IIFT 2019 Question Paper | Quants

CAT Questions

The best way to boost your IIFT prep is to practice the actual IIFT Question Papers. 2IIM offers you exactly that, in a student friendly format to take value from this. In the 2019 IIFT, quants were a mixed bag of questions of varying difficulty, with some routine questions and the others were very demanding. Some beautiful questions that laid emphasis on Learning ideas from basics and being able to comprehend more than remembering gazillion formulae and shortcuts.

Question 5: AB is the tangent on the circle at point A. The line BC meets the circle at points C and E. Line AD bisects the ∠ EAC. If ∠ EAC =60 degree and ∠ BAC : ∠ ACB = 2: 5. Find ∠ ABC:

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Video Explanation

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Explanatory Answer

From the above information we can see that ∠ EAD = ∠ DAC =30 °
And the ratio of ∠ BAC : ∠ ACB = 2 : 5. let's say the ∠ are 2x and 5x
∠ ACB is the exterior ∠ to the triangle AEC, which will be equal to the sum of ∠ EAC and ∠ AEC.
Further, ∠ AED = ∠ BAC (Alternate Segment Theorem!)

Alternate Segment Theorem: In any circle, the angle between a chord and a tangent through one of the end points of the chord is equal to the angle in the alternate segment.

From here we can plug this information in the equation:
∠ ACB = ∠ EAC + ∠ AEC
5x = 60 ° + 2x
3x = 60 °
x = 20 °
Now, the sum of ∠ in the triangle ACB:
2x + 5x + ∠ ABC = 180 °
So, ∠ ABC = 40 °

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The question is "Find ∠ ABC"

Hence, the answer is, "40"