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605-655 (Medium)|   Geometry|      
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amanvermagmat
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Three medians of triangle ABC intersect at a point G. Is triangle ABC 31 May 2018, 03:38
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D
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!

Difficulty:

45% (medium)

Question Stats:

57% (01:11) correct 43% (01:24) wrong based on 52 sessions

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Three medians of triangle ABC intersect at a point G. Is triangle ABC scalene?

(1) GA = GB

(2) GB = GC
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D
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Tulkin987
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Three medians of triangle ABC intersect at a point G. Is triangle ABC 31 May 2018, 03:57
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amanvermagmat
Three medians of triangle ABC intersect at a point G. Is triangle ABC scalene?

(1) GA = GB

(2) GB = GC
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First pay attention to this property of median: the centroid divides each median into parts in the ratio \(2:1\), with the centroid being twice as close to the midpoint of a side as it is to the opposite vertex.

So, point \(G\) is the centroid.

(1) If \(GA=GB\), according to the above property, medians with vertice \(A\) and \(B\) are equal. We have equilateral triangle. Answer is NO. Sufficient.

(2) The same is true. Medians with vertice \(B\) and \(C\) are equal, and we have equilateral triangle. Answer is NO. Sufficient.

Answer: D
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Three medians of triangle ABC intersect at a point G. Is triangle ABC 31 May 2018, 05:01
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Tulkin987
amanvermagmat
Three medians of triangle ABC intersect at a point G. Is triangle ABC scalene?

(1) GA = GB

(2) GB = GC

First pay attention to this property of median: the centroid divides each median into parts in the ratio \(2:1\), with the centroid being twice as close to the midpoint of a side as it is to the opposite vertex.

So, point \(G\) is the centroid.

(1) If \(GA=GB\), according to the above property, medians with vertice \(A\) and \(B\) are equal. We have equilateral triangle. Answer is NO. Sufficient.

(2) The same is true. Medians with vertice \(B\) and \(C\) are equal, and we have equilateral triangle. Answer is NO. Sufficient.

Answer: D
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Hello

Yes I agree that answer would be D. But may I point out that from first statement, GA=GB means that medians from A and B are equal, which tells us that triangle is isosceles. Not necessarily equilateral. Same from statement 2 also.

Of course still this information is sufficient to say NO to the question asked, and hence answer should be D.
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Three medians of triangle ABC intersect at a point G. Is triangle ABC 31 May 2018, 05:07
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amanvermagmat
Tulkin987
amanvermagmat
Three medians of triangle ABC intersect at a point G. Is triangle ABC scalene?

(1) GA = GB

(2) GB = GC

First pay attention to this property of median: the centroid divides each median into parts in the ratio \(2:1\), with the centroid being twice as close to the midpoint of a side as it is to the opposite vertex.

So, point \(G\) is the centroid.

(1) If \(GA=GB\), according to the above property, medians with vertice \(A\) and \(B\) are equal. We have equilateral triangle. Answer is NO. Sufficient.

(2) The same is true. Medians with vertice \(B\) and \(C\) are equal, and we have equilateral triangle. Answer is NO. Sufficient.

Answer: D


Hello

Yes I agree that answer would be D. But may I point out that from first statement, GA=GB means that medians from A and B are equal, which tells us that triangle is isosceles. Not necessarily equilateral. Same from statement 2 also.

Of course still this information is sufficient to say NO to the question asked, and hence answer should be D.
Show more

Yes, you are right! :thumbup:
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