CAT 2024 Question Paper | Quant Slot 3

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 7 The midpoints of sides AB, BC, and AC in △ ABC are M, N, and P, respectively. The medians drawn from A, B, and C intersect the line segments MP, MN and NP at X, Y, and Z, respectively. If the area of △ ABC is 1440 sq cm, then the area, in sq cm, of △ XYZ is

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Video Explanation

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Explanatory Answer

Comparing \(\triangle A B C\) and \(\triangle M N P\) \[ A M=M B ; A N=N C \] So, \(M N|\mid B C\). By midpoint theorem, \(\operatorname{ar}(\triangle ABC )=4 x \operatorname{ar}(\triangle MNP )\)
So, \(\operatorname{ar}(\Delta M N P)=\frac{1440}{4}=360\)

Similarly, Comparing \(\triangle X Y Z\) and \(\triangle M N P\) \[ P X=X M ; P Z=Z N \] So, \(X Z|\mid M N\).
By midpoint theorem, \[ \operatorname{ar}(\Delta MNP)=4 x \operatorname{ar}(\Delta XYZ) \] So, \(\operatorname{ar}(\triangle X Y Z)=\frac{360}{4}=90\)

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The question is "The midpoints of sides AB, BC, and AC in △ ABC are M, N, and P, respectively. The medians drawn from A, B, and C intersect the line segments MP, MN and NP at X, Y, and Z, respectively. If the area of △ ABC is 1440 sq cm, then the area, in sq cm, of △ XYZ is"

Hence, the answer is '90'

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