CAT 2021 Question Paper | Quant Slot 2

CAT Previous Year Paper | CAT Quant Questions | Question 17

CAT 2021 Quant was dominated by Arithmetic followed by Algebra. In Arithmetic, the questions were dominated by topics like Speed-time-distance, Mixture and Alligations. This year, there was a surprise. The questions from Geometry were relatively on the lower side as compared to the previous years. There were 8 TITA Qs this year. Overall this section was at a medium level of difficulty.

Question 17 : The sides AB and CD of a trapezium ABCD are parallel, with AB being the smaller side. P is the midpoint of CD and ABPD is a parallelogram. If the difference between the areas of the parallelogram ABPD and the triangle BPC is 10 sq cm, then the area, in sq cm, of the trapezium ABCD is

  1. 20
  2. 25
  3. 40
  4. 30

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Explanatory Answer

We can construct a Quadrilateral ABCD from the given information:
Trapezium with a triangle
Point P divides the line CD into two equal halves,
Further we know that the area of the parallelogram ABPD is twice the area of the triangle BCP, and hence the heights of both will also be the same.
Now, from here we can say that the area of the parallelogram will be twice the area of the triangle.
Let the area of the triangle be ‘A’. Then the area of the parallelogram BCP will be 2A.
So, this difference will be 2A - A = 10
Hence A = 10
Then the area of the parallelogram would be 2A + A = 30 sq cm

The answer is '30'

Choice D is the correct answer.

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