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I don't understand OA on this one.
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Director
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I am getting B as answer...let me know if that is right i would then explain
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gmat2me2 wrote: I am getting B as answer...let me know if that is right i would then explain
B = 90 degree
Angle ACB=60 degree, and angle CAB=30 degree,
Hence, the triangle must not be isosceles triangle.
A seems insufficient
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gmat2me2 wrote: I am getting B as answer...let me know if that is right i would then explain
Go for B
angle B = 90 degree
Angle ACB=60 degree, and angle CAB=30 degree,
Hence, the triangle must not be isosceles triangle.
(1) seems insufficient
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Director
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B will disporve its not an isoceles triangle
so answer = B
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It has to be B because the second stmt shows that the triangle abc is not isoceles triangle.
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Another vote for B.
In A , the angles of triangle ABC are not known to be equal or not.
In B, the angles are known and are 30,60
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mirhaque wrote: I don't understand OA on this one.
1 is suff too.
acb=2adc.....1
acb=cad+adc.....2 (external angle equal two other internal angle)
combining 1 & 2 adc=cad.
that means cd=ad.
This goes to prove that triangle abc is not isosceles
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mirhaque wrote: mirhaque wrote: I don't understand OA on this one. 1 is suff too. acb=2adc.....1 acb=cad+adc.....2 (external angle equal two other internal angle) combining 1 & 2 adc=cad. that means cd=ad. This goes to prove that triangle abc is not isosceles I dont think you can use that theorem here simply because angle A is shared between the triangles .
So your (2) in your explanation is a a doubt for me.
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Director
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mirhaque wrote: mirhaque wrote: I don't understand OA on this one. 1 is suff too. acb=2adc.....1 acb=cad+adc.....2 (external angle equal two other internal angle) combining 1 & 2 adc=cad. that means cd=ad. This goes to prove that triangle abc is not isosceles I get your point now mirhaque. the external angle of ADC is angle B and that should be suffiecient enough to say that A is also sufficient.....
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gmat2me2 wrote: mirhaque wrote: mirhaque wrote: I don't understand OA on this one. 1 is suff too. acb=2adc.....1 acb=cad+adc.....2 (external angle equal two other internal angle) combining 1 & 2 adc=cad. that means cd=ad. This goes to prove that triangle abc is not isosceles I get your point now mirhaque. the external angle of ADC is angle B and that should be suffiecient enough to say that A is also sufficient..... A is not sufficient.
I don't understand how you guys got A sufficient. B should be the answer.
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ashkg wrote: gmat2me2 wrote: mirhaque wrote: mirhaque wrote: I don't understand OA on this one. 1 is suff too. acb=2adc.....1 acb=cad+adc.....2 (external angle equal two other internal angle) combining 1 & 2 adc=cad. that means cd=ad. This goes to prove that triangle abc is not isosceles I get your point now mirhaque. the external angle of ADC is angle B and that should be suffiecient enough to say that A is also sufficient..... A is not sufficient. I don't understand how you guys got A sufficient. B should be the answer. Well the theorem the external angle of a triangle is equal to the sum of opposite angles is used here.
let acb = 2x while ADC = x
since ACB=2x ==>> ACD=180-2x
In triangle ACD angles A + D +C =180
So we have C =180-2x D =x So angle A for ACD has to be x.
So it is isoceles
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gmat2me2 wrote: ashkg wrote: gmat2me2 wrote: mirhaque wrote: mirhaque wrote: I don't understand OA on this one. 1 is suff too. acb=2adc.....1 acb=cad+adc.....2 (external angle equal two other internal angle) combining 1 & 2 adc=cad. that means cd=ad. This goes to prove that triangle abc is not isosceles I get your point now mirhaque. the external angle of ADC is angle B and that should be suffiecient enough to say that A is also sufficient..... A is not sufficient. I don't understand how you guys got A sufficient. B should be the answer. Well the theorem the external angle of a triangle is equal to the sum of opposite angles is used here. let acb = 2x while ADC = x since ACB=2x ==>> ACD=180-2x In triangle ACD angles A + D +C =180 So we have C =180-2x D =x So angle A for ACD has to be x. So it is isoceles The question is asking if trianlge ABC isosceles and not ACD.
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Looks I have drifted to the other triangle :-D
Anyway ...As per the question B would be enough.......Thanks ashkg.....
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For 1), if you draw a isoceles triangle with B a right angle and BA=BC, then you draw a nother isoceles triangle where AC=AD, then 1) would be satisfied. However you can also draw a right triangle ABC where BA<>BC, and then still draw a triangle where AC=AD to satisfy 1). In other words 1) is not sufficient to determine whether ABC is isoleles.
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