CAT 2023 Question Paper | Quant Slot 2

CAT Previous Year Paper | CAT Quant Questions | Question 17

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 17 : In a rectangle ABCD, AB = 9 cm and BC = 6 cm. P and Q are two points on BC such that the areas of the figures ABP, APQ, and AQCD are in geometric progression. If the area of the figure AQCD is four times the area of triangle ABP, then BP : PQ : QC is

  1. 1 : 1 : 2
  2. 1 : 2 : 4
  3. 2 : 4 : 1
  4. 1 : 2 : 1

🎉 Flat ₹ 8,000 off on our CAT '24 & '25 Courses!
Valid till 30th April


Register Now

Best CAT Online Coaching
Try upto 40 hours for free
Learn from the best!


2IIM : Best Online CAT Coaching.


Video Explanation


Best CAT Coaching in Chennai


CAT Coaching in Chennai - CAT 2022
Limited Seats Available - Register Now!


Explanatory Answer

Let BP = x, PQ = y and QC = z.
Break up of the Rectangle.
Since \( \operatorname { Ar } ( A B P ) , \operatorname { Ar } ( A P Q ) \& A r ( A Q C D ) \) are in \( G P \) and \( \operatorname { Ar } ( A Q C D ) = 4 \times \operatorname { Ar } ( A B P ) \)
\( \operatorname { Ar } ( A B P ) : \operatorname { Ar } ( A P Q ) : \operatorname { Ar } ( A Q C D ) = 1 : 2 : 4 \)
\( \frac { 9 x } { 2 } : \frac { 9 y } { 2 } : 27 + \frac { 9 z } { 2 } = 1 : 2 : 4 \)
\( x : y : 6 + z = 1 : 2 : 4 \)
\( y = 2 x \)
\( 6 + z = 4 x \)
x + y + z = 6
x + 2x + 4x – 6 = 6
x = \( \frac { 12 } { 7 } \)
z = 4x – 6 = \( \frac { 48 - 42 } { 7 } = \frac { 6 } { 7 } \)
∴ x = 2z
Therefore, \( x : y : z = 2 : 4 : 1 \)
BP : PQ : QC = 2 : 4 : 1


The question is " In a rectangle ABCD, AB = 9 cm and BC = 6 cm. P and Q are two points on BC such that the areas of the figures ABP, APQ, and AQCD are in geometric progression. If the area of the figure AQCD is four times the area of triangle ABP, then BP : PQ : QC is "

The answer is '2 : 4 : 1'

Choice C is the correct answer.

CAT Questions | CAT Quantitative Aptitude

CAT Questions | CAT DILR

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
WhatsApp: WhatsApp Now
Email: info@2iim.com