medium)|   Geometry|      
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Bunuel
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In the figure, lines l, m, and n intersect at O. Which one of the foll Updated on: 15 Jul 2019, 03:53
Originally posted by Bunuel on 09 Oct 2018, 23:25.
Last edited by Sajjad1994 on 15 Jul 2019, 03:53, edited 1 time in total.
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35% (medium)

Question Stats:

75% (02:15) correct 25% (02:42) wrong based on 76 sessions

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In the figure, lines l, m, and n intersect at O. Which one of the following must be true about the value of a ?


A. \(a < \frac{5}{8}\)

B. \(a = \frac{5}{7}\)

C. \(a = \frac{5}{6}\)

D. \(a = 1\)

E. \(a > 1\)


Source: Nova GMAT
Difficulty Level: 700

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B
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In the figure, lines l, m, and n intersect at O. Which one of the foll Updated on: 16 Oct 2018, 04:40
Originally posted by GMATinsight on 10 Oct 2018, 02:11.
Last edited by GMATinsight on 16 Oct 2018, 04:40, edited 1 time in total.
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Bunuel

In the figure, lines l, m, and n intersect at O. Which one of the following must be true about the value of a ?


A. \(a < \frac{5}{8}\)

B. \(a = \frac{5}{7}\)

C. \(a = \frac{5}{6}\)

D. \(a = 1\)

E. \(a > 1\)


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ay = x

also, x+10 = y i.e. x = y-10

i.e. ay = y-10

Also, ay + (x+10) = 180-120 = 60

i.e. x+x+10 = 60

i.e. x = 25

i.e. 25+10 = y

i.e. y = 35

now, ay = x

i.e. a*35 = 25

i.e. a = 5/7

Answer: Option B
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In the figure, lines l, m, and n intersect at O. Which one of the foll 15 Oct 2018, 10:55
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GMATinsight
Bunuel

In the figure, lines l, m, and n intersect at O. Which one of the following must be true about the value of a ?


A. \(a < \frac{5}{8}\)

B. \(a = \frac{5}{7}\)

C. \(a = \frac{5}{6}\)

D. \(a = 1\)

E. \(a > 1\)


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Attachment:
lines.jpg


ay = x

also, x+10 = y

i.e. ay = y

i.e. y(a-1)=0

i.e. either y = 0 or a = 1

i.e. a = 1 because y ≠0

Answer: Option D
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Hi GMATinsight,

How did you get ay=y in the third line ?
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In the figure, lines l, m, and n intersect at O. Which one of the foll 15 Oct 2018, 13:35
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GMATinsight


ay = x

also, x+10 = y

i.e. ay = y

i.e. y(a-1)=0

i.e. either y = 0 or a = 1

i.e. a = 1 because y ≠0

Answer: Option D
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Not sure I agree with this one.

From the diagram:
(1) y = x + 10
(2) ay = x
(3) x + 10 + ay + 240 + x + y = 360

Tidying up 3 a little:
x + ay + x + y = 110

substitute in (1) and (2) we can eliminate a and y from the equation:

x + x + x + x + 10 = 110

4 x = 100 -> x=25 -> y = 35

From (2), a = x/y = 25/35 = 5/7 -> ANSWER B
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In the figure, lines l, m, and n intersect at O. Which one of the foll 16 Oct 2018, 04:56
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GMATinsight
Bunuel

In the figure, lines l, m, and n intersect at O. Which one of the following must be true about the value of a ?


A. \(a < \frac{5}{8}\)

B. \(a = \frac{5}{7}\)

C. \(a = \frac{5}{6}\)

D. \(a = 1\)

E. \(a > 1\)


Show Spoiler
Attachment:
lines.jpg


ay = x

also, x+10 = y

i.e. ay = y

i.e. y(a-1)=0

i.e. either y = 0 or a = 1

i.e. a = 1 because y ≠0

Answer: Option D

Hi GMATinsight,

How did you get ay=y in the third line ?
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stne

I made some typo error followed by calculation error.

Please check edited my solution above again. I regret the inconvenience caused by my error. :)
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In the figure, lines l, m, and n intersect at O. Which one of the foll 17 Oct 2018, 00:11
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In the figure, lines l, m, and n intersect at O. Which one of the following must be true about the value of a ?


A. a<58a<58

B. a=57a=57

C. a=56a=56

D. a=1a=1

E. a>1


SOLN:
ay=x
a=x/y ( to be answered) (1)
x+10=y
x=y-10---(2)

we know y+ay+120=180
y+y-10+120=180
2y=70
y=35

substitute in (2)
x= 25

therefore as per (1) a = 25/35= 5/7 ( B)
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