Is triangle ABC isosceles? (1) Angle ABC is greater than 90 degrees.

Question

Is triangle ABC isosceles?

(1) Angle ABC is greater than 90 degrees.

(2) Median BD which joins AC at D, is NOT perpendicular to AC.

SonalSinha803 · Answer

According to statement 1, taking angle ABC greater than 90 or less than 90, both can give the probability of getting isosceles triangle as well as scalene. Hence, insufficient.

Statement 2 says, if the median is not perpendicular to AC, it is clear that the triangle is not isosceles. It is because a median of an isosceles triangle is always perpendicular to the opposite side.

Hence, sufficient.

Hence, option B.

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Hero8888 · Answer

Here is a good example how the triangle is Statement 2 can be isosceles. See attachment.
Answer (C)

GYANENDRA88 · Answer

Hero8888 ,
Let angle b=120, angble a=20 and angle c=40.
This triangle will fullfill both statements but it is not isosceles

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Hero8888 · Answer

Hi,  GYANENDRA88

You are right in this part, but you have to understand DS format of GMAT. You have to prove that a statement is definitely YES or definitely NO. Getting clear "NO" makes statement valid too.

GYANENDRA88 · Answer

Hero8888 ,
We can go with E

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nithinjohn · Answer

If I'm not mistaken, the median of the unequal side of an isoceles triangle is perpendicular to the opposite side. Here we don't know which two sides are equal. So we really can't say. hence statement B is insufficient. Correct answer shoudl be E in my opinion.

RetaketheGMAT · Answer

Statement 1 is not sufficient on its own but it does give us valuable info: that the two equal sides COULD only be AB and AC.

You need that along with Statement 2 which tells you that the median line would be AD if it was perpendicular to BC. Hence you need both statements (C) to definitely answer the question as NO.

bumpbot · Answer

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Is triangle ABC isosceles? (1) Angle ABC is greater than 90 degrees.

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