CAT 2023 Question Paper | Quant Slot 1

CAT Questions

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 9 : 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

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Video Explanation

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Explanatory Answer

The hour hand completes one full rotation in 12 hours, rotating in the clockwise direction.
08:48 is the time elapsed after 8.8 hours(and not 8.48 hours) from 12-o-clock. This means the angle covered by the hour hand is \( \frac { 8.8 } { 12 } \times 360 = 264 ^ { \circ } \)
At 8:48, the minutes’ hand would have covered \( \frac { 48 } { 60 } \times 360 = 288 ^ { \circ } \)
The difference is 24 degrees. Since the minutes’ hand is ahead of the hours’ hand at 8:48, We need a further separation of 12 degrees. Every minute the separation between them increases by \( \left( \frac { 1 } { 60 } - \frac { 1 } { 720 } \right) \times 360 = \frac { 11 } { 2 } \) degrees.
Therefore the time in minutes to achieve a difference of 12 degrees is, \( \frac { 12 } { \frac { 11 } { 2 } } = \frac { 24 } { 11 } \) degrees.

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The question is " 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 "

Hence, the answer is '\(\frac{24}{11}\)'

Choice B is the correct answer.

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