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What does q equal in the figure shown above where ABCD is a

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What does q equal in the figure shown above where ABCD is a [#permalink]

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New post 10 Aug 2013, 10:05
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Difficulty:

  55% (hard)

Question Stats:

70% (01:26) correct 30% (01:53) wrong based on 105 sessions

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What does q equal in the figure shown above where ABCD is a rectangle?

(1) The length of line segment AM is the same as the length of line segment LM.

(2) The length of line segment LN is the same as the length of line segment DN.

How close is this question to GMAT type ? took me more than 4 mins to solve .
[Reveal] Spoiler: OA

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Re: What does q equal in the figure shown above where ABCD is a [#permalink]

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New post 10 Aug 2013, 10:47
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guerrero25 wrote:
What does q equal in the figure shown above where ABCD is a rectangle?

(1) The length of line segment AM is the same as the length of line segment LM.

(2) The length of line segment LN is the same as the length of line segment DN.

How close is this question to GMAT type ? took me more than 4 mins to solve .


THIS QUESTION IS SIMILAR TO ONE QUESTION FROM GMAT-PREP.

(1) The length of line segment AM is the same as the length of line segment LM.
CLEARLY INSUFFICIENT since other leg forming this angle i.e LN is free to move.

(2) The length of line segment LN is the same as the length of line segment DN.
SAME AS A INSUFFICIENT.

COMBINING.

We can get X= W AND Y=Z(SEE IN DIAG)

NOW IN TRIANGLE KDA X+Y+80=180==>X+Y =100
MOREOVER W+q+Z=180
NOW WE KNOW X+Y = W+Z
therefore q = 80
hence sufficient
hence C
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Re: What does q equal in the figure shown above where ABCD is a [#permalink]

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New post 10 Aug 2013, 23:04
The way i did it after combining:

a+q+b = 180 --- Eq 1.
q + 80 + 2(a+ b) = 360
=> q + 80 + 2(180-q) = 360 (using Eq 1.)
=> q + 80 + 360 - 2q = 360
=> q = 80 (Ans)

Blueseas,
Can you please explain how you deduced "NOW WE KNOW X+Y = W+Z".

thanks.
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Re: What does q equal in the figure shown above where ABCD is a [#permalink]

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New post 10 Aug 2013, 23:10
nick28 wrote:
The way i did it after combining:

a+q+b = 180 --- Eq 1.
q + 80 + 2(a+ b) = 360
=> q + 80 + 2(180-q) = 360 (using Eq 1.)
=> q + 80 + 360 - 2q = 360
=> q = 80 (Ans)

Blueseas,
Can you please explain how you deduced "NOW WE KNOW X+Y = W+Z".

thanks.


SEE in your diagram ALD is a straight line RIGHT .
THEREFORE \(a+q+b = 180\) ....(1

NOW see triangle AKD....SUM OF ALL INTERIOR ANGLES OF TRIANGLE = 180
therefore \(a+80+b = 180\)....(2

now if you equate equations 1 and 2
you get \(a+q+b = a+80+b\)
on solving \(q=80\)

HOPE ITS CLEAR
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Re: What does q equal in the figure shown above where ABCD is a [#permalink]

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New post 11 Aug 2013, 00:21
blueseas wrote:
SEE in your diagram ALD is a straight line RIGHT .
THEREFORE \(a+q+b = 180\) ....(1

NOW see triangle AKD....SUM OF ALL INTERIOR ANGLES OF TRIANGLE = 180
therefore \(a+80+b = 180\)....(2

now if you equate equations 1 and 2
you get \(a+q+b = a+80+b\)
on solving \(q=80\)

HOPE ITS CLEAR


No, i wasn't asking for complete solution clarification. I did got the solution (as also posted above).
My question was in your 2nd post in this thread you mentioned "NOW WE KNOW X+Y = W+Z" , how did you come to this ?
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Re: What does q equal in the figure shown above where ABCD is a [#permalink]

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New post 11 Aug 2013, 00:24
nick28 wrote:
blueseas wrote:
SEE in your diagram ALD is a straight line RIGHT .
THEREFORE \(a+q+b = 180\) ....(1

NOW see triangle AKD....SUM OF ALL INTERIOR ANGLES OF TRIANGLE = 180
therefore \(a+80+b = 180\)....(2

now if you equate equations 1 and 2
you get \(a+q+b = a+80+b\)
on solving \(q=80\)

HOPE ITS CLEAR


No, i wasn't asking for complete solution clarification. I did got the solution (as also posted above).
My question was in your 2nd post in this thread you mentioned "NOW WE KNOW X+Y = W+Z" , how did you come to this ?


it is because X=W and Y=Z ...see my diagram (this information we got from statement 1 and 2)
therefore x+y = w+z
clear??
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Re: What does q equal in the figure shown above where ABCD is a [#permalink]

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New post 11 Aug 2013, 00:35
blueseas wrote:
it is because X=W and Y=Z ...see my diagram (this information we got from statement 1 and 2)
therefore x+y = w+z
clear??


Yes, it is clear now. I don't know why I missed it earlier :roll:

But still let me clear it for somebody else who might in haste get trapped with this similar question (although it is pretty clear from your earlier post )

X=W --- (1)
Y=Z --- (2)

from (1) --> X+Y = W + Y
using (2)=> X + Y = W + Z (i feel silly now writing this :shock: )

Thanks blueseas.
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Re: What does q equal in the figure shown above where ABCD is a [#permalink]

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Re: What does q equal in the figure shown above where ABCD is a [#permalink]

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New post 21 Sep 2017, 09:04
Basic concepts of geometry. Isosceles triangle, angle sum property of a triangle, and angles on the straight line.

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Re: What does q equal in the figure shown above where ABCD is a   [#permalink] 21 Sep 2017, 09:04
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