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Is the triangle above equilateral?

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Senior CR Moderator
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Is the triangle above equilateral?  [#permalink]

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New post 04 Feb 2018, 03:20
2
00:00
A
B
C
D
E

Difficulty:

  5% (low)

Question Stats:

92% (00:28) correct 8% (00:15) wrong based on 80 sessions

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Is the triangle above equilateral?

(1) x = y
(2) z = 60

Attachment:
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Capture.PNG [ 3.72 KiB | Viewed 1168 times ]

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Re: Is the triangle above equilateral?  [#permalink]

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New post 04 Feb 2018, 04:46
broall wrote:
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Is the triangle above equilateral?

(1) x = y
(2) z = 60


1. Case 1: However if x=y=45 degree, the triangle will be a right angled isosceles triangle.
Case 2: If x=y=60 degree, then the triangle is equilateral. (Insufficient)

2. Case 1: Though z=60, we have no idea about the angles x and y. We can't
say anything about the triangle.
Case 2: But if x=y also, then the triangle is equilateral. (Insufficient)

On combining the information from both the statements,
we can come to a clear conclusion that the triangle is equilateral - Case 2(Sufficient - Option C)

P.S in questions like these, the common mistake made is carrying over
the information from the first statement into the second statement, thereby committing a mistake

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Re: Is the triangle above equilateral?  [#permalink]

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New post 04 Feb 2018, 05:04
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Re: Is the triangle above equilateral?  [#permalink]

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New post 06 Feb 2018, 22:57
broall wrote:
Image
Is the triangle above equilateral?

(1) x = y
(2) z = 60

Attachment:
Capture.PNG


Forget conventional ways of solving math questions. For DS problems, the VA (Variable Approach) method is the quickest and easiest way to find the answer without actually solving the problem. Remember that equal numbers of variables and independent equations ensure a solution.

x + y + z = 180
Since we have 3 variables (x, y and z) and 1 equation, C is most likely to be the answer. So, we should consider 1) & 2) first.

Condition 1) & 2):
Since z = 60, x + y = 120.
And x = y implies x = y = 60.
Thus it is an equilateral triangle.

Therefore, the answer is C.

Normally, in problems which require 2 equations, such as those in which the original conditions include 2 variables, or 3 variables and 1 equation, or 4 variables and 2 equations, each of conditions 1) and 2) provide an additional equation. In these problems, the two key possibilities are that C is the answer (with probability 70%), and E is the answer (with probability 25%). Thus, there is only a 5% chance that A, B or D is the answer. This occurs in common mistake types 3 and 4. Since C (both conditions together are sufficient) is the most likely answer, we save time by first checking whether conditions 1) and 2) are sufficient, when taken together. Obviously, there may be cases in which the answer is A, B, D or E, but if conditions 1) and 2) are NOT sufficient when taken together, the answer must be E.
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Re: Is the triangle above equilateral? &nbs [#permalink] 06 Feb 2018, 22:57
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