CAT 2023 Slot 1 QA Q9 Geometry

Question 9 of the Quantitative Ability (QA) section, CAT 2023 Slot 1, with CAT's official answer and a worked solution.

The minor angle between the hours hand and minutes hand of a clock was observed at \(8: 48 \mathrm{am}\). The minimum duration, in minutes, after 8.48 am when this angle increases by \(50 \%\) is
  1. A
    \(\frac{36}{11}\)
  2. B
    \(\frac{24}{11}\)
  3. C
    2
  4. D
    4

Answer: (B) 24/11 Geometry MCQ

Solution

  1. At 8:48 the hour hand is at \(8\times30 + 48\times0.5 = 264^\circ\), the minute hand at \(48\times6 = 288^\circ\): angle \(24^\circ\).
  2. A 50% increase means \(36^\circ\), i.e. the gap must grow by \(12^\circ\).
  3. The minute hand is ahead and gains \(5.5^\circ\) per minute, so time \(= \frac{12}{5.5} = \frac{24}{11}\) minutes.

More Geometry questions from CAT

All 65 Geometry questions asked since 2017.