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CAT 2018 Slot 2 · Quant · Triangles · hard

In triangle ABC, D is a point on BC with BD : DC = 2 : 3, and E is a point on AD with AE : ED = 3 : 1. What is the ratio of the area of triangle ABE…

Single correct option

In triangle ABC, D is a point on BC with BD : DC = 2 : 3, and E is a point on AD with AE : ED = 3 : 1. What is the ratio of the area of triangle ABE to the area of triangle ABC?
  1. A. 1/4
  2. B. 3/10
  3. C. 3/8
  4. D. 2/5
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Answer: (B) 3/10

Triangles ABD and ADC share the apex A and have bases on BC, so their areas are in the ratio BD : DC = 2 : 3. So [ABD] = (2/5)[ABC].

Triangles ABE and EBD share apex B with bases on AD, so [ABE] : [EBD] = AE : ED = 3 : 1. So [ABE] = (3/4)[ABD].

[ABE] = (3/4)(2/5)[ABC] = (3/10)[ABC].

Tip: For triangles with the same apex whose bases lie on one line, the areas are proportional to the bases. Chain the ratios.
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Original question written in the CAT 2018 Slot 2 pattern and checked twice for the correct answer. Not an official question paper. How we write and check questions · Corrections policy · Report a mistake