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Retired Moderator V
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What is the value of x?  [#permalink]

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Question Stats: 8% (01:04) correct 92% (01:53) wrong based on 49 sessions

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GMATBusters’ Quant Quiz Question -8 What is the value of x?
A) Y = 55 deg
B) Z = 35 deg

Attachment: 1.JPG [ 44.02 KiB | Viewed 705 times ]

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Re: What is the value of x?  [#permalink]

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If we could solve the missing angle in the external triangle. we can get x.

1) we know y and we can get angle O only.
Not sufficient
2)we know z
As the two sides of the middle triangle are radii of the circle. missing angle=90-z.

Sufficient
Senior Manager  P
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Re: What is the value of x?  [#permalink]

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What is the value of x ?

(Statement1): Y = 55
<O = 2Y = 110
OA = OC = z —> z= (180–110)/2= 35
< A= 90
<A= 55 —> x= 180–55–75= 50
Sufficient

(Statement2): z= 35.
The same solution as statement1:
In AOC triangle, OA = OC —> <A= 35

If we look at the AED triangle, <A= 90–35= 55 —> x = 180–75–55= 50
Sufficient

Posted from my mobile device
Attachments A7CE3E3E-41F7-4E54-919E-961971DA6768.jpeg [ 2 MiB | Viewed 628 times ]

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Re: What is the value of x?  [#permalink]

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If we look at figure angle o is 2y

both the angle of the sides which pass through o is z

the 2 equations formed are
2z+2y=180
z+y=90

x+75+(90-z)=180
x-z=15

using both options individually, we can find the answer , so answer is D
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Re: What is the value of x?  [#permalink]

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What is the value of x?
A) Y = 55 deg
B) Z = 35 deg

#1
central angle = 110 , but no other info ; insufficient
#2
z= 35 , other angle not know ; insufficient
from 1&2
No new info
IMO E

Originally posted by Archit3110 on 08 Dec 2019, 01:49.
Last edited by Archit3110 on 08 Dec 2019, 20:08, edited 1 time in total.
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Re: What is the value of x?  [#permalink]

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Ans:D
The center angle = 2y.
hence, 2y+z+z =180 (For the triangle at center of circle)--------eqn (i)
Let the angle opposite to 75 degree be N (for the bottom most triangle)
Hence, N+Z=90(triangle at center of circle is isosceles) ----------eqn(ii)
75+N+x=180---------------------------------------------------------eqn(iii)
From eqn (i , ii and iii)
75+y+x=180---------------------------------------------------------eqn(iv)
(1)Y is given hence x can be found from eqn iv (Sufficient)
(2)Z is given hence x can be found from eqn ii and eqn iii(Sufficient)
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Re: What is the value of x?  [#permalink]

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Lets us first arrive at the equations basis given information y degree is marked as vertex D and side consecutive to D on left side is AD and on right side is BD and for x degree vertex is marked as C. Now Angle AOB = 2 y degree( By virtue of property that central angle is twice the subtended angle which is y degree or angle ADB).
OA=OB so angle OAB = angle OBA = z degree, angle BAC = 90-z as entire angle A is 90 degrees and angle OAB = z degrees
In triangle OAB , 2y+z+z = 180 so y+z=90 degrees....... eq 1
and in triangle BAC 90-z+75+x = 180 so x-z= 15 degrees...... eq 2
A) Y = 55 deg
so from here we can arrive at value of x after combining equation 1 and equation 2, x = 50 so statement 1 alone is sufficient
B) Z = 35 deg
From eq 2 x comes to 50 degrees so statement 2 alone is also sufficient
Senior Manager  P
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Re: What is the value of x?  [#permalink]

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Refer the attached sheet for explanation.

Imo. D
Attachments IMG_20191208_175949.jpg [ 2.96 MiB | Viewed 524 times ]

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GMAT 1: 610 Q43 V31 Re: What is the value of x?  [#permalink]

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1

EXPLANATION:

Let ABC be the triangle inscribed in the circle. And BXZ be the triangle inscribes outside the circle.

Now, We are not given, whether O is the center of the circle or not.
So we can conclusively decide. Even if both statements are given, we won't be able to find X.

NOTE:
If O is the center of the circle, then, D would be the answer.

This is because, OB and OC would be same (Radius), making OBC triangle as isoceles.

Using statement 1:
Y = 55 degrees. The angle subtended at the center would be twice. So Angle BOC = 110 degrees.
So angle Z and and angle OBC = 35 degrees (as 110 + x + x = 180, means 2x = 70, and x = 35).

So the angle XBZ = 90 - 35 = 55 degrees. So X = 180 - (55 + 75) = 45 degrees.

Using Statement 2:
We are directly given Z = 35 degrees. Following the above logic, we would arrive at the same result.

Hence, if O is the center of the circle, answer is D, else, the answer is E, as we are not given whether O is the center or not.
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Re: What is the value of x?  [#permalink]

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st 1: y=55 so angle at center will be 2*55=110 using subtended angle property.
since both the side connected to angle O are radius , hence angle opposite to these sides can be found by using triangle property.
therefore, angle z= (180-110)/2= 35
as angle opposite 75 is given as 90 Deg (combined with upper and lower triangle), we can get the angle in the lower triangle as we know angle of the upper part
so angle opposite 75 will be -- 90-35=65
we have two angles 65 & 75 we can get the x= 180-75-65= 40
so statement is sufficient

st2 : value of angle z =35 is given , following the above steps , we can get the angle of x-- sufficient

OA=D
Intern  Joined: 02 Sep 2019
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Re: What is the value of x?  [#permalink]

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In the given figure, if O is the center of the circle, then the question can be proceeded as follows:
By alternate segment theorem, v=y
(1) if y= 55 deg, v = y = 55 deg. Therefore, x = 180 - (75+y) = 180 - 130 = 50 deg. Clearly, sufficient.
(2) if z =35 deg, v= y = 90 - 35 = 55 deg. Therefore, x = 180 - (75+y) = 180 - 130 = 50 deg. Clearly, sufficient.
Therefore, both the statements are sufficient.

But, O is not given as the center of the circle. Choice E is the answer.
Attachments 20191208_191549.jpg [ 59.34 KiB | Viewed 494 times ]

Intern  Joined: 09 Dec 2019
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Re: What is the value of x?  [#permalink]

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In the above figure, since it is not mentioned that whether O is the center of the circle or not, nothing can be commented about the value of x.
(1) No unique value.
(2) No unique value.
(1) + (2) No unique value.

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Re: What is the value of x?  [#permalink]

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Thats a tricky one. The question never mentioned O is the centre of the circle. That makes the answer E.
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Re: What is the value of x?  [#permalink]

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[fraction][/fraction]
anurasi wrote:
Thats a tricky one. The question never mentioned O is the centre of the circle. That makes the answer E.

Yes, You are right anurasi , as we cannot assume anything on our own in DS questions. We have to just solve it by logic + Data Given.

IMO-E Re: What is the value of x?   [#permalink] 11 Dec 2019, 10:15
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