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In the diagram below, P = g + c − e and Q = a + f . What is the value

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In the diagram below, P = g + c − e and Q = a + f . What is the value  [#permalink]

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New post 17 Jul 2017, 23:28
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Re: In the diagram below, P = g + c − e and Q = a + f . What is the value  [#permalink]

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New post 17 Jul 2017, 23:49
Given : P = g + c − e and Q = a + f .
We have been asked to find the value of (P + Q)

1. BC = CD = DB = DE

From the following information, Triangle BCD is equilateral.
Hence Angle BCD = c = g = 60 degree

Angle BDE = 180 - 60 = 120(Since angle in a straight line is 180)
In Triangle BDE, Angle DBE = e = 30 degree

Angle ABE = 180 - 60 - 30 = 90 degree

Therefore, Q = a+f = 90 degree(since sum of angles in a triangle is 90 degree)

Also P = 120 - 30 = 90 degree. We can arrive at an unique value of P + Q = 180 degree(Sufficient)

2. AB = 1/2*AE
Knowing the relationship between AB and AE is not enough to figure the value of angles P,Q.
Insufficient(Option A)
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Re: In the diagram below, P = g + c − e and Q = a + f . What is the value  [#permalink]

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New post 18 Jul 2017, 07:14
pushpitkc wrote:
Given : P = g + c − e and Q = a + f .
We have been asked to find the value of (P + Q)

1. BC = CD = DB = DE

From the following information, Triangle BCD is equilateral.
Hence Angle BCD = c = g = 60 degree

Angle BDE = 180 - 60 = 120(Since angle in a straight line is 180)
In Triangle BDE, Angle DBE = e = 30 degree

Angle ABE = 180 - 60 - 30 = 90 degree

Therefore, Q = a+f = 90 degree(since sum of angles in a triangle is 90 degree)

Also P = 120 - 30 = 90 degree. We can arrive at an unique value of P + Q = 180 degree(Sufficient)

2. AB = 1/2*AE
Knowing the relationship between AB and AE is not enough to figure the value of angles P,Q.
Insufficient(Option A)



How you came to this conclusion.
In Triangle BDE, Angle DBE = e = 30 degree

I marked C as an answer
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In the diagram below, P = g + c − e and Q = a + f . What is the value  [#permalink]

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New post 18 Jul 2017, 08:38
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Adityagmatclub wrote:
pushpitkc wrote:
Given : P = g + c − e and Q = a + f .
We have been asked to find the value of (P + Q)

1. BC = CD = DB = DE

From the following information, Triangle BCD is equilateral.
Hence Angle BCD = c = g = 60 degree

Angle BDE = 180 - 60 = 120(Since angle in a straight line is 180)
In Triangle BDE, Angle DBE = e = 30 degree

Angle ABE = 180 - 60 - 30 = 90 degree

Therefore, Q = a+f = 90 degree(since sum of angles in a triangle is 90 degree)

Also P = 120 - 30 = 90 degree. We can arrive at an unique value of P + Q = 180 degree(Sufficient)

2. AB = 1/2*AE
Knowing the relationship between AB and AE is not enough to figure the value of angles P,Q.
Insufficient(Option A)



How you came to this conclusion.
In Triangle BDE, Angle DBE = e = 30 degree

I marked C as an answer


Since, we know that c=60 degree
Angle BDE = 180 - c = 180 - 60 = 120(Since angle in a straight line is 180)

Coming to Triangle BDE(Sum of angles in a triangle is 180 degree)
Angle DBE + e + BDE = 180 => e + DBE = 180 - BDE = 60 (because BDE = 120)
Also, DB = BE
So, e = DBE = x(Angles opposite equal sides are equal)
2x = 60 => x = 30

Therefore, e = DBE = 30 degree

Hope that helps!
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Re: In the diagram below, P = g + c − e and Q = a + f . What is the value  [#permalink]

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New post 18 Jul 2017, 08:40
Bunuel wrote:
In the diagram below, P = g + c − e and Q = a + f . What is the value of (P + Q)?
Image

(1) BC = CD = DB = DE
(2) AB = 1/2*AE


Attachment:
2017-07-18_1026.png



stat1: gives triangle BCD is equilateral implies each angle is 60..
also imples triangle BDE is isoscles with base angle 30 each and the other angle equal 120.. a and f can calulated hence

suff

stat 2: not suff..

ans A
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In the diagram below, P = g + c − e and Q = a + f . What is the value  [#permalink]

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New post 24 Jul 2017, 19:39
Property of a triangle-equal sides have same angle.

Statement 1
In ∆ BCD all sides are equal hence all the angles are same=60°
Similarly in ∆ DBE side DB=DE hence they have same angle.
Now angle BDC+angle BDE=180°(angle on a line)
BDC=60°+angle BDE=180°
Or
Angle BDE=180°-60°=120°
Since other 2 sides of the triangle which has angle BDE are equal we have
Angle BDE+DBE+e=180
Now DBE=e(side of equal length)
Hence 2e=180°-120°=60°
Or e=30°
Statement sufficient
Statement 2. Complete information about the sides of different ∆'s is not given hence not sufficient.

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Re: In the diagram below, P = g + c − e and Q = a + f . What is the value  [#permalink]

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New post 25 Jul 2017, 01:34
Ans A:
P+Q = 6e. And from Equilateral Triangle BCD, c=60 degree. Therefore, e=30 degree. Hence, P+Q= 180 degrees.
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Re: In the diagram below, P = g + c − e and Q = a + f . What is the value   [#permalink] 25 Jul 2017, 01:34
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In the diagram below, P = g + c − e and Q = a + f . What is the value

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