In the figure above, if the length of MO is 10, is MNO an equilateral

Question

https://gmatclub.com/forum/download/file.php?id=64126 In the figure above, if the length of MO is 10, is MNO an equilateral triangle? (1) The length of MN is 10. (2) h = 5\sqrt{3} Project DS Butler Data Sufficiency (DS3) For DS butler Questions Click Here 1.jpg

asishron29181 · Answer

In the figure above, if the length of MO is 10, is MNO an equilateral triangle?

(1) The length of MN is 10.
MO = MN = 10
The length of NO lies between,
10-10 < NO < 10+10
0 < NO < 20
NO could take any values from 0 to 20
Not sufficient.

(2) h=5√3
Area of MNO = 0.5 * b * h = 0.5 * 5√3 * 10
=25√3

Area of equilateral triangle = √3/4 * A^2 = 25√3

Sufficient.

IMO B

IanStewart · Answer

It's not clear what the answer to the question should be. Certainly Statement 1 is insufficient, because it only tells us the triangle is isosceles, and Statement 2 is clearly insufficient because we only know the length of one side and the length h. Even if we assume h is a height, by moving the line 'h' left or right we can easily make non-equilateral triangles.

When we use both Statements, we then need to know if 'h' is the height of the triangle. The diagram doesn't tell us 'h' is perpendicular to MO, and calling a length 'h' does not alone make that length into a height. If 'h' is not necessarily at 90 degrees to MO, then the answer is E. If 'h' is indeed the height of the triangle, then the answer is C (there are several ways to see that -- for example, we'd know two sides in the right triangle on the left, which would ensure it's a 30-60-90 triangle, and so we'd know 'h' divides MO into two equal parts of length 5, but then we know two lengths in the right triangle on the right and it's also a 30-60-90).

trshvn · Answer

Conceptually, if I were to give you a structure of the form ⊥ and ask that you complete the triangle, you’ll be forced to join the remaining two sides to the tip of the vertical line stretching out from the base. These remaining two sides must also fully extend to the endpoints of the base and so it follows from this logic that the lengths of your sides will be fixed, thus known. So, answer choice B is the correct answer for this question IMO.

IanStewart · Answer

That can be a good way to think about GMAT DS geometry questions, but it's important if you're doing this to recognize which features of the diagram are fixed and which are flexible. Here we don't know the position of the vertical line. It might be directly in the center of the line MO, in which case from Statement 2 the triangle will indeed be equilateral. But it might be off-center as well, and if it is, the triangle will not be equilateral.

We also don't even know that the vertical-looking line is actually vertical; the question would need to tell us explicitly that it is at 90 degrees to line MO. I'd bet the question writer intends for that line to be a height, just because they called it "h", but a line is not a height just because it's labeled with a particular letter. So we really know neither the position nor the angle of the vertical-looking line, and we can freely draw the diagram in all kinds of ways using Statement 2, one of which will make the triangle equilateral and the rest of which will not.

akshat26 · Answer

where are the options
?

riddhisiddhi · Answer

E is the answer

Reason
Statement 1: MN =10
ON can be 10 or may be not 
No angles are also given.
 Not sufficient to answer

Statement 2:
H= 5√3
It could be equilateral or not

No angles given

Combining both
Not sufficient

E is the answer

Posted from my mobile device

Bunuel · Answer

This is a data sufficiency question. Options for DS questions are always the same.

The data sufficiency problem consists of a question and two statements, labeled (1) and (2), in which certain data are given. You have to decide whether the data given in the statements are sufficient for answering the question. Using the data given in the statements, plus your knowledge of mathematics and everyday facts (such as the number of days in July or the meaning of the word counterclockwise), you must indicate whether—

A. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked.
B. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked.
C. BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficient to answer the question asked.
D. EACH statement ALONE is sufficient to answer the question asked.
E. Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data specific to the problem are needed.

I suggest you to go through the following post  ALL YOU NEED FOR QUANT .

Hope this helps.

sumitkrocks · Answer

In the figure above, if the length of MO is 10, is MNO an equilateral triangle?

Statement (1) The length of MN is 10.

We can only say MNO is an isosceles triangle.
Not sufficient 
 
Statement (2)  h = 5\sqrt{3} 
h is a line joining a vertex and opposite side, we do not know the angle at base. 
No relevant information- Not sufficient

Combined:

No relevant information is added to statement 1

E is the answer.

Jarvis07 · Answer

The answer is (E).
I hate algebra so let us try something else:
A) The first option does not get us anywhere because, with this option, we have a triangle with two fixed sides. We can move these sides any way we want and make a brand-new triangle. Please note that h is not defined, so we can put any value to it as long as it remains shorter than the third side.
B) Statement 2 is insufficient as we have only been provided with the length of one side and the length 'h'. Even if we consider 'h' to be a height, we can easily create non-equilateral triangles by adjusting the position of the line representing 'h' to the left or right.

Together, unless we know the angle at which h is positioned on MO, we will not be able to determine whether the triangle is quadrilateral or not.

In the figure above, if the length of MO is 10, is MNO an equilateral

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GMAT Data Sufficiency (DS) Questions

In the figure above, if the length of MO is 10, is MNO an equilateral

Prep Toolkit

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

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From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards