# CAT 2023 Question Paper | Quant Slot 1

###### CAT Previous Year Paper | CAT Quant Questions | Question 18

CAT 2023 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 18 : A quadrilateral ABCD is inscribed in a circle such that AB : CD = 2 : 1 and BC : AD = 5 : 4. If AC and BD intersect at the point E, then AE : CE equals

1. 1 : 2
2. 5 : 8
3. 8 : 5
4. 2 : 1

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$$angle D A C = $angle D B C$$Angles subtended by the chord DC on the same side.$
$$angle A D B = $angle A C B$$Angles subtended by the chord AB on the same side.$
$$angle A E D = $angle B E C$$Vertically Opposite angles.$

Therefore, $$triangle A E D $sim \triangle B E C$ $\frac { A E } { B E } = \frac { E D } { E C } = \frac { A D } { B C } = \frac { 4 } { 5 }$ $\angle A B D = \angle A C D$$Angles subtended by the chord AD on the same side.$
$$angle B A C = $angle B D C$$Angles subtended by the chord BC on the same side.$
$$angle A E B = $angle D E C$$Vertically Opposite angles.$

Therefore, $$triangle A E B $sim \triangle D E C$ $\frac { A E } { E D } = \frac { B E } { E C } = \frac { A B } { D C } = \frac { 2 } { 1 }$ $\frac { A E } { E D } \times \frac { E D } { E C } = \frac { 2 } { 1 } \times \frac { 4 } { 5 } = \frac { 8 } { 5 }$ Therefore, AE : EC = 8 : 5 The question is " A quadrilateral ABCD is inscribed in a circle such that AB : CD = 2 : 1 and BC : AD = 5 : 4. If AC and BD intersect at the point E, then AE : CE equals " ##### Hence, the answer is '8 : 5' Choice C is the correct answer. ###### Best CAT Online Coaching Try upto 40 hours for free Learn from the best! ###### Prepare for CAT 2024 with 2IIM's Daily Preparation Schedule ###### Know all about CAT Exam Syllabus and what to expect in CAT ###### Already have an Account? ###### Best CAT Coaching in Chennai Attend a Demo Class ###### Best Indore IPM & Rohtak IPM CoachingSignup and sample 9 full classes for free. Register now! ## CAT Questions | CAT Quantitative Aptitude ## CAT Questions | Verbal Ability for CAT ##### Where is 2IIM located? 2IIM Online CAT Coaching A Fermat Education Initiative, 58/16, Indira Gandhi Street, Kaveri Rangan Nagar, Saligramam, Chennai 600 093 ##### How to reach 2IIM? Mobile:$91$ 99626 48484 / 94459 38484
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