emmak wrote:

Attachment:

The attachment **1.gif** is no longer available

In the figure above, what is the value of x?

(1) AD = AE = BE = CD = BC

(2) x = y

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 3063 times ]

_________________

Ankit

You must Believe

GMAT Quant Tutor

How to start GMAT preparations?

How to Improve Quant Score?

Gmatclub Topic Tags

Check out my GMAT debrief

Quant Formula Sheet

How to Solve :

Statistics || Reflection of a line || Remainder Problems || Inequalities