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In the figure, what is the value of x ?

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Math Expert
Joined: 02 Sep 2009
Posts: 59728
In the figure, what is the value of x ?  [#permalink]

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03 Apr 2019, 23:14
00:00

Difficulty:

25% (medium)

Question Stats:

76% (01:14) correct 24% (01:38) wrong based on 46 sessions

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In the figure, what is the value of x ?

(A) 90

(B) 95

(C) 100

(D) 105

(E) 115

Attachment:

#GREpracticequestion In the figure, what is the value of x .jpg [ 27.41 KiB | Viewed 562 times ]

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Senior Manager
Joined: 13 Feb 2018
Posts: 492
GMAT 1: 640 Q48 V28
Re: In the figure, what is the value of x ?  [#permalink]

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04 Apr 2019, 00:07
3 things are necessary here

1) Opposite angles are the same;
2) Angles of the equilateral triangle;
3) Triangle with sides 3, 4, 5 is a right triangle as $$3^2+4^2=5^2$$;

if you catch those 3 concepts quickly, you wont waste 7 minutes like me

After some smooth calculations, you get
360=60+90+2x
x=105

IMO
Ans: D
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Re: In the figure, what is the value of x ?  [#permalink]

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04 Apr 2019, 02:19
LHS is right angled we get 90* and RHS is equilaterlal ∆ 60*
so sum of quadrilaterial = 150+2x= 360
x= 105
IMO D

[

quote="Bunuel"]
In the figure, what is the value of x ?

(A) 90

(B) 95

(C) 100

(D) 105

(E) 115

Attachment:
#GREpracticequestion In the figure, what is the value of x .jpg
[/quote]
Senior Manager
Status: love the club...
Joined: 24 Mar 2015
Posts: 265
Re: In the figure, what is the value of x ?  [#permalink]

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04 Apr 2019, 09:20
Who told you all that the leftmost triangle is a right triangle ?

thanks
GMAT Club Legend
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Concentration: Sustainability, Marketing
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Re: In the figure, what is the value of x ?  [#permalink]

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04 Apr 2019, 09:21
testcracker wrote:
Who told you all that the leftmost triangle is a right triangle ?

thanks

testcracker
∆ with sides 3:4:5 is a right angled triangle ....
Senior Manager
Joined: 25 Feb 2019
Posts: 335
Re: In the figure, what is the value of x ?  [#permalink]

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04 Apr 2019, 09:44
IMO D

triangle with sides 5 , 4 , 3 form a pythagoras triplet

25 = 16+9

hope this helps

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Joined: 29 Oct 2012
Posts: 21
Re: In the figure, what is the value of x ?  [#permalink]

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04 Apr 2019, 09:51
Left most triangle is a right angle triangle
Right most triangle is an equilateral triangle= Each angle = 60
Sum of the angle of the middle figure =360
360 = 2x+60+90
x=105 i.e D
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Re: In the figure, what is the value of x ?  [#permalink]

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07 Apr 2019, 18:58
Bunuel wrote:

In the figure, what is the value of x ?

(A) 90

(B) 95

(C) 100

(D) 105

(E) 115

Attachment:
#GREpracticequestion In the figure, what is the value of x .jpg

Since the triangle on the left side is a 3-4-5 right triangle the angle opposite the side of 5 is 90 degrees. Thus, the unlabeled angle on the left of the quadrilateral is also 90 degrees.

The triangle on the right hand side is equilateral so the angle opposite the base of 1 is 60 degrees. Thus, the unlabeled angle on the right of the quadrilateral is also 60 degrees.

A quadrilateral has 360 degrees. Therefore, we can create the following equation for the angles of the quadrilateral in the middle:

90 + x + x + 60 = 360

2x = 210

x = 105

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Re: In the figure, what is the value of x ?   [#permalink] 07 Apr 2019, 18:58
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