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# In the figure, lines l, m, and n intersect at O. Which one of the foll

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Joined: 02 Sep 2009
Posts: 58453
In the figure, lines l, m, and n intersect at O. Which one of the foll  [#permalink]

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Updated on: 15 Jul 2019, 03:53
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Difficulty:

55% (hard)

Question Stats:

73% (02:22) correct 27% (02:37) wrong based on 55 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

Attachment:

lines.jpg [ 18.47 KiB | Viewed 1125 times ]

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Originally posted by Bunuel on 09 Oct 2018, 23:25.
Last edited by SajjadAhmad on 15 Jul 2019, 03:53, edited 1 time in total.
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Re: In the figure, lines l, m, and n intersect at O. Which one of the foll  [#permalink]

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Updated on: 16 Oct 2018, 04:40
Bunuel wrote:

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. $$a > 1$$

Attachment:
lines.jpg

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

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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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Re: In the figure, lines l, m, and n intersect at O. Which one of the foll  [#permalink]

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15 Oct 2018, 10:55
GMATinsight wrote:
Bunuel wrote:

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. $$a > 1$$

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

Hi GMATinsight,

How did you get ay=y in the third line ?
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Joined: 15 Oct 2018
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Re: In the figure, lines l, m, and n intersect at O. Which one of the foll  [#permalink]

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15 Oct 2018, 13:35
GMATinsight wrote:

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

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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Re: In the figure, lines l, m, and n intersect at O. Which one of the foll  [#permalink]

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16 Oct 2018, 04:56
stne wrote:
GMATinsight wrote:
Bunuel wrote:

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. $$a > 1$$

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

Hi GMATinsight,

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

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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Re: In the figure, lines l, m, and n intersect at O. Which one of the foll  [#permalink]

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17 Oct 2018, 00:11
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)
Re: In the figure, lines l, m, and n intersect at O. Which one of the foll   [#permalink] 17 Oct 2018, 00:11
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