Is the triangle above equilateral?

Question

https://gmatclub.com/forum/download/file.php?id=39829 Is the triangle above equilateral? (1) x = y (2) z = 60 Capture.PNG

pushpitkc · Answer

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

Bunuel · Answer

Check  Properties of Polygons Questions  from our  Special Questions Directory .

MathRevolution · Answer

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.

CrackverbalGMAT · Answer

From statement I alone, x = y. There is no information about z.

If x = y = z, the triangle is equilateral; otherwise the triangle is just an isosceles triangle.
Statement I alone is insufficient. Answer option A and D can be eliminated.

From statement II alone, z = 60. There is no information about the angles x and y.
Statement II alone is insufficient. Answer option B can be eliminated.

Combining statements I and II, we have the following:

From statement II, z = 60; therefore, x + y = 120
From statement I, x = y and hence x = y = 60

Since all three angles are equal to 60, the triangle is an equilateral triangle
The combination of statements is sufficient. Answer option E can be eliminated.

The correct answer option is C.

Hope that helps!
Aravind BT

bumpbot · Answer

Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.

Is the triangle above equilateral?

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards

GMAT Data Sufficiency (DS) Questions

Is the triangle above equilateral?

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards