Solutions to CAT Geometry Data Sufficiency Questions

Have given below the solutions to the questions on geometry DS. The solutions are courtesy Vimal Gopinath (person incharge of 2IIM Bengaluru)

Qn 1: Is triangle ABC obtuse angled?
I) a^2 + b^2 > c^2 - Not enough. We don’t have info about b^2 or a^2
II) The circumcenter of the triangle does not lie inside the triangle - Not enough. The triangle could be right-angled as well.
Combination is also not enough, it is valid for both right angled and obtuse angled triangles.
D

Qn 2: Do the two circles with centers A and B and radii R and r intersect each other
I) AB > R - r – Not enough. May intersect, may be “parallel” or "disjoint"
II) AB > R + r – Sufficient. Circles cant intersect. Have to be separate.
A

Qn 3: Trapezium ABCD is such that AB is parallel to CD. Is this trapezium anisosceles trapezium?
I) Angle B and D are supplementary Sufficient. If two base angles are equal, then the trapezium has to be isosceles.
II) The quadrilateral is inscribed inside a circle. Sufficient. All trapeziums inscribed in circles have to be isosceles. (Think about the proof for this)
C

Qn 4: Circle C has center O, and a chord AB such that angle AOB = 80 degrees.Does point E lie inside the circle

I) Angle AEB > 50 degrees Insufficient.E could lie on the minor segment ADB or slightly outside or slightly inside the circle.
II) Angle AEB < 30 degrees. Sufficient. All the angles inside the circle will be in the range from 40 – 140 degrees. Anything less than 40 will have to be outside the circle.)
A

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IIM CAT Preparation Tips: Solutions to CAT Geometry Data Sufficiency Questions

Aug 30, 2011

Solutions to CAT Geometry Data Sufficiency Questions

Have given below the solutions to the questions on geometry DS. The solutions are courtesy Vimal Gopinath (person incharge of 2IIM Bengaluru)

Qn 1: Is triangle ABC obtuse angled?
I) a^2 + b^2 > c^2 - Not enough. We don’t have info about b^2 or a^2
II) The circumcenter of the triangle does not lie inside the triangle - Not enough. The triangle could be right-angled as well.
Combination is also not enough, it is valid for both right angled and obtuse angled triangles.
D

Qn 2: Do the two circles with centers A and B and radii R and r intersect each other
I) AB > R - r – Not enough. May intersect, may be “parallel” or "disjoint"
II) AB > R + r – Sufficient. Circles cant intersect. Have to be separate.
A

Qn 3: Trapezium ABCD is such that AB is parallel to CD. Is this trapezium anisosceles trapezium?
I) Angle B and D are supplementary Sufficient. If two base angles are equal, then the trapezium has to be isosceles.
II) The quadrilateral is inscribed inside a circle. Sufficient. All trapeziums inscribed in circles have to be isosceles. (Think about the proof for this)
C

Qn 4: Circle C has center O, and a chord AB such that angle AOB = 80 degrees.Does point E lie inside the circle

I) Angle AEB > 50 degrees Insufficient.E could lie on the minor segment ADB or slightly outside or slightly inside the circle.
II) Angle AEB < 30 degrees. Sufficient. All the angles inside the circle will be in the range from 40 – 140 degrees. Anything less than 40 will have to be outside the circle.)
A

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At 4:36 PM ,  maniac said...

Qn 4: Circle C has center O, and a chord AB such that angle AOB = 80 degrees.Does point E lie inside the circle
II) Angle AEB < 30 degrees. Sufficient. All the angles inside the circle will be in the range from 40 – 140 degrees,

although the answer is A, but in my opinion the range of the angles inside the circle would be from 40- 180,
minor sector, min 40--> then it increases to 180 then it decreases and on major sector angle=140.

At 9:40 AM ,  Bee said...

Hi "Maniac", Your observation is spot on. Thanks, again.