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Math Expert V
Joined: 02 Sep 2009
Posts: 59725
In the figure, lines l and k are parallel. If a is an acute angle, the  [#permalink]

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Difficulty:   15% (low)

Question Stats: 91% (02:02) correct 9% (04:07) wrong based on 23 sessions

### HideShow timer Statistics In the figure, lines $$l$$ and $$k$$ are parallel. If a is an acute angle, then which one of the following must be true?

(A) $$b > 10$$

(B) $$b > 15$$

(C) $$b < 20$$

(D) $$b < 30$$

(E) $$b > 45$$

Source: Nova GMAT
Difficulty Level: 550

Attachment: #GREpracticequestion In the figure, lines l and k are parallel.jpg [ 18.37 KiB | Viewed 639 times ]

_________________

Originally posted by Bunuel on 18 Mar 2019, 00:03.
Last edited by SajjadAhmad on 22 Jul 2019, 05:46, edited 1 time in total.
GMAT Club Legend  V
Joined: 18 Aug 2017
Posts: 5483
Location: India
Concentration: Sustainability, Marketing
GPA: 4
WE: Marketing (Energy and Utilities)
Re: In the figure, lines l and k are parallel. If a is an acute angle, the  [#permalink]

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1
Bunuel wrote: In the figure, lines $$l$$ and $$k$$ are parallel. If a is an acute angle, then which one of the following must be true?

(A) $$b > 10$$

(B) $$b > 15$$

(C) $$b < 20$$

(D) $$b < 30$$

(E) $$b > 45$$

Attachment:
The attachment #GREpracticequestion In the figure, lines l and k are parallel.jpg is no longer available

solution attached
AjjayKannan
anshkool4u
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File comment: Solution attached IMG_20190320_224102905.jpg [ 3.52 MiB | Viewed 425 times ]

Originally posted by Archit3110 on 18 Mar 2019, 01:27.
Last edited by Archit3110 on 20 Mar 2019, 10:13, edited 2 times in total.
Intern  B
Joined: 26 Dec 2018
Posts: 21
Re: In the figure, lines l and k are parallel. If a is an acute angle, the  [#permalink]

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an explanation for the answer, please. Option E seems to be the right one
Manager  S
Joined: 18 Oct 2018
Posts: 90
Location: India
GMAT 1: 710 Q50 V36 GPA: 4
Re: In the figure, lines l and k are parallel. If a is an acute angle, the  [#permalink]

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Consider another line m parallel to line k and l,passing through angle b,dividing the angle into angle X and angle a-x.
Now,between angle m and l,angle b+30=angle X
Thus,b+30=X

Between angle k and m,angle b=angle a-x

Thus,angle a=X+a-x= b+30+b=2b+30

Given angle a is acute.
Thus,2b+30<90
b<30.
Hence b.

Press Kudos if u liked my solution

Posted from my mobile device

Originally posted by anshkool4u on 20 Mar 2019, 09:25.
Last edited by anshkool4u on 20 Mar 2019, 09:33, edited 1 time in total.
Intern  B
Joined: 26 Dec 2018
Posts: 21
Re: In the figure, lines l and k are parallel. If a is an acute angle, the  [#permalink]

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anshkool4u wrote:
Consider another line m parallel to line k and l,passing through angle b,dividing the angle into angle X and angle a-x.
Now,between angle m and l,angle b+30=angle X
Thus,b+30=X

Between angle k and m,angle b=angle a-x

Thus,angle a=X+a-x= b+30+b=2b+30

Given angle a is obtuse.
Thus,2b+30<90
b<30.
Hence b.

Press Kudos if u liked my solution

Posted from my mobile device

Angle a is acute not obtuse
Manager  S
Joined: 18 Oct 2018
Posts: 90
Location: India
GMAT 1: 710 Q50 V36 GPA: 4
Re: In the figure, lines l and k are parallel. If a is an acute angle, the  [#permalink]

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Sorry for the typing mistake.
But I hope,u must have got the clear intent from the solution

Posted from my mobile device
Intern  B
Joined: 26 Dec 2018
Posts: 21
Re: In the figure, lines l and k are parallel. If a is an acute angle, the  [#permalink]

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if b+30 is alternate angle and by sum of all angles in a triangle is 180 logic.

[m]B+30 + B + 180 - a = 180[/m]

which is [m]B = [fraction](a-30)/2[/fraction][/m]

When a is acute angle, B will always be equal and below 30 degrees.

Anything wrong in this?

Originally posted by AjjayKannan on 20 Mar 2019, 09:46.
Last edited by AjjayKannan on 20 Mar 2019, 10:17, edited 1 time in total.
Manager  S
Joined: 18 Oct 2018
Posts: 90
Location: India
GMAT 1: 710 Q50 V36 GPA: 4
Re: In the figure, lines l and k are parallel. If a is an acute angle, the  [#permalink]

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Nothing wrong in this solution.
The only mistake is in the last line,B=(a-30)/2.
For any value of a between 0-89,b will be less than 30 degree.

Ex. When a=89,b=29.5
When a=30,b=0

Posted from my mobile device Re: In the figure, lines l and k are parallel. If a is an acute angle, the   [#permalink] 20 Mar 2019, 10:10
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