CAT 2024 Question Paper | Quant Slot 2

CAT Questions

CAT 2024 Quant was dominated by Algebra followed by Arithmetic. 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 5 \(A B C D\) is a trapezium in which \(A B\) is parallel to \(C D\). The sides \(A D\) and \(B C\) when extended, intersect at point \(E\). If \(A B=2 \mathrm{~cm}, C D=1 \mathrm{~cm}\), and perimeter of \(A B C D\) is 6 cm , then the perimeter, in cm , of \(\triangle A E B\) is

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Video Explanation

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Explanatory Answer

By AAA similarity, \(\triangle\) AEC is similar to \(\triangle DEC\) \[ A B / D C=A E / D E=B E / C E=2 / 1 \] Therefore DE \(=x cm\) and CE \(=y cm\) Now Perimeter of triangle AEB \(=2+2 x+2 y=2+2(x+y)=2+2(3)=8 cm\)

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The question is "\(A B C D\) is a trapezium in which \(A B\) is parallel to \(C D\). The sides \(A D\) and \(B C\) when extended, intersect at point \(E\). If \(A B=2 \mathrm{~cm}, C D=1 \mathrm{~cm}\), and perimeter of \(A B C D\) is 6 cm , then the perimeter, in cm , of \(\triangle A E B\) is"

Hence, the answer is '8'

Choice C is the correct answer.

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