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# Is triangle XYZ an equilateral triangle?

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Math Expert
Joined: 02 Sep 2009
Posts: 58464
Is triangle XYZ an equilateral triangle?  [#permalink]

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24 Aug 2018, 05:18
00:00

Difficulty:

15% (low)

Question Stats:

75% (00:39) correct 25% (00:34) wrong based on 50 sessions

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Is triangle XYZ an equilateral triangle?

(1) Angle X is 60°.
(2) Side XY is equal to side YZ.

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Re: Is triangle XYZ an equilateral triangle?  [#permalink]

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24 Aug 2018, 05:23
Statement 1 is insufficient.
No idea about angles X and Y.

From 2: It can be either isoscles or equilateral.

Combining 1&2 is suficient.

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Re: Is triangle XYZ an equilateral triangle?  [#permalink]

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24 Aug 2018, 05:28
Bunuel wrote:
Is triangle XYZ an equilateral triangle?

(1) Angle X is 60°.
(2) Side XY is equal to side YZ.
St1: it can be any triangle as we have restricted only one angle. Other angles can be 60,60 or 40,20

St2: it can be an isosceles triangle or an equilateral triangle.

Combining
Sufficient
C

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Re: Is triangle XYZ an equilateral triangle?  [#permalink]

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24 Aug 2018, 09:56

Solution

To find:
• If triangle XYZ is an equilateral triangle or not

Approach and Working:
• In equilateral triangle,
o All sides are equal
o All angles are equal to 60 degrees

Analysing Statement 1
• We are given that ∠X = 600
• We do not have information about any other angle
Therefore, Statement 1 alone is not sufficient to answer this question

Analysing Statement 2
• We are given that XY = YZ
• We do not have any information about the third side, ZX
Therefore, Statement 2 alone is not sufficient to find an answer.

Combining Both Statements
• Combining both the statements, we get
o XY = YZ, implies ∠Y = ∠Z, and
o ∠X = 60 degrees, implies ∠Y + ∠Z = 180 – 60 = 120 degrees
o From the above two equations, we get, ∠Y = ∠Z = 60 degrees
Thus, Statement (1) and (2) TOGETHER are sufficient to answer the question

Hence, the correct answer is option C.

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Re: Is triangle XYZ an equilateral triangle?  [#permalink]

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25 Aug 2018, 10:58
Bunuel wrote:
Is triangle XYZ an equilateral triangle?

(1) Angle X is 60°.
(2) Side XY is equal to side YZ.

(1) Angle X is 60°.
no information on sides .
Y+Z =120
insufficient

(2) Side XY is equal to side YZ.
The triangle can be an isosceles or an equilateral triangle
insufficient.

using both the statements.
x=z=60
y=180-120=60
x=y=z=60
sufficient
Re: Is triangle XYZ an equilateral triangle?   [#permalink] 25 Aug 2018, 10:58
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