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A
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Difficulty:
95%
(hard)
Question Stats:
44% (02:16) correct
56%
(02:47)
wrong
based on 195
sessions
History
Date
Time
Result
Not Attempted Yet
Attachment:
1.gif [ 2.64 KiB | Viewed 10149 times ]
(1) AD = AE = BE = CD = BC
(2) x = y
02 May 2013, 01:32
Kudos
Bookmarks
A little simpler way
Statement 1:
Angle BEC = z; As AE = EB = CD ==> we have Angle EBD = Angle ECD =x (Isosceles Triangle)
z = 2x (exterior angle theorem)
As BE = BC ==> z = x+y ==> 2x = x + y; means y =x
For Triangle ABC, Angle ACB + Angle CBA + Angle BAC = 180
(x+y) + (x+y) + x = 180
as x = y ==> x =y = 36
Statement 1 sufficient
Statement 2: clearly insufficient
Ans A
Statement 1:
Angle BEC = z; As AE = EB = CD ==> we have Angle EBD = Angle ECD =x (Isosceles Triangle)
z = 2x (exterior angle theorem)
As BE = BC ==> z = x+y ==> 2x = x + y; means y =x
For Triangle ABC, Angle ACB + Angle CBA + Angle BAC = 180
(x+y) + (x+y) + x = 180
as x = y ==> x =y = 36
Statement 1 sufficient
Statement 2: clearly insufficient
Ans A
General Discussion
28 Mar 2013, 05:34
Kudos
Bookmarks
emmak
Figure attached
STAT1.
Consider Triangle BCD
sum of all three angles = 180
so, y + b + d + e = 180
Also, BC = CD
=> b = d + e
so, equation becomes
y + d + e + d + e = 180
y + 2d + 2e= 180 ... (1)
Consider traingle BCE
sum of all three angles = 180
so, a + c+ y + e = 180
Also, BC = BE
so, a = c+y
so, equation becomes
y + c + y+ c+ y = 180
3y + 2c = 180 ...(2)
Consider traingle ABC
sum of all three angles = 180
so, x + y + c+ d + e = 180 ...(3)
Consider traingle AEB
AE = EB
so, x = d ...(4)
Consider traingle ADC
AD = DC
so, x = c ...(5)
putting d=x (1) becomes
2x + y + 2e = 180 ...(6)
putting c=x in (2) becomes
2x + 3y = 180 ...(7)
putting c=x and d=x in (3) we have
3x+y+e=180 ...(8)
mutiply (8) by 2 and subtract from (6) we have
4x + y = 180 ...(9)
equating (7) and (9) we have
2x+ 3y = 4x+y
=> 2y = 2x
or x=y
putting x=y in (7) we have
5x= 180
x= 36
So, STAT1 is sufficient
STAT2
STAT2 is not sufficient as we dont have relationship between any other angles.
So, Answer will be A.
Will reply in sometime with a smaller and more geometric solution if i get in sometime!
Hope it helps!
Attachments
figure.png [ 14.6 KiB | Viewed 9833 times ]
