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13 Nov 2018, 01:19
Kudos
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B
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
65%
(hard)
Question Stats:
39% (00:55) correct
61%
(00:57)
wrong
based on 269
sessions
History
Date
Time
Result
Not Attempted Yet
In the figure above, triangle MNO is equilateral. What is the area of triangle MNO ?
(1) NP has a length of \(5\sqrt{3}\).
(2) MN has a length of 10.
Attachment:
2018-11-13_1215.png [ 33.02 KiB | Viewed 6413 times ]
Pure algebraic questions like this one are no longer part of the GMAT Data Sufficiency syllabus.
For relevant Data Sufficiency questions, please check the Data Sufficiency forum:
Data Sufficiency Forum
Data Sufficiency Forum
13 Nov 2018, 01:30
Kudos
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Bunuel
(D) is our answer.
There are two different approaches to solving this question.
A Precise approach relies on knowledge of geometric rules:
(1) NP is a leg in a 30-60-90 triangle NPO meaning we can calculate the hypotenuse (which is the side of the triangle). Then we have the height and base of a triangle and can calculate its area.
(2) a useful equation to remember is that the area of an equilateral triangle is \(\frac{a^2\sqrt{3}}{4}\), where 'a' is the length of a side.
(Remember 1-2-3-4 i.e. length - square - sqrt(3) - div by 4)
Then both are sufficient.
A second approach, which does not rely on knowledge of geometric rules is Alternative.
An equilateral triangle is a regular polygon and there is only ONE way to draw a regular polygon.
That is - once you know the length of just one of the sides/heights/chords/etc. you know all of the shape's properties. (Try it out - you can SEE this)
So both (1) and (2) are sufficient.
13 Nov 2018, 02:02
Kudos
Bookmarks
The area of equilateral triangle is = \(s^2 *\sqrt{3}/4\)
where the height is\(s * \sqrt{3}/2\)
30:60:90
\(s:s\sqrt{3}:2s\)
we know the height is the side that corresponds to the 60 angle so \(s\sqrt{3} = 5\sqrt{3}\)
From that we can find the side s = 5 and accordingly find the area of the triangle.
Statement 1 is sufficient.
For statement 2
We are given a side of the equilateral triangle so using the equation we can find the area.
Sufficient.
Answer choice D
where the height is\(s * \sqrt{3}/2\)
30:60:90
\(s:s\sqrt{3}:2s\)
we know the height is the side that corresponds to the 60 angle so \(s\sqrt{3} = 5\sqrt{3}\)
From that we can find the side s = 5 and accordingly find the area of the triangle.
Statement 1 is sufficient.
For statement 2
We are given a side of the equilateral triangle so using the equation we can find the area.
Sufficient.
Answer choice D
13 Nov 2018, 03:50
Kudos
Bookmarks
No need of calculating the answer , we just need to check whether given information in statements is sufficient to answer the question or not.
stmnt1: using formula height of triangle= a* (sqrt 3/2)
we can solve for 'a' side of triangle and find area
sufficient
stmnt 2: one side letgh is given area of equilateral triangle would be sqrt 3 a^2/4
sufficient
D is correct option..
stmnt1: using formula height of triangle= a* (sqrt 3/2)
we can solve for 'a' side of triangle and find area
sufficient
stmnt 2: one side letgh is given area of equilateral triangle would be sqrt 3 a^2/4
sufficient
D is correct option..
