CAT 2021 Question Paper | Quant Slot 2

CAT Previous Year Paper | CAT Quant Questions | Question 11

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 11 : Let D and E be points on sides AB and AC, respectively, of a triangle ABC, such that AD : BD = 2 : 1 and AE : CE = 2 : 3. If the area of the triangle ADE is 8 sq cm, then the area of the triangle ABC, in sq cm, is


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Explanatory Answer

Triangle
The area of the triangle ADE = 8 sqcm.
\\frac{1}{2}) × (AD) (AE) × sin(A) = 8
\\frac{1}{2}) × (2x) (2y) × sin(A) = 8
xy × sin(A) = 4
The area of the triangle ABC = \\frac{1}{2}) × (AB) (AC) × sin(A)
= \\frac{1}{2}) × (3x) (5y) × sin(A)
= \\frac{15}{2}) × (xy) × sin(A)
= \\frac{15}{2}) (4) (since xy sin A = 4)
= 30 sq cm


The answer is '30'

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